Soret and Dufour effects on magnetohydrodynamic (MHD) flow of Casson fluid
|
|
- Ethel Stevens
- 5 years ago
- Views:
Transcription
1 Appl. Math. Mech. -Engl. Ed., 33(10), (2012) DOI /s c Shanghai University and Springer-Verlag Berlin Heidelberg 2012 Applied Mathematics and Mechanics (English Edition) Soret and Dufour effects on magnetohydrodynamic (MHD) flow of Casson fluid T. HAYAT 1,2, S. A. SHEHZAD 1, A. ALSAEDI 2 (1. Department of Mathematics, Quaid-I-Azam University, Islamabad 44000, Pakistan; 2. Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia) Abstract This article studies the Soret and Dufour effects on the magnetohydrodynamic (MHD) flow of the Casson fluid over a stretched surface. The relevant equations are first derived, and the series solution is constructed by the homotopic procedure. The results for velocities, temperature, and concentration fields are displayed and discussed. Numerical values of the skin friction coefficient, the Nusselt number, and the Sherwood number for different values of physical parameters are constructed and analyzed. The convergence of the series solutions is examined. Key words Soret and Dufour effects, magnetohydrodynamic (MHD) flow, Casson fluid, heat and mass transfer Chinese Library Classification O Mathematics Subject Classification 76A05 1 Introduction Non-Newtonian fluid flows generated by a stretching sheet have been widely analyzed for the importance in several manufacturing processes such as extrusion of molten polymers through a slit die for the production of plastic sheets, processing of food stuffs, paper production, and wire and fiber coating. The quality of the final product in such processes greatly depends on the rate of cooling in the heat transfer process. The magnetohydrodynamic (MHD) parameter is one of the important parameters by which the cooling rate can be controlled and the product of the desired quality can be achieved. Crane [1] provided the closed form solution for steady and two-dimensional incompressible boundary layer flows of viscous fluids generated by a stretching surface. This flow problem has been extended under diverse physical aspects. At the present, we only refer some recent representative studies on stretched flows. Hassani et al. [2] investigated the analytical solutions for the boundary layer flow of a nanofluid past a stretching surface. Kazem et al. [3] studied the stagnation point flow of a viscous fluid over a porous stretching surface. Hayat et al. [4] discussed the slip effects on the flow of a second grade fluid past a streched surface in a porous space. Rahman [5] studied the Hiemenz flow of a viscous fluid over a linearly stretching sheet. He analyzed the heat and mass transfer characteristics in the presence of Soret and Dufour effects. Yao and Chen [6] analytically discussed the Falkner-Skan equation with the Received May 18, 2011 / Revised Dec. 28, 2011 Project supported by the Deanship of Scientific Research (DSR) of King Abdulaziz University of Saudi Arabia Corresponding author T. HAYAT, Professor, Ph. D., pensy t@yahoo.com
2 1302 T. HAYAT, S. A. SHEHZAD, and A. ALSAEDI stretching boundary. Fang et al. [7] carried out a study on the unsteady boundary layer flow over a stretched surface. Yao et al. [8] analyzed the effects of the convective surface boundary condition on the boundary layer flow of a viscous fluid. Hayat et al. [9] presented an analysis for the flow of a Maxwell fluid with heat and mass transfer in the presence of a chemical reaction. Hayat et al. [10] preseted a study on the radiation effects on the MHD flow induced by a streching sheet. Ahmad and Asghar [11] analyzed the boundary layer flow of a second grade fluid over a sheet stretched with arbitrary velocities. Muhaimina et al. [12] discussed the boundary layer flow of a viscous fluid over a porous shrinking sheet in the presence of suction. Having in mind the above reported studies on the boundary layer flow, we venture further in the regime of two-dimensional flows of the Casson fluid. In addition, the Soret and Dufour effects are considered. The fluid is taken to be electrically conducting and the flow is induced by a stretching surface. The Soret effect (thermal diffusion) is the occurrence of a diffusion flux because of a temperature gradient, whereas the Dufour effect is the occurrence of a heat flux due to a chemical potential gradient. Such effects have worth in the areas of geoscience and chemical engineering. The thermal diffusion effect has been utilized for isotope separation and in mixtures between gases with very light molecular weight (e.g., H 2 and He) and of medium molecular weight (e.g., N 2 and air), and the diffusion-thermo effect is significant. Moreover, the coupled heat and mass transfer have several applications in engineering problems. Such specific applications include the migration of moisture through air contained in fibrous insulation and grain storage insulations and chemical pollutants spreading into soil and medicine diffusion in blood veins [13]. Moreover, most of the performed experiments about blood suggested the blood as a Casson fluid [14 15]. Having all these in mind, the layout of this article is as follows. The problem formulation is presented in Section 2. Sections 3 and 4 develop the solutions and the related convergence analysis by the homotopy analysis method [16]. Vosughi et al. [17] also presented an optimal homotopy analysis method for the calculation of strong nonlinear problems. Homotopy solutions for interesting problems have been developed in Refs. [18 26]. Section 5 in this paper presents the graphical illustrations. Section 6 contains the main conclusions. 2 Mathematical model Let us consider the steady MHD flow of an incompressible Casson fluid over a heated stretching surface at y = 0. The surface is elastic. The x-axis is chosen to be parallel to the surface and the y-axis is normal to the surface. The motion in an incompressible fluid is induced because of the stretching property. This occurs in view of the elastic properties of the surface parallel to the x-axis through equal and opposite forces when the origin is fixed (see Refs. [27 28]). A constant magnetic field B 0 is exerted in the transverse direction to the surface. The induced magnetic field is negligible due to small magnetic Reynolds numbers. We also considered the heat and mass transfer processes in the presence of Soret and Dufour effects. The rheological equation of state for an isotropic and incompressible flow of the Casson fluid is ( τ ij = 2 µ B + p y )e ij, π π c, (1) 2π where π = e ij e ij with e ij being the (i, j)th component of the deformation rate, π depicts the product of the component of the deformation rate with itself, π c denotes a critical value of this product based on the non-newtonian model, µ B indicates the plastic dynamic viscosity of non-newtonian fluids, and p y is the yield stress of the fluid. The resulting boundary layer equations in the MHD flow under consideration are u x + v = 0, (2) y
3 Soret and Dufour effects on magnetohydrodynamic (MHD) flow of Casson fluid 1303 u u (1 x + v u y = ν + 1 ) 2 u β y 2 σb2 0 ρ u, (3) u T x + v T y = α 2 T T y 2 + D mk T 2 C C s c p y 2, (4) u C x + v C y = D 2 C m y 2 + D mk T 2 T T m y 2, (5) where u and v denote the velocity components in the x- and y-directions, respectively, β = µ B 2πc /p y is the Casson parameter, T the fluid temperature, C is the concentration field, ν is the kinematic viscosity, ρ is the fluid density, D m is the mass diffusivity, α T is the thermal conductivity, k T is the thermal-diffusion ratio, c p is the specific heat, C s is the concentration susceptibility, T m is the fluid mean temperature, and σ is the fluid electrical conductivity. The boundary conditions for the present analysis can be written as { u = uw (x) = cx, T = T w (x) = T + ax, (6) v = 0, C = C w (x) = C + bx at y = 0, and u 0, T T, C C (7) as y, where c, a, and b are all positive constants and have the dimension (time) 1. For the stretching flow c > 0. Here, T w and C w are the variable temperature and concentration, respectively. T is the uniform ambient temperature, and C is the uniform ambient concentration. Using the following transformations: c η = y ν, u = cxf (η), v = cνf(η), (8) θ(η) = T T T w T, φ(η) = C C C w C, the continuity equation (1) is identically satisfied, and the other equations become ( ) f + ff f 2 Ha 2 f = 0, (9) β 1 Pr θ + fθ f θ + Dfφ = 0, (10) φ + PrLefφ PrLef φ + SrLeθ = 0, (11) f(0) = 0, f (0) = 1, f ( ) = 0, (12) θ(0) = 1, θ( ) = 0, (13) φ(0) = 1, φ( ) = 0. (14) In these expressions, the prime indicates the differentiation with respect to η, Ha, Pr, and Le are the Hartman number, the Prandtl number, and the Lewis number expressed by Ha 2 = σ ρc B2 0, Pr = υ α T, Le = α T D e,
4 1304 T. HAYAT, S. A. SHEHZAD, and A. ALSAEDI and Df and Sr are the Dufour number and the Soret number defined by Df = D mk T C s c p (C w C ) (T w T )υ, Sr = D mk T T m α T (T w T ) (C w C ). (15) The dimensionless expressions of the local skin-friction coefficient, the local Nusselt number, and the local Sherwood number are where Re x = u w (x)x/ν is the local Reynolds number. 3 Series solutions Re 1 2 x Cf = (1 + 1/β)f (0), (16) Nu(Re x ) 1 2 = θ (0), (17) Sh(Re x ) 1 2 = φ (0), (18) In order to proceed the desired solutions, we select the following initial guesses and auxiliary linear operators: f 0 (η) = (1 exp( η)), θ 0 (η) = exp( η), φ 0 (η) = exp( η), (19) L f = d3 f dη 3 df dη, L θ = d2 θ dη 2 θ, L φ = d2 φ φ, (20) dη2 L f (C 1 + C 2 exp(η) + C 3 exp( η)) = 0, (21) { Lθ (C 4 exp(η) + C 5 exp( η)) = 0, L φ (C 6 exp(η) + C 7 exp( η)) = 0, (22) in which C i (i = 1, 2,, 7) denote the arbitrary constants. 3.1 Zeroth- and mth-order deformation problems Let the non-linear operators N f, N θ and N φ be in the forms N f ( ˆf(η, p)) = ( ) 3 ˆf(η, p) β η 3 + ˆf(η, p) 2 ˆf(η, p) η 2 ( ˆf(η, p) ) 2 Ha 2 ˆf(η, p), (23) η η N θ ( ˆf(η, p), ˆθ(η, p), ˆφ(η, p)) = 1 2ˆθ(η, p) Pr η 2 + ˆf(η, p) ˆθ(η, p) η ˆθ(η, p) ˆf(η, p) η N φ ( ˆf(η, p), ˆθ(η, p), ˆφ(η, p)) = 2 ˆφ(η, p) η 2 + PrLe ˆf(η, p) ˆφ(η, p) η PrLeˆφ(η, p) ˆf(η, p) η + Df 2 ˆφ(η, p) η 2, (24) + SrLe 2ˆθ(η, p) η 2. (25) Let p [0, 1] and f, θ, and φ be non-zero auxiliary parameters. Then, the zeroth-order
5 Soret and Dufour effects on magnetohydrodynamic (MHD) flow of Casson fluid 1305 problems have the forms (1 p)l f ( ˆf(η, p) f 0 (η)) = pħ f N f ( ˆf(η, p), ˆθ(η, p), ˆφ(η, p)), (26) (1 p)l θ (ˆθ(η, p) θ 0 (η)) = pħ θ N θ ( ˆf(η, p), ˆθ(η, p), ˆφ(η, p)), (27) (1 p)l φ (ˆφ(η, p) φ 0 (η)) = pħ φ N φ ( ˆf(η, p), ˆθ(η, p), ˆφ(η, p)), (28) ˆf(η; p) = 0, p) = 1, p) = 0, η=0 η η η=0 η= (29) η= ˆθ(η; p) = 1, ˆθ(η; p) = 0, (30) η=0 η= ˆφ(η; p) = 1, ˆφ(η; p) = 0. (31) η=0 For the mth-order deformation problems, we first differentiate Eqs.(26) (31) m times with respect to p, divide them by m!, and then set p = 0. Then, we have L f (f m (η) χ m f m 1 (η)) = ħ f R f m(η), (32) L θ (θ m (η) χ m θ m 1 (η)) = ħ θ R θ m(η), (33) L φ (φ m (η) χ m φ m 1 (η)) = ħ φ R φ m(η), (34) f m (0) = 0, f m (0) = 0, f m ( ) = 0, θ m (0) = 0, θ m ( ) = 0, (35) φ m (0) = 0, φ m ( ) = 0, m 1 R f m(η) = (1 + 1/β)f m 1(η) + (f m 1 k f k f m 1 kf k) Ha 2 f m 1(η), (36) k=0 R θ m(η) = 1 m 1 Pr θ m 1(η) + (f m 1 k θ k f m 1 kθ k ) + Dfφ m 1(η), (37) k=0 m 1 R φ m (η) = φ m 1 (η) + PrLe (f m 1 k φ k f m 1 k φ k) + SrLeθ m 1 (η), (38) k=0 χ m = { 0, m 1, 1, m > 1. By using Taylor s series, we have ˆf(η; p) = f 0 (η) + f m (η) = 1 m! f m (η)p m, m=1 m ˆf(η; p) p m, p=0 (39) (40)
6 1306 T. HAYAT, S. A. SHEHZAD, and A. ALSAEDI ˆθ(η; p) = θ 0 (η) + θ m (η)p m, m=1 θ m (η) = 1 mˆθ(η; p) m! p m, p=0 ˆφ(η; p) = φ 0 (η) + φ m (η) = 1 m! φ m (η)p m, m=1 m ˆφ(η; p) p m. p=0 (41) (42) For p = 0 and p = 1, one may write ˆf(η; 0) = f 0 (η), ˆf(η; 1) = f(η), (43) ˆθ(η; 0) = θ 0 (η), ˆθ(η; 1) = θ(η), (44) ˆφ(η; 0) = φ 0 (η), ˆφ(η; 1) = φ(η). (45) The auxiliary parameters are selected so that the series solutions converge for p = 1. Therefore, f(η) = f 0 (η) + θ(η) = θ 0 (η) + φ(η) = φ 0 (η) + f m (η), (46) m=1 θ m (η), (47) m=1 φ m (η). (48) The general solutions (f m, θ m, and φ m ) in terms of the special solutions (f m, θ m, and φ m ) are given by m=1 f m (η) = f m (η) + C 1 + C 2 exp(η) + C 3 exp( η), (49) θ m (η) = θ m (η) + C 4 exp(η) + C 5 exp( η), (50) φ m (η) = φ m(η) + C 6 exp(η) + C 7 exp( η). (51) 4 Convergence of homotopy solutions The convergence of the series solutions (46) (48) is examined by the parameters f, θ, and φ. For this aim, we draw the -curves for the 20th-order approximation in Fig.1. From these curves, it is found that the admissible ranges of f, θ, and φ are 1.1 f 0.15, 1.3 θ 0.4, 1.2 φ 0.4. The series (32) (34) converge in the whole region of η when f = 0.6 and θ = φ = 0.8. Table 1 indicates that how many terms for each physical quantity are necessary in the convergent solution. It is noticed that less terms are required in the convergent expression of the velocities.
7 Soret and Dufour effects on magnetohydrodynamic (MHD) flow of Casson fluid 1307 Fig. 1 ħ-curves for functions f (0), θ (0), and φ (0) at 20th-order approximation with β = 1.5, Ha = 0.5, Pr = 0.7,, Df = 0.5, and Le = 1.0 Table 1 Convergence of homotopy solutions for different orders of approximations when β = 1.5, Ha = 0.5, Pr = 0.7, Df = 0.5,, Le = 1.3, f = 0.6, and θ = φ = 0.8 Order f (0) θ (0) φ (0) Discussion In this section, we aim to discuss the effects of several important parameters on the velocity, temperature, concentration, the skin-friction coefficient, the local Nusselt number, and the local Sherwood number. The results are plotted in Figs and listed in Tables 2 and 3. The effects of the Casson parameter β and the Hartman number Ha on the velocity f (η) are shown in Figs.2 and 3. Figure 2 shows that the Casson parameter decreases both the velocity and the boundary layer thickness. Figure 3 shows that the velocity decreases when Ha increases. The Hartman number is due to the Lorentz force, which opposes the flow. That is why the velocity is a decreasing function of the Hartman number. Fig. 2 Effects of β on f (η) with Ha = 0.5 Fig. 3 Effects of Ha on f (η) with β = 1.0 Figures 4 9 are plotted to see the effects of the Casson parameter β, the Hartman number Ha, the Prandtl number Pr, the Lewis number Le, the Dufour number Df, and the Soret number Sr on the velocity θ(η). From Figs. 4 and 5, we can see that the temperature and the thermal boundary layer thickness are increasing functions of β and Ha. Figure 6 shows that both the temperature and the thermal boundary layer thickness decrease when the Prandtl number
8 1308 T. HAYAT, S. A. SHEHZAD, and A. ALSAEDI increases the thermal diffusivity, and the temperature increases by increasing the Lewis and Dufour numbers. Figures 7 and 8 show that an increase in the temperature due to the Dufour number is larger than that due to the Lewis number. Figure 9 depicts that an increase in the Soret number shows decreases in the temperature and the associated boundary layer thickness. Fig. 4 Effects of β on θ(η) with Ha = 0.5, Pr = 0.7, Le = 1.0, Df = 0.5, and Fig. 5 Effects of Ha on θ(η) with β = 1.0, Pr = 0.7, Le = 1.0, Df = 0.5, and Fig. 6 Effects of Pr on θ(η) with β = 1.0, Ha = 0.5, Le = 1.0, Df = 0.5, and Fig. 7 Effects of Le on θ(η) with β = 1.0, Ha = 0.5, Pr = 0.7, Df = 0.5, and Fig. 8 Effects of Df on θ(η) with β = 1.0, Ha = 0.5, Pr = 0.7, Le = 1.0, and Fig. 9 Effects of Sr on θ(η) with β = 1.0, Ha = 0.5, Pr = 0.7, Le = 1.0, and Df = 0.5 The variation of several parameters on the concentration field φ(η) are presented in Figs The effects of the Casson parameter and the Hartman number on the concentration profile
9 Soret and Dufour effects on magnetohydrodynamic (MHD) flow of Casson fluid 1309 are qualitatively similar. Such observations in a qualitative sense are similar to those of the temperature (see Figs. 10 and 11). The concentration field decrease when the Prandtl number increases. The increase in the Lewis number leads to decreases in the concentration profile and the associated boundary layer thickness. It is interesting to note from Figs. 7 and 13 that the Lewis number has opposite effects on the temperature and concentration. Here, we also observed Fig. 10 Effects of β on φ(η) with Ha = 0.5, Pr = 0.7, Le = 1.0, Df = 0.5, and Fig. 11 Effects of Ha on φ(η) with β = 1.0, Pr = 0.7, Le = 1.0, Df = 0.5, and Fig. 12 Effects of Pr on φ(η) with β = 1.0, Ha = 0.5, Le = 1.0, Df = 0.5, and Fig. 13 Effects of Le on φ(η) with β = 1.0, Ha = 0.5, Pr = 0.7, Df = 0.5, and Fig. 14 Effects of Df on φ(η) with β = 1.0, Ha = 0.5, Pr = 0.7, Le = 1.0, and Fig. 15 Effects of Sr on φ(η) with β = 0.1, Ha = 0.5, Pr = 0.7, Le = 1.0, Df = 0.5
10 1310 T. HAYAT, S. A. SHEHZAD, and A. ALSAEDI that the variation of the concentration profile is larger when compared with the temperature profile. Figure 14 depicts that an increase in the Dufour number decreases the concentration field. An increase in the Soret number increases the concentration and the boundary layer thickness. The effects of the Soret number on the temperature and concentration fields are quite opposite. Table 2 shows the numerical values of the skin-friction coefficient for different values of β and Ha. An increase in β decreases the skin-friction coefficient whereas an increase in Ha increases the skin-friction coefficient. The numerical values of the local Nusselt number and the local Sherwood numbers are presented in Table 3 for different values of β, Ha, Pr, Sr, Df, and Le. The values of the local Nusselt number and the local Sherwood number increase by increasing Pr, whereas the local Nusselt number increases by increasing Sr. The local Sherwood number decreases when Sr increases. Table 2 Numerical values of skin friction coefficient (1 + 1/β)f (0) for different values of β and Ha β Ha (1 + 1/β)f (0) Table 3 Numerical values of local Nusselt number θ (0) and local Sherwood number φ (0) for different values of β, Ha, Pr, Sr, Df, and Le β Ha Pr Sr Df Le θ (0) φ (0) Conclusions The MHD flow of the Casson fluid with the Soret and Dufour effects is examined. The results are as follows. (i) The increases in the Casson parameter β and the Hartman number Ha decrease the velocity f (η) while increase the temperature and concentration profiles. (ii) The temperature, the concentration, and the boundary layer thickness decrease by increasing the Prandtl number Pr.
11 Soret and Dufour effects on magnetohydrodynamic (MHD) flow of Casson fluid 1311 (iii) The effects of the Soret number Sr on θ(η) and φ(η) are reverse. (iv) The thermal boundary layer thickness and the temperature field increase when Df increases. (v) The impacts of β and Ha on the skin-friction coefficient are opposite. References [1] Crane, L. J. Flow past a stretching plate. Journal of Applied Mathematics and Physics (ZAMP), 21, (1970) [2] Hassani, M., Tabar, M. M., Nemati, H., Domairry, G., and Noori, F. An analytical solution for boundary layer flow of a nanofluid past a stretching sheet. International Journal of Thermal Sciences, 50, (2011) [3] Kazem, S., Shaban, M., and Abbasbandy, S. Improved analytical solutions to a stagnation-point flow past a porous stretching sheet with heat generation. Journal of the Franklin Institute, 348, (2011) [4] Hayat, T., Javed, T., and Abbas, Z. Slip flow and heat transfer of a second grade fluid past a stretching sheet through a porous space. International Journal of Heat and Mass Transfer, 51, (2008) [5] Rahman, G. M. A. Thermal-diffusion and MHD for Soret and Dufour s effects on Hiemenz flow and mass transfer of fluid flow through porous medium onto a stretching surface. Physica B, 405, (2010) [6] Yao, B. and Chen, J. Series solution to the Falkner-Skan equation with stretching boundary. Applied Mathematics and Computation, 208, (2009) [7] Fang, T., Zhang, J., and Yao, S. A new family of unsteady boundary layers over a stretching surface. Applied Mathematics and Computation, 217, (2010) [8] Yao, S., Fang, T., and Zhang, J. Heat transfer of a generalized stretching/shrinking wall problem with convective boundary conditions. Communications in Nonlinear Science and Numerical Simulation, 16, (2011) [9] Hayat, T., Awais, M., Qasim, M., and Hendi, A. A. Effects of mass transfer on the stagnation point flow of an upper-convected Maxwell (UCM) fluid. International Journal of Heat and Mass Transfer, 54, (2011) [10] Hayat, T., Qasim, M., and Abbas, Z. Radiation and mass transfer effects on the magnetohydrodynamic unsteady flow induced by a stretching sheet. Zeitschrift für Naturforschung, 65a, (2010) [11] Ahmad, A. and Asghar, S. Flow of a second grade fluid over a sheet stretching with arbitrary velocities subject to a transverse magnetic field. Applied Mathematics Letters, 24, (2011) [12] Muhaimina, Kandasamy, R., and Hashim, I. Effect of chemical reaction, heat and mass transfer on nonlinear boundary layer past a porous shrinking sheet in the presence of suction. Nuclear Engineering and Design, 240, (2010) [13] Kandasamy, R., Periasamy, K., and Prabhu, K. K. S. Chemical reaction, heat and mass transfer on MHD flow over a vertical stretching surface with heat source and thermal stratification effects. International Journal of Heat and Mass Transfer, 48, (2005) [14] Mrill, E. W., Benis, A. M., Gilliland, E. R., Sherwood, T. K., and Salzman, E. W. Pressure flow relations of human blood hollow fibers at low flow rates. Journal of Applied Physiology, 20, (1965) [15] McDonald, D. A. Blood Flows in Arteries, 2nd ed., Arnold, London (1974) [16] Liao, S. J. Beyond Perturbation: Introduction to Homotopy Analysis Method, CRC Press, Boca Raton (2003) [17] Vosughi, H., Shivanian, E., and Abbasbandy, S. A new analytical technique to solve Volterra s integral equations. Mathematical Methods in the Applied Sciences, 34, (2011) [18] Abbasbandy, S. and Shirzadi, A. Homotopy analysis method for a nonlinear chemistry problem. Studies in Nonlinear Sciences, 1, (2010)
12 1312 T. HAYAT, S. A. SHEHZAD, and A. ALSAEDI [19] Ziabakhsh, Z., Domairry, G., Bararnia, H., and Babazadeh, H. Analytical solution of flow and diffusion of chemically reactive species over a nonlinearly stretching sheet immersed in a porous medium. Journal of the Taiwan Institute of Chemical Engineers, 41, (2010) [20] Rashidi, M. M., Pour, S. A. M., and Abbasbandy, S. Analytic approximate solutions for heat transfer of a micropolar fluid through a porous medium with radiation. Communications in Nonlinear Science and Numerical Simulation, 16, (2011) [21] Hayat, T., Shehzad, S. A., Qasim, M., and Obaidat, S. Steady flow of Maxwell fluid with convective boundary conditions. Zeitschrift für Naturforschung, 66a, (2011) [22] Hayat, T., Shehzad, S. A., Qasim, M., and Obaidat, S. Radiative flow of a Jeffery fluid in a porous medium with power law heat flux and heat source. Nuclear Engineering and Design, 243, (2012) [23] Hayat, T. and Qasim, M. Influence of thermal radiation and Joule heating on MHD flow of a Maxwell fluid in the presence of thermophoresis. International Journal of Heat and Mass Transfer, 53, (2010) [24] Yao, B. Approximate analytical solution to the Falkner-Skan wedge flow with the permeable wall of uniform suction. Communications in Nonlinear Science and Numerical Simulation, 14, (2009) [25] Rashidi, M. M. and Pour, S. A. M. Analytic approximate solutions for unsteady boundary-layer flow and heat transfer due to a stretching sheet by homotopy analysis method. Nonlinear Analysis: Modelling and Control, 15, (2010) [26] Liao, S. J. An optimal homotopy-analysis approach for strongly nolinear differential equations. Communications in Nonlinear Science and Numerical Simulation, 15, (2010) [27] Vyas, P. Radiative MHD flow over a non-isothermal stretching sheet in a porous medium. Applied Mathematical Sciences, 4, (2010) [28] Turkyilmazoglu, M. Multiple solutions of heat and mass transfer of MHD slip flow for the viscoelastic fluid over a stretching sheet. International Journal of Thermal Sciences, 50, (2011)
Flow of variable thermal conductivity fluid due to inclined stretching cylinder with viscous dissipation and thermal radiation
Appl. Math. Mech. -Engl. Ed., 356, 717 728 2014 DOI 10.1007/s10483-014-1824-6 c Shanghai University and Springer-Verlag Berlin Heidelberg 2014 Applied Mathematics and Mechanics English Edition Flow of
More informationResearch Article Analytic Solution for MHD Falkner-Skan Flow over a Porous Surface
Applied Mathematics Volume 01, Article ID 13185, 9 pages doi:10.1155/01/13185 Research Article Analytic Solution for MHD Falkner-Skan Flow over a Porous Surface Fatheah A. Hendi 1 and Majid Hussain 1 Department
More informationMAGNETOHYDRODYNAMIC FLOW OF NANOFLUID OVER PERMEABLE STRETCHING SHEET WITH CONVECTIVE BOUNDARY CONDITIONS
THERMAL SCIENCE, Year 016, Vol. 0, No. 6, pp. 1835-1845 1835 MAGNETOHYDRODYNAMIC FLOW OF NANOFLUID OVER PERMEABLE STRETCHING SHEET WITH CONVECTIVE BOUNDARY CONDITIONS by Tasawar HAYAT a,b, Maria IMTIAZ
More informationIMPACT OF MAGNETIC FIELD IN RADIATIVE FLOW OF CASSON NANOFLUID WITH HEAT AND MASS FLUXES
THERMAL SCIENCE: Year 2018, Vol. 22, No. 1A, pp. 137-145 137 IMPACT OF MAGNETIC FIELD IN RADIATIVE FLOW OF CASSON NANOFLUID WITH HEAT AND MASS FLUXES by Tariq HUSSAIN a,*, Shafqat HUSSAIN a b,c, and Tasawar
More informationMAGNETOHYDRODYNAMIC FLOW OF POWELL-EYRING FLUID BY A STRETCHING CYLINDER WITH NEWTONIAN HEATING
THERMAL SCIENCE: Year 2018, Vol. 22, No. 1B, pp. 371-382 371 MAGNETOHYDRODYNAMIC FLOW OF POWELL-EYRING FLUID BY A STRETCHING CYLINDER WITH NEWTONIAN HEATING by Tasawar HAYAT a,b, Zakir HUSSAIN a*, Muhammad
More informationEffect of Thermal Radiation on the Casson Thin Liquid Film Flow over a Stretching Sheet
Global Journal of Pure and Applied Mathematics. ISSN 0973-768 Volume 3, Number 6 (207), pp. 575-592 Research India Publications http://www.ripublication.com Effect of Thermal Radiation on the Casson Thin
More informationBoundary Layer Flow and Heat Transfer due to an Exponentially Shrinking Sheet with Variable Magnetic Field
International Journal of Scientific Research Engineering & Technology (IJSRET), ISSN 78 088 Volume 4, Issue 6, June 05 67 Boundary ayer Flow and Heat Transfer due to an Exponentially Shrinking Sheet with
More informationFlow and heat transfer in a Maxwell liquid film over an unsteady stretching sheet in a porous medium with radiation
DOI 10.1186/s40064-016-2655-x RESEARCH Open Access Flow and heat transfer in a Maxwell liquid film over an unsteady stretching sheet in a porous medium with radiation Shimaa E. Waheed 1,2* *Correspondence:
More informationThe three-dimensional flow of a non-newtonian fluid over a stretching flat surface through a porous medium with surface convective conditions
Global Journal of Pure and Applied Mathematics. ISSN 973-1768 Volume 13, Number 6 (217), pp. 2193-2211 Research India Publications http://www.ripublication.com The three-dimensional flow of a non-newtonian
More informationEffect of Magnetic Field on Steady Boundary Layer Slip Flow Along With Heat and Mass Transfer over a Flat Porous Plate Embedded in a Porous Medium
Global Journal of Pure and Applied Mathematics. ISSN 973-768 Volume 3, Number 2 (27), pp. 647-66 Research India Publications http://www.ripublication.com Effect of Magnetic Field on Steady Boundary Layer
More information1 Introduction. A generalized Fourier and Fick's perspective for stretching flow of Burgers fluid with temperature-dependent thermal conductivity
3 4 5 6 7 8 9 0 3 4 5 6 7 8 9 0 3 4 5 6 7 8 9 30 A generalized Fourier and Fick's perspective for stretching flow of Burgers fluid with temperature-dependent thermal conductivity Muhammad Waqas a,*, Muhammad
More informationResearch Article Effects of Thermocapillarity and Thermal Radiation on Flow and Heat Transfer in a Thin Liquid Film on an Unsteady Stretching Sheet
Mathematical Problems in Engineering Volume 22, Article ID 2732, 4 pages doi:.55/22/2732 Research Article Effects of Thermocapillarity and Thermal Radiation on Flow and Heat Transfer in a Thin Liquid Film
More informationCasson Fluid Flow and Heat Transfer Past a Symmetric Wedge
Heat Transfer Asian Research, 42 (8), 2013 Casson Fluid Flow and Heat Transfer Past a Symmetric Wedge Swati Mukhopadhyay, 1 Iswar Chandra Mondal, 1 and Ali J. Chamkha 2 1 Department of Mathematics, The
More informationRiyadh 11451, Saudi Arabia. ( a b,c Abstract
Effects of internal heat generation, thermal radiation, and buoyancy force on boundary layer over a vertical plate with a convective boundary condition a Olanrewaju, P. O., a Gbadeyan, J.A. and b,c Hayat
More informationIJENS-RPG [IJENS Researchers Promotion Group] House No. 78-B, Street No. 20, Sector G-6/2, Islamabad-Pakistan Date of Birth September 12, 1984
DR. MUHAMMAD QASIM Assistant Professor Department of Mathematics COMSATS Insitute of Information Technology, Park Road, Shahzad town, Islamabad-Pakistan Phone (Office): +92-051-9240823 (Cell) : + 92-0300-5126594
More informationUnsteady MHD Mixed Convection Flow, Heat and Mass Transfer over an Exponentially Stretching Sheet with Suction, Thermal Radiation and Hall Effect
IOSR Journal of Mathematics (IOSR-JM) e-issn: 2278-5728, p-issn: 239-765X. Volume 2, Issue 4 Ver. III (Jul. - Aug.26), PP 66-77 www.iosrjournals.org Unsteady MHD Mixed Convection Flow, Heat and Mass Transfer
More informationRamasamy Kandasamy Department of Mathematics, Institute of Road and Transport Technology Erode , India kandan
Journal of Computational and Applied Mechanics, Vol. 6., No. 1., (2005), pp. 27 37 NONLINEAR HYDROMAGNETIC FLOW, HEAT AND MASS TRANSFER OVER AN ACCELERATING VERTICAL SURFACE WITH INTERNAL HEAT GENERATION
More informationGroup Theoretical Analysis of non-newtonian Fluid Flow, Heat and Mass Transfer over a Stretching Surface in the Presence of Thermal Radiation
Journal of Applied Fluid Mechanics, Vol. 9, No. 3, pp. 1515-1524, 2016. Available online at www.jafmonline.net, ISSN 1735-3572, EISSN 1735-3645. DOI: 10.18869/acadpub.jafm.68.228.24069 Group Theoretical
More informationMELTING HEAT TRANSFER IN THE STAGNATION-POINT FLOW OF THIRD GRADE FLUID PAST A STRETCHING SHEET WITH VISCOUS DISSIPATION
THERMAL SCIENCE: Year 0, Vol. 7, No., pp. 865-875 865 MELTING HEAT TRANSFER IN THE STAGNATION-POINT FLOW OF THIRD GRADE FLUID PAST A STRETCHING SHEET WITH VISCOUS DISSIPATION by Tasawar HAYAT a, b, Zahid
More informationMHD Flow and Heat Transfer over an. Exponentially Stretching Sheet with Viscous. Dissipation and Radiation Effects
Applied Mathematical Sciences, Vol. 7, 3, no. 4, 67-8 MHD Flow and Heat Transfer over an Exponentially Stretching Sheet with Viscous Dissipation and Radiation Effects R. N. Jat and Gopi Chand Department
More informationAmerican Academic & Scholarly Research Journal Special Issue - January 2012
Proceeding of 2 nd International Conference on Mathematics and Information Sciences, 9-13 Nov. 2011, Sohag, Egypt American Academic & Scholarly Research Journal Special Issue - January 2012 Heat and mass
More informationRadiation Effect on MHD Casson Fluid Flow over a Power-Law Stretching Sheet with Chemical Reaction
Radiation Effect on MHD Casson Fluid Flow over a Power-Law Stretching Sheet with Chemical Reaction Motahar Reza, Rajni Chahal, Neha Sharma Abstract This article addresses the boundary layer flow and heat
More informationHydromagnetic stagnation point flow over a porous stretching surface in the presence of radiation and viscous dissipation
Applied and Computational Mathematics 014; 3(5): 191-196 Published online September 0, 014 (http://www.sciencepublishinggroup.com/j/acm) doi: 10.11648/j.acm.0140305.11 ISSN: 38-5605 (Print); ISSN:38-5613
More informationThe Chemical Diffusion and Bouyancy Effects on MHD Flow of Casson Fluids Past a Stretching Inclined Plate with Non-Uniform Heat Source
J. Appl. Environ. Biol. Sci., 7(6)135-14, 017 017, TextRoad Publication ISSN: 090-474 Journal of Applied Environmental and Biological Sciences www.textroad.com The Chemical Diffusion and Bouyancy Effects
More informationParash Moni Thakur. Gopal Ch. Hazarika
International Journal of Scientific and Innovative Mathematical Research (IJSIMR) Volume 2, Issue 6, June 2014, PP 554-566 ISSN 2347-307X (Print) & ISSN 2347-3142 (Online) www.arcjournals.org Effects of
More informationFREE CONVECTION OF HEAT TRANSFER IN FLOW PAST A SEMI-INFINITE FLAT PLATE IN TRANSVERSE MAGNETIC FIELD WITH HEAT FLUX
American Journal of Applied Sciences 11 (9): 148-1485, 14 ISSN: 1546-939 14 P. Geetha et al., This open access article is distributed under a Creative Commons Attribution (CC-BY) 3. license doi:1.3844/ajassp.14.148.1485
More informationNumerical study of entropy generation and melting heat transfer on MHD generalised non-newtonian fluid (GNF): Application to optimal energy
Pramana J. Phys. (2018) 90:64 https://doi.org/10.1007/s12043-018-1557-6 Indian Academy of Sciences Numerical study of entropy generation and melting heat transfer on MHD generalised non-newtonian fluid
More informationInfluence of the Order of Chemical Reaction and Soret Effect on Mass Transfer of a Binary Fluid Mixture in Porous Media
Influence of the Order of Chemical Reaction and Soret Effect on Mass Transfer of a Binary Fluid Mixture in Porous Media B.R.Sharma, Debozani Borgohain Department of Mathematics, Dibrugarh University, Dibrugarh-786004,
More informationJournal of Engineering Science and Technology Review 2 (1) (2009) Research Article
Journal of Engineering Science and Technology Review 2 (1) (2009) 118-122 Research Article JOURNAL OF Engineering Science and Technology Review www.jestr.org Thin film flow of non-newtonian fluids on a
More informationEffect of Variable Viscosity on Hydro Magnetic Flow and Heat Transfer Over a Stretching Surface with Variable Temperature
37 Effect of Variable Viscosity on Hydro Magnetic Flow and Heat Transfer Over a Stretching Surface with Variable Temperature M. Y. Akl Department of Basic Science, Faculty of Engineering (Shopra Branch),
More informationRadiative Mhd Stagnation Point Flow Over A Chemical Reacting Porous Stretching Surface With Convective Thermal Boundary Condition
INTERNATIONAL JOURNAL OF SCIENTIFIC & TECHNOLOGY RESEARCH VOLUME 3, ISSUE 1, DECEMBER 014 ISSN 77-8616 Radiative Mhd Stagnation Point Flow Over A Chemical Reacting Porous Stretching Surface With Convective
More informationMHD stagnation-point flow and heat transfer towards stretching sheet with induced magnetic field
Appl. Math. Mech. -Engl. Ed., 32(4), 409 418 (2011) DOI 10.1007/s10483-011-1426-6 c Shanghai University and Springer-Verlag Berlin Heidelberg 2011 Applied Mathematics and Mechanics (English Edition) MHD
More informationJOURNAL OF INTERNATIONAL ACADEMIC RESEARCH FOR MULTIDISCIPLINARY Impact Factor 1.393, ISSN: , Volume 2, Issue 7, August 2014
HOMOTOPY ANALYSIS TO THERMAL RADIATION EFFECTS ON HEAT TRANSFER OF WALTERS LIQUID-B FLOW OVER A STRETCHING SHEET FOR LARGE PRANDTL NUMBERS HYMAVATHI TALLA* P.VIJAY KUMAR** V.MALLIPRIYA*** *Dept. of Mathematics,
More informationMixed convection boundary layers in the stagnation-point flow toward a stretching vertical sheet
Meccanica (2006) 41:509 518 DOI 10.1007/s11012-006-0009-4 Mied convection boundary layers in the stagnation-point flow toward a stretching vertical sheet A. Ishak R. Nazar I. Pop Received: 17 June 2005
More informationEffect of radiation with temperature dependent viscosity and thermal conductivity on unsteady a stretching sheet through porous media
Nonlinear Analysis: Modelling and Control, 2010, Vol. 15, No. 3, 257 270 Effect of radiation with temperature dependent viscosity and thermal conductivity on unsteady a stretching sheet through porous
More informationFlow and Heat Transfer of Maxwell Fluid with Variable Viscosity and Thermal Conductivity over an Exponentially Stretching Sheet
American Journal of Fluid Dynamics 013, 3(4): 87-95 DOI: 10.593/j.ajfd.0130304.01 Flow and Heat Transfer of Maxwell Fluid with Variable Viscosity and Thermal Conductivity over an Exponentially Stretching
More information*Corresponding Author: Surajit Dutta, Department of Mathematics, C N B College, Bokakhat, Golaghat, Assam, India
International Journal of Scientific and Innovative Mathematical Research (IJSIMR) Volume 6, Issue, 8, PP -6 ISSN 347-37X (Print) & ISSN 347-34 (Online) DOI: http://dx.doi.org/.43/347-34.6 www.arcjournals.org
More informationEFFECTS OF RADIATION ON CONVECTION HEAT TRANSFER OF Cu-WATER NANOFLUID PAST A MOVING WEDGE
THERMAL SCIENCE, Year 016, Vol. 0, No., pp. 437-447 437 EFFECTS OF RADIATION ON CONVECTION HEAT TRANSFER OF Cu-WATER NANOFLUID PAST A MOVING WEDGE by Faiza A. SALAMA a,b * a Department of Mathematics,
More informationBoundary layer flow of nanofluid over an exponentially stretching surface
NANO IDEA Boundary layer flow of nanofluid over an exponentially stretching surface Sohail Nadeem 1* and Changhoon Lee 2 Open Access Abstract The steady boundary layer flow of nanofluid over an exponential
More informationDepartment of mathematics, Osmania University, Hyderabad, Telangana , India.
ISSN(online)- 2378-74X Volume 2, 26 5 Pages Research Article Introduction Open Access MHD Flow of Casson Fluid With Slip Effects over an Exponentially Porous Stretching Sheet in Presence of Thermal Radiation,
More informationStagnation Point Flow of Non-Newtonian Fluid and Heat Transfer over a Stretching/Shrinking Sheet in a Porous Medium
Stagnation Point Flow of Non-Newtonian Fluid and Heat Transfer over a Stretching/Shrinking Sheet in a Porous Medium Mahantesh.M.Nandeppanavar *,1 Shilpa.J.M 1,2 1. Department of PG and UG studies and research
More informationChapter Introduction
Chapter 4 Mixed Convection MHD Flow and Heat Transfer of Nanofluid over an Exponentially Stretching Sheet with Effects of Thermal Radiation and Viscous Dissipation 4.1 Introduction The study of boundary
More informationNonlinear Radiation Effects on Hydromagnetic Boundary Layer Flow and Heat Transfer over a Shrinking Surface
Journal of Applied Fluid Mechanics, Vol. 8, No. 3, pp. 613-61, 015. Available online at www.jafmonline.net, ISSN 1735-357, EISSN 1735-3645. DOI: 10.18869/acadpub.jafm.73.38.636 Nonlinear Radiation Effects
More informationBoundary Layer Flow of Williamson Fluid with Chemically Reactive Species using Scaling Transformation and Homotopy Analysis Method
Math. Sci. Lett. 3, No. 3, 199-205 (2014) 199 Mathematical Sciences Letters An International Journal http://dx.doi.org/10.12785/msl/030311 Boundary Layer Flow of Williamson Fluid with Chemically Reactive
More informationMHD Flow of Micropolar Fluid due to a Curved Stretching Sheet with Thermal Radiation
Journal of Applied Fluid Mechanics, Vol. 9, No. 1, pp. 131-138, 2016. Available online at www.jafmonline.net, ISSN 1735-3572, EISSN 1735-3645. MHD Flow of Micropolar Fluid due to a Curved Stretching Sheet
More informationMHD Non-Newtonian Power Law Fluid Flow and Heat Transfer Past a Non-Linear Stretching Surface with Thermal Radiation and Viscous Dissipation
Journal of Applied Science and Engineering, Vol. 17, No. 3, pp. 267274 (2014) DOI: 10.6180/jase.2014.17.3.07 MHD Non-Newtonian Power Law Fluid Flow and Heat Transfer Past a Non-Linear Stretching Surface
More informationHeat and Mass Transfer over an unsteady Stretching Surface embedded in a porous medium in the presence of variable chemical reaction
Vol:5, No:2, 20 Heat and Mass Transfer over an unsteady Stretching Surface embedded in a porous medium in the presence of variable chemical reaction TGEmam International Science Index, Mathematical and
More informationInfluence of Non-linear Radiation Heat Flux on Rotating Maxwell Fluid over a Deformable Surface: A Numerical Study
Commun. Theor. Phys. 69 (28) 46 466 Vol. 69, No. 4, April, 28 Influence of Non-linear Radiation Heat Flux on Rotating Maxwell Fluid over a Deformable Surface: A Numerical Study M. Mustafa,, A. Mushtaq,
More informationImpact of Arrhenius activation energy in viscoelastic nanomaterial flow subject to binary chemical reaction and nonlinear mixed convection
Impact of Arrhenius activation energy in viscoelastic nanomaterial flo subject to binary chemical reaction and nonlinear mied convection Salman Ahmad 1,*, Muhammad Ijaz Khan 1, M. Waleed Ahmed Khan 1,
More informationEffects of Thermal Radiation on Unsteady Magnetohydrodynamic Flow of a Micropolar Fluid with Heat and Mass Transfer
Effects of Thermal Radiation on Unsteady Magnetohydrodynamic Flow of a Micropolar Fluid with Heat and Mass Transfer Tasawar Hayat a,b and Muhammad Qasim a a Department of Mathematics, Quaid-I-Azam University
More informationDiffusive Species in MHD Squeezed Fluid Flow Through non-darcy Porous Medium with Viscous Dissipation and Joule Heating
Journal of Magnetics 3() 33-33 (08) ISSN (Print) 6-750 ISSN (Online) 33-6656 https://doi.org/0.483/jmag.08.3..33 Diffusive Species in MHD Squeezed Fluid Flow Through non-darcy Porous Medium with Viscous
More informationAvailable online at (Elixir International Journal) Applied Mathematics. Elixir Appl. Math. 51 (2012)
10809 P. Sreenivasulu et al./ Elixir Appl. Math. 51 (01) 10809-10816 Available online at www.elixirpublishers.com (Elixir International Journal) Applied Mathematics Elixir Appl. Math. 51 (01) 10809-10816
More informationVidyasagar et al., International Journal of Advanced Engineering Technology E-ISSN A.P., India.
Research Paper MHD CONVECTIVE HEAT AND MASS TRANSFER FLOW OVER A PERMEABLE STRETCHING SURFACE WITH SUCTION AND INTERNAL HEAT GENERATION/ABSORPTION G.Vidyasagar 1 B.Ramana P. Bala Anki Raddy 3 Address for
More informationMHD Boundary Layer Flow of Casson Fluid Over a Stretching/Shrinking Sheet Through Porous Medium
ISSN 2224-7467 (Paper) ISSN 2225-93 (Online) Vol.47, 27 MHD Boundary Layer Flow of Casson Fluid Over a Stretching/Shrinking Sheet Through Porous Medium * M. Eswara Rao S. Sreenadh Department of Mathematics,
More informationMHD MIXED CONVECTION SLIP FLOW NEAR A STAGNATION-POINT ON A NON-LINEARLY VERTICAL STRETCHING SHEET IN THE PRESENCE OF VISCOUS DISSIPATION
THERMAL SCIENCE: Year 7, Vol., No. 6B, pp. 73-745 73 MHD MIXED CONVECTION SLIP FLOW NEAR A STAGNATION-POINT ON A NON-LINEARLY VERTICAL STRETCHING SHEET IN THE PRESENCE OF VISCOUS DISSIPATION by Stanford
More informationEFFECTS OF HEAT SOURCE/SINK ON MAGNETOHYDRODYNAMIC FLOW AND HEAT TRANSFER OF A NON-NEWTONIAN POWER-LAW FLUID ON A STRETCHING SURFACE
THERMAL SCIENCE, Year 206, Vol. 20, No. 6, pp. 80-8 80 EFFECTS OF HEAT SOURCE/SINK ON MAGNETOHYDRODYNAMIC FLOW AND HEAT TRANSFER OF A NON-NEWTONIAN POWER-LAW FLUID ON A STRETCHING SURFACE by Kishan NAIKOTI
More informationHeat and mass transfer in nanofluid thin film over an unsteady stretching sheet using Buongiorno s model
Eur. Phys. J. Plus (2016) 131: 16 DOI 10.1140/epjp/i2016-16016-8 Regular Article THE EUROPEAN PHYSICAL JOURNAL PLUS Heat and mass transfer in nanofluid thin film over an unsteady stretching sheet using
More informationInternational Journal of Pure and Applied Mathematics
Volume 117 No. 11 2017, 317-325 ISSN: 1311-8080 (printed version); ISSN: 1314-3395 (on-line version) url: http://www.ijpam.eu ijpam.eu MHD Flow of a Nanofluid and Heat transfer over an Exponentially Shrinking
More informationBoundary Layer Stagnation-Point Flow of Micropolar Fluid over an Exponentially Stretching Sheet
International Journal of Fluid Mechanics & Thermal Sciences 2017; 3(3): 25-31 http://www.sciencepublishinggroup.com/j/ijfmts doi: 10.11648/j.ijfmts.20170303.11 ISSN: 2469-8105 (Print); ISSN: 2469-8113
More informationInternational Journal of Innovative Research in Science, Engineering and Technology. (An ISO 3297: 2007 Certified Organization)
ISSN(Online): 239-8753 Influence of Chemical Reaction, Heat Source, Soret and Dufour Effects on Heat And Mass Transfer in Boundary Layer Flow Over a Stretching Cylinder Embedded in a Porous Medium using
More informationK. Sharada 1* and B. Shankar 2 Department of mathematics, Osmania University, Hyderabad, Telangana, India.
Global Journal of Pure and Applied Mathematics. ISSN 0973-1768 Volume 13, Number 9 (2017), pp. 5965-5975 Research India Publications http://www.ripublication.com Effect of partial slip and convective boundary
More informationMHD flow and heat transfer due to a linearly stretching sheet. with induced magnetic field: Exact solution. Tarek M. A.
MHD flow and heat transfer due to a linearly stretching sheet with induced magnetic field: Exact solution Tarek M. A. El-Mistikawy Dept. Eng. Math. & Phys., Faculty of Engineering, Cairo University, Giza
More informationMHD boundary layer flow and heat transfer characteristics of a nanofluid over a stretching sheet
Acta Univ. Sapientiae, Mathematica, 9, 1 (2017) 140 161 DOI: 10.1515/ausm-2017-0009 MHD boundary layer flow and heat transfer characteristics of a nanofluid over a stretching sheet M. Ferdows Department
More informationKabita Nath Department of Mathematics Dibrugarh University Dibrugarh, Assam, India
Influence of Chemical Reaction, Heat Source, Soret and Dufour Effects on Separation of a Binary Fluid Mixture in MHD Natural Convection Flow in Porous Media B.R.Sharma Department of Mathematics Dibrugarh
More informationData Analysis and Heat Transfer in Nanoliquid Thin Film Flow over an Unsteady Stretching Sheet
Data Analysis and Heat Transfer in Nanoliquid Thin Film Flow over an Unsteady Stretching Sheet Prashant G Metri Division of Applied Mathematics, Mälardalen University, Västerås, Sweden prashant.g.metri@mdh.se
More informationResearch Article Boundary Layer Flow and Heat Transfer with Variable Fluid Properties on a Moving Flat Plate in a Parallel Free Stream
Applied Mathematics Volume 2012, Article ID 372623, 10 pages doi:10.1155/2012/372623 Research Article Boundary Layer Flow and Heat Transfer with Variable Fluid Properties on a Moving Flat Plate in a Parallel
More informationFlow of a micropolar fluid in channel with heat and mass transfer
Flow of a micropolar fluid in channel with heat and mass transfer PRECIOUS SIBANDA and FAIZ GA AWAD University of KwaZulu-Natal School of Mathematical Sciences Private Bag X, Scottsville Pietermaritzburg
More informationUnsteady MHD Convective Heat and Mass Transfer of a Casson Fluid Past a Semi-infinite Vertical Permeable Moving Plate with Heat Source/Sink
Unsteady MHD Convective Heat and Mass Transfer of a Casson Fluid Past a Semi-infinite Vertical Permeable Moving Plate with Heat Source/Sink Sekhar Kuppala R Viswanatha Reddy G Sri Venkateswara University,
More informationNumerical Analysis of Magneto-Hydrodynamic Flow of Non-Newtonian Fluid Past Over a Sharp Wedge in Presence of Thermal Boundary Layer
Numerical Analysis of Magneto-Hydrodynamic Flow of Non-Newtonian Fluid Past Over a Sharp Wedge in Presence of Thermal Boundary Layer Ramesh Yadav *, Santosh Kumar Dixit # and Navneet Kumar Singh #3 * Assistant
More informationMHD FLOW AND HEAT TRANSFER FOR MAXWELL FLUID OVER AN EXPONENTIALLY STRETCHING SHEET WITH VARIABLE THERMAL CONDUCTIVITY IN POROUS MEDIUM
S599 MHD FLOW AND HEAT TRANSFER FOR MAXWELL FLUID OVER AN EXPONENTIALLY STRETCHING SHEET WITH VARIABLE THERMAL CONDUCTIVITY IN POROUS MEDIUM by Vijendra SINGH a and Shweta AGARWAL b * a Department of Applied
More informationThe University of the West Indies, St. Augustine, Trinidad and Tobago. The University of the West Indies, St. Augustine, Trinidad and Tobago
Unsteady MHD Free Convection Couette Flow Through a Vertical Channel in the Presence of Thermal Radiation With Viscous and Joule Dissipation Effects Using Galerkin's Finite Element Method Victor M. Job
More informationMHD flow of radiating and chemically reacting viscoelastic fluid through a porous medium in porous vertical channel with constant suction
International Journal of Engineering Science Invention Volume Issue 3 ǁ March. 013 MHD flow of radiating and chemically reacting viscoelastic fluid through a porous medium in porous vertical channel with
More informationInfluence of non-uniform heat source/sink on stagnation point flow of a MHD Casson nanofluid flow over an exponentially stretching surface
Global Journal of Pure and Applied Mathematics. ISSN 973-768 Volume 3, Number (27), pp. 79-733 Research India Publications http://www.ripublication.com Influence of non-uniform heat source/sink on stagnation
More informationInternational Journal of Mathematical Archive-9(5), 2018, Available online through ISSN
International Journal of Mathematical Archive-9(5), 2018, 191-202 Available online through www.ijma.info ISSN 2229 5046 MAGNETOHYDRODYNAMIC TWO-PHASE DUSTY FLUID FLOW AND HEAT MODEL OVER RIGA PLATE WITH
More informationA new numerical approach for Soret effect on mixed convective boundary layer flow of a nanofluid over vertical frustum of a cone
Inter national Journal of Pure and Applied Mathematics Volume 113 No. 8 2017, 73 81 ISSN: 1311-8080 printed version); ISSN: 1314-3395 on-line version) url: http://www.ijpam.eu ijpam.eu A new numerical
More informationLaplace Technique on Magnetohydrodynamic Radiating and Chemically Reacting Fluid over an Infinite Vertical Surface
International Journal of Engineering and Technology Volume 2 No. 4, April, 2012 Laplace Technique on Magnetohydrodynamic Radiating and Chemically Reacting Fluid over an Infinite Vertical Surface 1 Sahin
More informationNonlinear Analysis: Modelling and Control, 2008, Vol. 13, No. 4,
Nonlinear Analysis: Modelling and Control, 2008, Vol. 13, No. 4, 513 524 Effects of Temperature Dependent Thermal Conductivity on Magnetohydrodynamic (MHD) Free Convection Flow along a Vertical Flat Plate
More informationA new approach for local similarity solutions of an unsteady hydromagnetic free convective heat transfer flow along a permeable flat surface
International Journal of Advances in Applied Mathematics and Mechanics Volume, Issue : (3) pp. 39-5 Available online at www.ijaamm.com IJAAMM ISSN: 347-59 A new approach for local similarity solutions
More informationMHD Stagnation Point Flow and Heat Transfer of Williamson Fluid over Exponential Stretching Sheet Embedded in a Thermally Stratified Medium
Global Journal of Pure and Applied Mathematics. ISSN 973-1768 Volume 13, Number 6 (17), pp. 33-56 Research India Publications http://www.ripublication.com MHD Stagnation Point Flow and Heat Transfer of
More informationMIXED CONVECTION SLIP FLOW WITH TEMPERATURE JUMP ALONG A MOVING PLATE IN PRESENCE OF FREE STREAM
THERMAL SCIENCE, Year 015, Vol. 19, No. 1, pp. 119-18 119 MIXED CONVECTION SLIP FLOW WITH TEMPERATURE JUMP ALONG A MOVING PLATE IN PRESENCE OF FREE STREAM by Gurminder SINGH *a and Oluwole Daniel MAKINDE
More informationVariable Viscosity Effect on Heat Transfer over a. Continuous Moving Surface with Variable Internal. Heat Generation in Micropolar Fluids
Applied Mathematical Sciences, Vol. 6, 2012, no. 128, 6365-6379 Variable Viscosity Effect on Heat Transfer over a Continuous Moving Surface ith Variable Internal Heat Generation in Micropolar Fluids M.
More informationA comprehensive note on thermally stratified flow and non-fourier heat flux theory
A comprehensive note on thermally stratified flow and non-fourier heat flux theory Muhammad Ijaz Khan a,*, Muhammad Waqas a, Tasawar Hayat a,b and Ahmed Alsaedi b a Department of Mathematics, Quaid-I-Azam
More informationV. SINGH and *Shweta AGARWAL
NUMERICAL SOLUTION OF MHD FLOW AND HEAT TRANSFER FOR MAXWELL FLUID OVER AN EXPONENTIALLY STRETCHING SHEET WITH VARIABLE THERMAL CONDUCTIVITY IN POROUS MEDIUM V. SINGH and *Shweta AGARWAL Department of
More informationHeat and Mass Transfer
1 Comments on six papers published by S.P. Anjali Devi and R. Kandasamy in Heat and Mass Transfer, ZAMM, Mechanics Research Communications, International Communications in Heat and Mass Transfer, Communications
More informationTHE UNSTEADY FREE CONVECTION FLOW OF ROTATING MHD SECOND GRADE FLUID IN POROUS MEDIUM WITH EFFECT OF RAMPED WALL TEMPERATURE
THE UNSTEADY FREE CONVECTION FLOW OF ROTATING MHD SECOND GRADE FLUID IN POROUS MEDIUM WITH EFFECT OF RAMPED WALL TEMPERATURE 1 AHMAD QUSHAIRI MOHAMAD, ILYAS KHAN, 3 ZULKHIBRI ISMAIL AND 4* SHARIDAN SHAFIE
More informationThermally Radiative Rotating Magneto-Nanofluid Flow over an Exponential Sheet with Heat Generation and Viscous Dissipation: A Comparative Study
Commun. Theor. Phys. 69 (2018 317 328 Vol. 69, No. 3, March 1, 2018 Thermally Radiative Rotating Magneto-Nanofluid Flow over an Exponential Sheet with Heat Generation and Viscous Dissipation: A Comparative
More informationIntroduction. Page 1 of 6. Research Letter. Authors: Philip O. Olanrewaju 1 Jacob A. Gbadeyan 1 Tasawar Hayat 2 Awatif A. Hendi 3.
Page of 6 Effects of internal heat generation, thermal radiation buoyancy force on a boundary layer over a vertical plate with a convective surface boundary condition Authors: Philip O. Olanrewaju Jacob
More informationFlow of micropolar fluid between two orthogonally moving porous disks
Appl. Math. Mech. -Engl. Ed., 33(8), 963 974 (2012) DOI 10.1007/s10483-012-1598-8 c Shanghai University and Springer-Verlag Berlin Heidelberg 2012 Applied Mathematics and Mechanics (English Edition) Flow
More informationMHD Boundary Layer Nanofluid flow of Heat Transfer over a Nonlinear Stretching Sheet Presence of Thermal Radiation and Partial Slip with Suction
Global Journal of Pure and Applied Mathematics. ISSN 0973-1768 Volume 13, Number 9 (017), pp. 497-4941 Research India Publications http://www.ripublication.com MHD Boundary Layer Nanofluid flow of Heat
More informationDual Solution of MHD Stagnation-Point Flow towards a Stretching Surface
Engineering, 010,, 99-305 doi:10.436/eng.010.4039 Published Online April 010 (http://www. SciRP.org/journal/eng) 99 Dual Solution of MHD Stagnation-Point Flow towards a Stretching Surface Abstract T. R.
More informationThermal and Concentration Stratifications Effects in Radiative Flow of Jeffrey Fluid over a Stretching Sheet
Thermal and Concentration Stratifications Effects in Radiative Flow of Jeffrey Fluid over a Stretching Sheet T. Hayat 1,2, Tariq Hussain 3, S. A. Shehzad 4 *, A. Alsaedi 2 1 Department of Mathematics,
More informationComputers and Mathematics with Applications. Laminar flow and heat transfer in the boundary-layer of non-newtonian fluids over a stretching flat sheet
Computers and Mathematics with Applications 57 (2009) 1425 1431 Contents lists available at ScienceDirect Computers and Mathematics with Applications journal homepage: www.elsevier.com/locate/camwa Laminar
More informationEffect of radiation on MHD nanofluid flow considering effective thermal conductivity and viscosity due to Brownian motion
ISSN (e): 2250 3005 Volume 07 Issue 11 November 2017 International Journal of Computational Engineering Research (IJCER) Effect of radiation on MHD nanofluid flow considering effective thermal conductivity
More informationBuoyancy-driven radiative unsteady magnetohydrodynamic heat transfer over a stretching sheet with non-uniform heat source/sink
Buoyancy-driven radiative unsteady magnetohydrodynamic heat transfer over a stretching sheet with non-uniform heat source/sink Dulal Pal 1 Department of Mathematics, Visva-Bharati University, Institute
More informationMixed convection of Non-Newtonian fluid flow and heat transfer over a Non-linearly stretching surface
Int. J. Adv. Appl. Math. and Mech. 3(1) (2015) 28 35 (ISSN: 2347-2529) Journal homepage: www.ijaamm.com International Journal of Advances in Applied Mathematics and Mechanics Mixed convection of Non-Newtonian
More informationUNSTEADY MAGNETOHYDRODYNAMICS THIN FILM FLOW OF A THIRD GRADE FLUID OVER AN OSCILLATING INCLINED BELT EMBEDDED IN A POROUS MEDIUM
THERMAL SCIENCE, Year 2016, No. 5, pp. 875-887 875 UNSTEADY MAGNETOHYDRODYNAMICS THIN FILM FLOW OF A THIRD GRADE FLUID OVER AN OSCILLATING INCLINED BELT EMBEDDED IN A POROUS MEDIUM by Fazal GHANI a, Taza
More informationViscous dissipation effect on MHD nanofluid flow on an exponentially radiating stretching sheet thermally stratified medium
Volume 118 No. 10 2018, 147-165 ISSN: 1311-8080 (printed version); ISSN: 1314-3395 (on-line version) url: http://www.ijpam.eu doi: 10.12732/ijpam.v118i10.57 ijpam.eu Viscous dissipation effect on MHD nanofluid
More informationResearch Article Lie Group Analysis of Unsteady Flow and Heat Transfer over a Porous Surface for a Viscous Fluid
Journal of Applied Mathematics Volume 202, Article ID 675287, 7 pages doi:0.55/202/675287 Research Article Lie Group Analysis of Unsteady Flow and Heat Transfer over a Porous Surface for a Viscous Fluid
More informationNUMERICAL COMPUTATIONS ON FLOW AND HEAT TRANSFER OF CASSON FLUID DUE TO OSCILLATORY MOVING SURFACE
NUMERICAL COMPUTATIONS ON FLOW AND HEAT TRANSFER OF CASSON FLUID DUE TO OSCILLATORY MOVING SURFACE by Sami ULLAH KHAN a, Nasir ALI b, Tahir MUSHTAQ c, Amar RAUF a,,* and Sabir Ali SHEHZAD a a,* Department
More informationHeat source/sink and thermal conductivity effects on micropolar nanofluid flow over a MHD radiative stretching surface
Heat source/sink and thermal conductivity effects on micropolar nanofluid flow over a MHD radiative stretching surface Srinivas Maripala 1 and Kishan Naikoti 2 1Department of mathematics, Sreenidhi Institute
More information