Natural Convective Boundary Layer Flow over a Horizontal Plate Embedded in a Porous Medium Saturated with a Nanofluid
|
|
- Stanley Fox
- 5 years ago
- Views:
Transcription
1 Journal of Modern Physics, 011,, 6-71 doi:10.46/jp Published Online February 011 ( Natural Convective Boundary Layer Flow over a Horizontal Plate Ebedded in a Porous Mediu Saturated with a Nanofluid Abstract Raa Subba Reddy Gorla 1, Ali Chakha 1 Cleveland State University, Cleveland, USA Public Authority for Applied Education and Training, Shuweikh, Kuwait E-ail: r.gorla@csuohio.edu, achakha@yahoo.co Received Septeber 5, 010; revised October 8, 010; accepted October 11, 010 A boundary layer analysis is presented for the natural convection past a horizontal plate in a porous ediu saturated with a nano fluid. Nuerical results for friction factor, surface heat transfer rate and ass transfer rate have been presented for paraetric variations of the buoyancy ratio paraeter Nr, Brownian otion paraeter Nb, therophoresis paraeter Nt and Lewis nuber Le. The dependency of the friction factor, surface heat transfer rate (Nusselt nuber) and ass transfer rate on these paraeters has been discussed. Keywords: Natural Convection, Porous Mediu, Nanofluid 1. Introduction The study of convective heat transfer in nanofluids is gaining a lot of attention. The nanofluids have any applications in the industry since aterials of nanoeter size have unique physical and cheical properties. Nanofluids are solid-liquid coposite aterials consisting of solid nanoparticles or nanofibers with sizes typically of n suspended in liquid. Nanofluids have attracted great interest recently because of reports of greatly enhanced theral properties. For exaple, a sall aount (<1% volue fraction) of Cu nanoparticles or carbon nanotubes dispersed in ethylene glycol or oil is reported to increase the inherently poor theral conductivity of the liquid by 40% and 150%, respectively [1,]. Conventional particle-liquid suspensions require high concentrations (>10%) of particles to achieve such enhanceent. However, probles of rheology and stability are aplified at high concentrations, precluding the widespread use of conventional slurries as heat transfer fluids. In soe cases, the observed enhanceent in theral conductivity of nanofluids is orders of agnitude larger than predicted by well-established theories. Other perplexing results in this rapidly evolving field include a surprisingly strong teperature dependence of the theral conductivity [] and a three-fold higher critical heat flux copared with the base fluids [4,5]. These enhanced theral properties are not erely of acadeic interest. If confired and found consistent, they would ake nanofluids proising for applications in theral anageent. Furtherore, suspensions of etal nanoparticles are also being developed for other purposes, such as edical applications including cancer therapy. The interdisciplinary nature of nanofluid research presents a great opportunity for exploration and discovery at the frontiers of nanotechnology. Porous edia heat transfer probles have several engineering applications such as geotheral energy recovery, crude oil extraction, ground water pollution, theral energy storage and flow through filtering edia. Cheng and Minkowycz [6] presented siilarity solutions for free convective heat transfer fro a vertical plate in a fluid-saturated porous ediu. Gorla and co-workers [7,8] solved the nonsiilar proble of free convective heat transfer fro a vertical plate ebedded in a saturated porous ediu with an arbitrarily varying surface teperature or heat flux. Chen and Chen [9] and Mehta and Rao [10] presented siilarity solutions for free convection of non-newtonian fluids over horizontal surfaces in porous edia. Nakayaa and Koyaa [11] studied the natural convection over a non-isotheral body of arbitrary geoetry placed in a porous ediu. All these studies were concerned with Newtonian fluid flows. The boundary layer flows in nano fluids have been analyzed re- Copyright 011 SciRes.
2 6 cently by Nield and Kuznetsov and Kuznetsov [1] and Nield and Kuznetsov [1]. A clear picture about the nanofluid boundary layer flows is still to eerge. The present work has been undertaken in order to analyze the natural convection past an isotheral horizontal plate in a porous ediu saturated by a nanofluid. The effects of Brownian otion and therophoresis are included for the nanofluid. Nuerical solutions of the boundary layer equations are obtained and discussion is provided for several values of the nanofluid paraeters governing the proble.. Analysis We consider the steady free convection boundary layer flow past a horizontal plate placed in a nano-fluid saturated porous ediu. The co-ordinate syste is selected such that x-axis is in the horizontal direction. We consider the two-diensional proble. Figure 1 shows the coordinate syste and flow odel. At the surface, the teperature T and the nano-particle fraction take constant values T W and ϕ W, respectively. The abient values, attained as y tends to infinity, of T and are denoted by T and ϕ, respectively. The Oberbeck-Boussinesq approxiation is eployed and the hoogeneity and local theral equilibriu in the porous ediu are assued. We consider the porous ediu whose porosity is denoted by ε and pereability by K. The Darcy velocity is denoted by v. The following four field equations ebody the conservation of total ass, oentu, theral energy, and nano-particles, respectively. The field variables are the Darcy velocity v, the teperature T and the nano-particle volue fraction..v 0 (1) f v P v p 1 f 1 T T g t K () T c c v f T t () D T k T c D p BT T T T Figure 1. Coordinate syste and flow odel. 1 D T v DB T (4) t T We write v u,v. Here, μ and β are the density, viscosity and voluetric volue expansion coefficient of the fluid; p f the density of the particles; g the gravitational acceleration; c the effective heat capacity and k effective theral conductivity of the porous ediu and D B the Brownian diffusion coefficient and D T the therophoretic diffusion coefficient. The flow is assued to be slow so that an advective ter and a Forchheier quadratic drag ter do not appear in the oentu equation. The boundary conditions are taken to be v 0, T T W, W, at y 0, (5) u 0, T T,, as y (6) We consider the steady state flow. In keeping with the Oberbeck-Boussinesq approxiation and an assuption that the nano-particle concentration is dilute, the oentu equation ay be written as: 0 P v K (7) P f1ft T g We now ake the standard boundary layer approxiation based on a scale analysis and write the governing equations. u v 0 (8) x y P u (9) x K P 1 f g T T P fg y (10) T T T DT T u v T DB x y y y T y (11) 1 D T T u v DB (1) x y y T y where k c p, c c (1) f One can eliinate P fro Equations (9) and (10) by cross-differentiation. At the sae tie one can introduce a strea line function ψ such that the continuity is autoatically satisfied: f Copyright 011 SciRes.
3 64 R. S. R. GORLA ET AL. u, v (14) dy dx We are then left with the following three equations. 1 gk T P f gk f y x (15) x L e D The transfored boundary conditions are: 0: S 0, 1, f 1 : S 0, 0, f 0 B () () T T T DT T T D B y x x y y y T y (16) D T 1 T DB y x x y y T y (17) Proceeding with the analysis we introduce the following diensionless variables: Ra x y Rax x 1 1 f gkax S Ra T T T T W 1/ x f (18) W We assue that T w and are constants. Substituting the expressions in Equation (18) into the governing Equations (15)-(17) we obtain the following transfored equations: S Nr f 0 (19) 1 S N b f Nt 0 (0) 1 N t f Le S f 0 N b (1) where the four paraeters are defined as: N r N b N t P fw T T 1 f W c DB W P c, f c DT TW T P c T, f, The local friction factor ay be written as u y y0 Ra x.s" 0 Cfx U Re x.pr The heat transfer rate at the surface is given by: T qw kf y y0 The heat transfer coefficient is given by: qw h TW T Local Nusselt nuber is given by: 1 x 0 hx Nux Ra, (4) kf The ass transfer rate at the surface is given by: NW D h W y y0 where h = ass transfer coefficient, The local Sherwood nuber is given by: 1 h x Sh Rax f, 0. Results and Discussion.1. Nuerical Method (5) D The syste of Equations (19)-(1) with the boundary conditions () is solved nuerically by eans of an efficient, iterative, tri-diagonal iplicit finite-difference ethod discussed previously by Blottner [1]. Equations (19)-(1) are discretized using three-point central difference forulae with S' replaced by another variable V. The direction is divided into 196 nodal points and a variable step size is used to account for the sharp changes in the variables in the region close to the surface where viscous effects doinate. The initial step size used is and the growth factor K such that n Kn 1 (where the subscript n is the nuber of nodes inus one). This gives 5 which repre- ax Copyright 011 SciRes.
4 65 sents the edge of the boundary layer at infinity. The ordinary differential equations are then converted into linear algebraic equations that are solved by the Thoas algorith discussed by Blottner [14]. Iteration is eployed to deal with the nonlinear nature of the governing equations. The convergence criterion eployed in this work was based on the relative difference between the current and the previous iterations. When this difference or error reached 10-5, the solution was assued converged and the iteration process was terinated. Equations (19)-(1) were solved nuerically to satisfy the boundary conditions () for paraetric values of Le, Nr (buoyancy ratio nuber), Nb (Brownian otion paraeter) and Nt (therophoresis paraeter) using finite difference ethod. Tables 1-5 indicate results for wall values for the gradients of velocity, teperature and concentration functions which are proportional to the friction factor, Nusselt nuber and Sherwood nuber, respectively. Fro Tables 1-, we notice that as Nr and Nt increase, the friction factor increases whereas the heat transfer rate (Nusselt nuber) and ass transfer rate (Sherwood nuber) decrease. As Nb increases, the fric- Table 1. Effects of N r on S"(0), θ'(0) and f'(0) for N b = 0., N t = 0.1 and Le = 10. N r S"(0) θ'(0) f'(0) E E E-05.67E E-04.46E E E E E E E Table. Effects of N t on S"(0), θ'(0) and f'(0) for N b = 0., N r = 0.5 and Le = 10. N t S"(0) θ'(0) f'(0) E E E E E-07.95E E E E E Table. Effects of N b on S"(0), θ'(0) and f'(0) for N r =0.5, N t =0.1 and Le=10. N b S"(0) θ'(0) f'(0) E E E E E E E E E E Table 4. Effects of Le on S"(0), θ'(0) and f'(0) for N b =0., N r = 0.5, and N t = 0.1. Le S"(0) θ'(0) f'(0) E E E E E E E E E Table 5. Effects of Le on S"(0), θ'(0) and f'(0) for N b = 0, N r = 0, and N t = 0. Le S"(0) θ'(0) f'(0) E E E E E E E E E tion factor and surface ass transfer rates increase whereas the surface heat transfer rate decreases. Results fro Table 4 indicate that as Le increases, the heat and ass transfer rates increase. Fro Table 5, we observe that the nano fluids display drag reducing and heat and ass transfer rate reducing characteristics. Figures -4 indicate that as Nr increases, the velocity decreases and the teperature and concentration increase. Siilar effects are observed fro Figures 5-10 as Nt and Nb vary. Figure 11 illustrates the variation of velocity within the boundary layer as Le increases. The velocity increases as Le increases. Fro Figures 1 and 1, we ob- serve that as Le increases, the teperature and concentration within the boundary layer decrease and the theral and concentration boundary later thicknesses decrease. The influence of nanoparticles on natural convection is odeled by accounting for Brownian otion and therophoresis as well as non-isotheral boundary conditions. The thickness of the boundary layer for the ass fraction is saller than the theral boundary layer thickness for Large values of Lewis nuber Le. The contribution of N t to heat and ass transfer does not depend on the value of Le. The Brownian otion and therophoresis of nano particles increases the effective theral conductivity of the nanofluid. Both Brownian diffusion and therophoresis give rise to cross diffusion ters that are siilar to the failiar Soret and Dufour cross diffusion ters that arise with a binary fluid discussed by Lakshi Narayana et al. [15]. 4. Concluding Rearks In this paper, we presented a boundary layer analysis for the natural convection past a non-isotheral vertical Copyright 011 SciRes.
5 Copyright 011 SciRes Nr=0,0.1,0.,0.,0.4,0.5Nb=0.Nt=0.1Le=10S' 1Figure. Effects of Nr on velocity profiles Nb=0.Nt=0.1Le=10Nr=0,0.1,0.,0.,0.4,0.5 Figure. Effects of N r on teperature profiles Nb=0.Nt=0.1Le=10Nr=0,0.1,0.,0.,0.4,0.5f Figure 4. Effects of N r on volue fraction profiles.
6 Copyright 011 SciRes Nb=0.Nr=0.5Le=10Nt=0.1,0.,0.,0.4,0.5S' Figure 5. Effects of N t on velocity profiles Nb=0.Nr=0.5Le=10Nt=0.1,0.,0.,0.4,05. Figure 6. Effects of N t on teperature profiles Nb=0.Nr=0.5Le=10Nt=0.1,0.,0.,0.4,0.5f Figure 7. Effects of N t on volue fraction profiles.
7 Copyright 011 SciRes Nr=0.5Nt=0.1Le=10Nb=0.1,0.,0.,0.4,0.5S' Figure 8. Effects of N b on velocity profiles Nr=0.5Nt=0.1Le=10Nb=0.1,0.,0.,0.4,0.5 Figure 9. Effects of N b on teperature profiles Nr=0.5Nt=0.1Le=10Nb=0.1,0.,0.,0.4,0.5f Figure 10. Effects of N b on volue fraction profiles.
8 Copyright 011 SciRes Le=100,1000Le=10Nb=0.Nr=0.5Nt=0.1Le=1S' Figure 11. Effects of Le on velocity profiles Nb=0.Nr=0.5Nt=0.1Le=1,10,100,1000 Figure 1. Effects of Le on teperature profiles Nb=0.Nr=0.5Nt=0.1Le=1,10,100,1000f Figure 1. Effects of Le on volue fraction profiles.
9 plate in a porous ediu saturated with a nano fluid. Nuerical results for friction factor, surface heat transfer rate and ass transfer rate have been presented for paraetric variations of the buoyancy ratio paraeter Nr, Brownian otion paraeter Nb, therophoresis paraeter Nt and Lewis nuber Le. The results indicate that as Nr and Nt increase, the friction factor increases whereas the heat transfer rate (Nusselt nuber) and ass transfer rate (Sherwood nuber) decrease. As Nb increases, the friction factor and surface ass transfer rates increase whereas the surface heat transfer rate decreases. As Le increases, the heat and ass transfer rates increase. Nano fluids display drag reducing and heat and ass transfer rate reducing characteristics. 5. References [1] J. A. Eastan, S. U. S. Choi, S. Li, W. Yu and L. J. Thopson, Anoalously Increased Effective Theral Conductivities Containing Copper Nanoparticles, Applied Physics Letters, Vol. 78, No. 6, 001, pp doi:10.106/ [] S. U. S. Choi, Z. G. Zhang, W. Yu, F. E. Lockwood and E. A. Grulke, Anoalous Theral Conductivity Enhanceent on Nanotube Suspensions, Applied Physics Letters, Vol. 79, No. 14, 001, pp doi:10.106/ [] H. E. Patel, S. K. Das, T. Sundararajan, A. Sreekuaran, B. George and T. Pradeep, Theral Conductivities of Naked and Monolayer Protected Metal Nanoparticle Based Nanofluids: Manifestation of Anoalous Enhanceent and Cheical Effects, Applied Physics Letters, Vol. 14, No. 8, 00, pp doi:10.106/ [4] S. M. You, J. H. Ki and K. H. Ki, Effect of Nanoparticles on Critical Heat Flux of Water in Pool Boiling Heat Transfer, Applied Physics Letters, Vol. 8, No. 16, 00, pp doi:10.106/ [5] P. Vassallo, R. Kuar and S. D Aico, Pool Boiling Heat Transfer Experients in Silica-Water Nanofluids, International Journal of Heat and Mass Transfer, Vol. 47, No., 004, pp doi: /s (0)0061- [6] P. Cheng and W. J. Minkowycz, Free Convection about a Vertical Flat Plate Ebedded in a Saturated Porous Mediu with Applications to Heat Transfer fro a Dike, Journal of Geophysics Res., Vol. 8, 1977, pp doi:10.109/jb08i014p0040 [7] R. S. R. Gorla and R. Tornabene, Free Convection fro a Vertical Plate with Nonunifor Surface Heat Flux and Ebedded in a Porous Mediu, Transport in Porous Media Journal, Vol., 1988, pp doi: /bf00688 [8] R. S. R. Gorla and A. Zinolabedini, Free Convection Fro a Vertical Plate With Nonunifor Surface Teperature and Ebedded in a Porous Mediu, Journal of Energy Resources Technology, Vol. 109, 1987, pp doi: /1.119 [9] H. T. Chen and C. K. Chen, Natural Convection of Non-Newtonian Fluids about a Horizontal Surface in a Porous Mediu, Journal of Energy Resources Technology, Vol. 109, 1987, pp doi: /1.16 [10] K. N. Mehta and K. N. Rao, Buoyancy-Induced Flow of Non-Newtonian Fluids in a Porous Mediu Past a Horizontal Plate with Nonunifor Surface Heat Flux, International Journal of Engineering Science, Vol., 1994, pp [11] A. Nakayaa and H. Koyaa, Buoyancy-Induced Flow of Non-Newtonian Fluids Over a Non-Isotheral Body of Arbitrary Shape in a Fluid-Saturated Porous Mediu, Applied Scientific Research, Vol. 48, 1991, pp doi: /bf [1] D. A. Nield and A. V. Kuznetsov, The Cheng Minkowycz Proble for Natural Convective Boundary Layer Flow in a Porous Mediu Saturated by a Nanofluid, International Journal of Heat and Mass Transfer, Vol. 5, 009, pp doi: /j.ijheatasstransfer [1] D. A. Nield and A. V. Kuznetsov, Theral Instability in a Porous Mediu Layer Saturated by a Nanofluid, International Journal of Heat and Mass Transfer, Vol. 5, No. 5-6, 009, pp doi: /j.ijheatasstransfer [14] F. G. Blottner, Finite-Difference Methods of Solution of the Boundary-Layer Equations, Journal of AIAA, Vol. 8, 1970, pp doi:10.514/.564 [15] P. A. L. Narayana, P. V. S. N. Murthy and R. S. R. Gorla, Soret-Driven Therosolutal Convection Induced by Inclined Theral and Solutal Gradients in a Shallow Horizontal Layer of a Porous Mediu, Journal of Fluid Mechanics, Vol. 61, 008, pp doi: /s Copyright 011 SciRes.
10 71 Noenclature D B Brownian diffusion coefficient D T therophoretic diffusion coefficient f rescaled nano-particle volue fraction g gravitational acceleration vector k effective theral conductivity of the porous ediu K pereability of porous ediu Le Lewis nuber Nr Buoyancy Ratio Nb Brownian otion paraeter Nt therophoresis paraeter Nu Nusselt nuber P pressure q wall heat flux Ra x local Rayleigh nuber Re Reynolds nuber S diensionless strea function T teperature T W wall teperature of the vertical plate T abient teperature U reference velocity u, v Darcy velocity coponents (x,y) Cartesian coordinates α Greek Sybols: theral diffusivity of porous ediu β voluetric expansion coefficient of fluid ε porosity η diensionless distance θ diensionless teperature μ viscosity of fluid ρ f fluid density ρ p nano-particle ass density (ρc) f heat capacity of the fluid (ρc) effective heat capacity of porous ediu (ρc) p effective heat capacity of nano-particle aterial τ paraeter defined by equation (1) ϕ nano-particle volue fraction ϕ W nano-particle volue fraction at the wall of the vertical plate ϕ abient nano-particle volue fraction ψ strea function Copyright 011 SciRes.
NATURAL CONVECTIVE BOUNDARY LAYER FLOW OVER A HORIZONTAL PLATE EMBEDDED
International Journal of Microscale and Nanoscale Thermal.... ISSN: 1949-4955 Volume 2, Number 3 2011 Nova Science Publishers, Inc. NATURAL CONVECTIVE BOUNDARY LAYER FLOW OVER A HORIZONTAL PLATE EMBEDDED
More informationFollow this and additional works at: Part of the Materials Science and Engineering Commons
Engineering Conferences International ECI Digital Archives 5th International Conference on Porous Media and Their Applications in Science, Engineering and Industry Refereed Proceedings Suer 6-24-204 Effect
More informationENTROPY GENERATION ANALYSIS OF THE REVISED CHENG-MINKOWYCZ PROBLEM FOR NATURAL CONVECTIVE BOUNDARY LAYER FLOW OF NANOFLUID IN A POROUS MEDIUM
Rashidi, M. M., et al.: Entropy Generation Analysis of the Revised Cheng-Minkowycz THERMAL SCIENCE, Year 15, Vol. 19, Suppl. 1, pp. S169-S178 S169 ENTROPY GENERATION ANALYSIS OF THE REVISED CHENG-MINOWYCZ
More informationEffect of Darcy Dissipation on Melting From a Vertical Plate with Variable Temperature Embedded In Porous Medium
IOSR Journal of Matheatics (IOSR-JM) e-issn: 78-578, p-issn: 319-765X. Volue 10, Issue 4 Ver. IV (Jul-Aug. 014), PP 10-107 Effect of Darcy Dissipation on Melting Fro a Vertical Plate with Variable Teperature
More informationMELTING HEAT TRANSFER IN A NANOFLUID FLOW PAST A PERMEABLE CONTINUOUS MOVING SURFACE
Journal of Naval Architecture and Marine Engineering December, 2011 DOI: 10.3329/jname.v8i2.6830 http://www.banglajol.info MELTING HEAT TRANSFER IN A NANOFLUID FLOW PAST A PERMEABLE CONTINUOUS MOVING SURFACE
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 informationEffect of chemical reaction and viscous dissipation on MHD nanofluid flow over a horizontal cylinder : analytical solution
Effect of cheical reaction and viscous dissipation on MHD nanofluid flo over a horizontal cylinder : analytical solution hukla, N, Rana, P, Beg, OA and ingha, B http://dx.doi.org/1.163/1.497365 Title Authors
More informationEffects of Radiation on Free Convection Flow past an Upward Facing Horizontal Plate in a Nanofluid in the Presence of Internal Heat Generation
Effects of Radiation on Free Convection Flow past an Upward Facing Horizontal Plate in a Nanofluid in the Presence of Internal Heat Generation M.B.K.MOORTHY Department of Mathematics Institute of Road
More informationSTUDY OF THE EFFECTIVE THERMAL CONDUCTIVITY OF NANOFLUIDS
Proceedings of IMECE25 25 ASME International Mechanical Engineering Congress and Exposition Noveber 5-, 25, Orlando, Florida, USA IMECE5-828 STUDY OF THE EFFECTIVE THERMAL CONDUCTIVITY OF NANOFLUIDS Ratnesh
More informationEffect of Thermal Radiation and Stratification on Natural Convection over an Inclined Wavy Surface in a Nanofluid Saturated Porous Medium
Effect of Theral Radiation and Stratification on atural Convection over an Inclined Wavy Surface in a anofluid Saturated Porous Mediu D. Srinivasacharya, and P. Vijay Kuar Abstract An analysis is carried
More informationAn Application of HAM for MHD Heat Source Problem. with Variable Fluid Properties
Advances in Theoretical and Applied Mechanics, Vol. 7, 14, no., 79-89 HIKARI Ltd, www.-hiari.co http://dx.doi.org/1.1988/ata.14.4814 An Application of HAM for MHD Heat Source Proble with Variable Fluid
More informationMagnetohydrodynamic (MHD) Plane Poiseuille Flow With Variable Viscosity and Unequal Wall Temperatures
Iranian Journal of Cheical Engineering Vol. 11, No. 1 (Winter), 014, IAChE Resea rch note Magnetohydrodynaic (MHD) Plane Poiseuille Flow With Variable Viscosity and Unequal Wall Teperatures A. Kuar Jhankal
More informationENTROPY GENERATION IN HEAT AND MASS TRANSFER IN POROUS CAVITY SUBJECTED TO A MAGNETIC FIELD
HEFAT 9 th International Conference on Heat Transfer, Fluid Mechanics and Thermodynamics 6 8 July Malta ENTROPY GENERATION IN HEAT AND MASS TRANSFER IN POROUS CAVITY SUBJECTED TO A MAGNETIC FIELD Nawaf
More informationINFLUENCE OF VARIABLE PERMEABILITY ON FREE CONVECTION OVER VERTICAL FLAT PLATE EMBEDDED IN A POROUS MEDIUM
INFLUENCE OF VARIABLE PERMEABILITY ON FREE CONVECTION OVER VERTICAL FLAT PLATE EMBEDDED IN A POROUS MEDIUM S. M. M. EL-Kabeir and A. M. Rashad Department of Mathematics, South Valley University, Faculty
More informationA Numerical Investigation of Turbulent Magnetic Nanofluid Flow inside Square Straight Channel
A Nuerical Investigation of Turbulent Magnetic Nanofluid Flow inside Square Straight Channel M. R. Abdulwahab Technical College of Mosul, Mosul, Iraq ohaedalsafar2009@yahoo.co Abstract A nuerical study
More informationentropy ISSN by MDPI
Entropy, 007, 9, 118-131 Full Research Paper entropy ISSN 1099-4300 007 by MDPI www.dpi.org/entropy On Darcy-Brinkan Equation: Viscous Flow Between Two Parallel Plates Packed with Regular Square Arrays
More informationFarid Samara 1, Dominic Groulx 1 and Pascal H. Biwole 2 1
Farid Saara 1, Doinic Groulx 1 and Pascal H. Biwole 2 1 Departent of Mechanical Engineering, Dalhousie University 2 Departent of Matheatics and Interactions, Université of Nice Sophia-Antipolis Excerpt
More informationUnsteady MHD free Convective flow in a Rotating System with Soret Effect on n th order chemical reaction S.Anuradha 1 K.Sasikala 2
Vol. 7Issue 1, January 018, ISSN: 30-094 Ipact Factor: 6.765 Journal Hoepage: http://.ijes.co.in, Eail: ijesj@gail.co Double-Blind Peer Revieed Refereed Open Access International Journal - Included in
More informationOn the characterization of non-linear diffusion equations. An application in soil mechanics
On the characterization of non-linear diffusion equations. An application in soil echanics GARCÍA-ROS, G., ALHAMA, I., CÁNOVAS, M *. Civil Engineering Departent Universidad Politécnica de Cartagena Paseo
More informationSpine Fin Efficiency A Three Sided Pyramidal Fin of Equilateral Triangular Cross-Sectional Area
Proceedings of the 006 WSEAS/IASME International Conference on Heat and Mass Transfer, Miai, Florida, USA, January 18-0, 006 (pp13-18) Spine Fin Efficiency A Three Sided Pyraidal Fin of Equilateral Triangular
More informationInt. J. of Applied Mechanics and Engineering, 2018, vol.23, No.1, pp DOI: /ijame
Int. J. of Applied Mechanics and Engineering, 018, vol.3, No.1, pp.137-159 DOI: 10.1515/ijae-018-0009 EFFECTS OF HEAT SOURCE/SINK AND CHEMICAL REACTION ON MHD MAXWELL NANOFLUID FLOW OVER A CONVECTIVELY
More informationEFFECTS OF VARIABLE VISCOSITY AND THERMAL CONDUCTIVITY ON NATURAL-CONVECTION OF NANOFLUIDS PAST A VERTICAL PLATE IN POROUS MEDIA
EFFECTS OF VARIABLE VISCOSITY AND THERMAL CONDUCTIVITY ON NATURAL-CONVECTION OF NANOFLUIDS PAST A VERTICAL PLATE IN POROUS MEDIA A. Noghrehabadi M. Ghalambaz A. Ghanbarzadeh Department of Mechanical Engineering
More informationNumerically repeated support splitting and merging phenomena in a porous media equation with strong absorption. Kenji Tomoeda
Journal of Math-for-Industry, Vol. 3 (C-), pp. Nuerically repeated support splitting and erging phenoena in a porous edia equation with strong absorption To the eory of y friend Professor Nakaki. Kenji
More informationExplicit Analytic Solution for an. Axisymmetric Stagnation Flow and. Heat Transfer on a Moving Plate
Int. J. Contep. Math. Sciences, Vol. 5,, no. 5, 699-7 Explicit Analytic Solution for an Axisyetric Stagnation Flow and Heat Transfer on a Moving Plate Haed Shahohaadi Mechanical Engineering Departent,
More informationNon-Uniform Heat Source/Sink and Thermal Radiation Effects on the Stretched Flow of Cylinder in a Thermally Stratified Medium
Journal of Applied Fluid Mechanics, Vol. 10, No., pp. 915-94, 016. Available online at www.jafonline.net, ISSN 175-57, EISSN 175-645. DOI: 10.18869/acadpub.jaf.7.40.4008 Non-Unifor Heat Source/Sink and
More informationHeat Transfer in a Nanofluid Flow past a Permeable Continuous Moving Surface
Cleveland State University EngagedScholarship@CSU ETD Archive 2010 Heat Transfer in a Nanofluid Flow past a Permeable Continuous Moving Surface Sarvang D. Shah Cleveland State University How does access
More informationSolidification of Porous Material under Natural Convection by Three Phases Modeling
Solidification of Porous Material under Natural Convection by Three Phases Modeling Hassan Basirat Tabrizi, Meber, IAENG and F. Sadeghpour Abstract The perforance of natural convective flow over a rectangular
More informationEffects of thermophoresis on mixed convection flow from a moving vertical plate in a parallel free stream in the presence of thermal radiation
IOSR Journal of Matheatics (IOSR-JM) e-issn: 78-578p-ISSN: 319-765X Volue 7 Issue 4 (Jul. - Aug. 013) PP 8-9 Effects of therophoresis on ixed convection flow fro a oving vertical plate in a parallel free
More informationMixed Convection Flow of Casson Nanofluid over a Stretching Sheet with Convectively Heated Chemical Reaction and Heat Source/Sink
Journal of Applied Fluid Mechanics Vol. 8 No. 4 pp. 803-813 015. Available online at www.jafonline.net ISSN 1735-357 EISSN 1735-3645. DOI: 10.18869/acadpub.jaf.73.38.995 Mixed Convection Flow of Casson
More informationFree convection flow of Couple Stress fluid between parallel Disks
International Conference on Fluid Dynaics and Therodynaics Technologies (FDTT ) IPCSIT vol.33() () IACSIT Press, Singapore Free convection flow of Couple Stress fluid between parallel Disks D. Srinivasacharya
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 informationEffect of Variable Viscosity on Convective Heat and Mass Transfer by Natural Convection from Vertical Surface in Porous Medium
Effect of Variable Viscosity on Convective Heat and Mass Transfer by Natural Convection from Vertical Surface in Porous Medium M.B.K.MOORTHY, K.SENTHILVADIVU Department of Mathematics, Institute of Road
More informationInfluence of Viscous Dissipation on Free Convection in a Non-Darcy Porous Medium Saturated with Nanofluid in the Presence of Magnetic Field
20 The Open Transport Phenomena Journal, 2013, 5, 20-29 Send Orders for Reprints to reprints@benthamscience.net Open Access Influence of Viscous Dissipation on Free Convection in a Non-Darcy Porous Medium
More informationAnalytical Expression for the Hydrodynamic Fluid Flow through a Porous Medium
Analytical Expression for the Hydronaic Fluid Flow through a Porous Mediu * V.Ananthasway 1, S.Ua Maheswari 1 Departent of Matheatics, The Madura College (Autonoous), Maduri, Tail Nadu, India M. Phil.,
More informationTemperature and Internal Heat Generation in a Porous Medium
TECHNISCHE MECHANIK, Band 21, Heft 4, (20011313318 Manuskripteingang: 20. September 200] Free Convection over 3 Vertical Flat Plate with a Variable Wall Temperature and Internal Heat Generation in a Porous
More informationDaniel López Gaxiola 1 Student View Jason M. Keith
Suppleental Material for Transport Process and Separation Process Principles Chapter Principles of Moentu Transfer and Overall Balances In fuel cells, the fuel is usually in gas or liquid phase. Thus,
More informationThree-Dimensional MHD Flow of Casson Fluid in Porous Medium with Heat Generation
Journal of Applied Fluid Mechanics, Vol. 9, No. 1, pp. 15-3, 016. Available online at www.jafonline.net, ISSN 1735-357, EISSN 1735-3645. Three-Diensional MHD Flow of Casson Fluid in Porous Mediu with Heat
More informationMagneto hydrodynamic Fluid Flow past Contracting Surface Taking Account of Hall Current
ISSN: 39-5967 ISO 900:008 Certified Volue 7, Issue 3, May 08 Magneto hydrodynaic Fluid Flow past Contracting Surface Taing Account of Hall Current Sauel K. Muondwe, Mathew Kinyanu David Theur Kang ethe
More informationREPRODUCING KERNEL PARTICLE METHOD FOR CONDUCTION RADIATION INTERACTION IN 3D PARTICIPATING MEDIA
Proceedings of the Asian Conference on Theral Sciences 2017, 1st ACTS March 26-30, 2017, Jeu Island, Korea ACTS-P00337 REPRODUCING KERNEL PARTICLE METHOD FOR CONDUCTION RADIATION INTERACTION IN 3D PARTICIPATING
More informationSD Numerical Simulation Technique for Hydrodynamic Flow Gas- Solids Mixing Mantilla Núñez, Irla* 1 S. De Vicente C. 2
SD Nuerical Siulation Technique for Hydrodynaic Flow Gas- Solids Mixing Mantilla Núñez, Irla* S. De Vicente C. National University of Engineering, Lia, Perú, Polytechnic University of Madrid. *Lia 5, irlan@uni.edu.pe.
More informationEffect of Mass and Partial Slip on Boundary Layer Flow of a Nanofluid over a Porous Plate Embedded In a Porous Medium
IOSR Journal of Mechanical and Civil Engineering (IOSR-JMCE) e-issn: 2278-1684,p-ISSN: 2320-334X, Volume 13, Issue 4 Ver. II (Jul. - Aug. 2016), PP 42-49 www.iosrjournals.org Effect of Mass and Partial
More informationData-Driven Imaging in Anisotropic Media
18 th World Conference on Non destructive Testing, 16- April 1, Durban, South Africa Data-Driven Iaging in Anisotropic Media Arno VOLKER 1 and Alan HUNTER 1 TNO Stieltjesweg 1, 6 AD, Delft, The Netherlands
More informationAnalytical investigation of unsteady CuO nanofluid flow, heat and mass transfer between two parallel disks
Indian Journal o Cheical Technology Vol. 5, May 8, pp. 8-86 Analytical investigation o unsteady CuO nanoluid low, heat and ass transer between two parallel disks Azii M, Ganji DD, Azii A*,3 & Riazi R 4
More informationFORCED CONVECTION BOUNDARY LAYER MAGNETOHYDRODYNAMIC FLOW OF NANOFLUID OVER A PERMEABLE STRETCHING PLATE WITH VISCOUS DISSIPATION
S587 FORCED CONVECTION BOUNDARY LAYER MAGNETOHYDRODYNAMIC FLOW OF NANOFLUID OVER A PERMEABLE STRETCHING PLATE WITH VISCOUS DISSIPATION by Meisam HABIBI MATIN a,b and Pouyan JAHANGIRI c * a Department of
More information8.1 Force Laws Hooke s Law
8.1 Force Laws There are forces that don't change appreciably fro one instant to another, which we refer to as constant in tie, and forces that don't change appreciably fro one point to another, which
More informationHEAT TRANSFER IN FERROFLUID IN CHANNEL WITH POROUS WALLS
HEAT TRANSFER IN FERROFLUID IN CHANNEL WITH POROUS WALLS T. Strek Institute of Applied Mechanics, Poznan University of Technology, Poland Abstract The viscous, two-diensional, incopressible and lainar
More informationma x = -bv x + F rod.
Notes on Dynaical Systes Dynaics is the study of change. The priary ingredients of a dynaical syste are its state and its rule of change (also soeties called the dynaic). Dynaical systes can be continuous
More informationEffect of Variable Viscosity on Convective Heat and Mass Transfer by Natural Convection from Horizontal Surface in Porous Medium
Effect of Variable Viscosity on Convective Heat and Mass Transfer by Natural Convection from Horizontal Surface in Porous Medium M. B. K. MOORTHY, K. SENTHILVADIVU Department of Mathematics, Institute
More information1.1 Heat and Mass transfer in daily life and process/mechanical engineering Heat transfer in daily life: Heating Cooling Cooking
1. Introduction 1.1 Heat and Mass transfer in daily life and process/echanical engineering Heat transfer in daily life: Heating Cooling Cooking ransfer of heat along a teperature difference fro one syste
More informationNUMERICAL SIMULATION OF COLD AIR JET ATTACHMENT TO NON ADIABATIC WALLS
Eleventh International IBPSA Conference Glasgow, Scotland July 27-30, 2009 NUMERICAL SIMULATION OF COLD AIR JET ATTACHMENT TO NON ADIABATIC WALLS Nikola Mirkov 1, Žana Stevanović 1, and Žarko Stevanović
More informationReading from Young & Freedman: For this topic, read the introduction to chapter 25 and sections 25.1 to 25.3 & 25.6.
PHY10 Electricity Topic 6 (Lectures 9 & 10) Electric Current and Resistance n this topic, we will cover: 1) Current in a conductor ) Resistivity 3) Resistance 4) Oh s Law 5) The Drude Model of conduction
More informationMAGNETOHYDRODYNAMIC FLOW OF NANOFLUID WITH HOMOGENEOUS-HETEROGENEOUS REACTIONS AND VELOCITY SLIP
THERMAL SCIENCE, Year 017, Vol. 1, No., pp. 901-913 901 MAGNETOHYDRODYNAMIC FLOW OF NANOFLUID WITH HOMOGENEOUS-HETEROGENEOUS REACTIONS AND VELOCITY SLIP by Tasawar HAYAT a,b, Maria IMTIAZ a*, and Ahad
More informationChapter 7: Natural Convection
7-1 Introduction 7- The Grashof Number 7-3 Natural Convection over Surfaces 7-4 Natural Convection Inside Enclosures 7-5 Similarity Solution 7-6 Integral Method 7-7 Combined Natural and Forced Convection
More informationNumerical Solution of the MRLW Equation Using Finite Difference Method. 1 Introduction
ISSN 1749-3889 print, 1749-3897 online International Journal of Nonlinear Science Vol.1401 No.3,pp.355-361 Nuerical Solution of the MRLW Equation Using Finite Difference Method Pınar Keskin, Dursun Irk
More informationEFFECT OF THE NON-CONDENSABLE GAS TYPE DURING CONDENSATION OF WATER VAPOR
THERMAL SCIENCE: Year 217, Vol. 21, No. 6A, pp. 2457-2468 2457 EFFECT OF THE NON-CONDENSABLE GAS TYPE DURING CONDENSATION OF WATER VAPOR by Kaoutar ZINE-DINE *, Youness EL HAMMAMI, Rachid MIR, Touria MEDIOUNI,
More information(a) Why cannot the Carnot cycle be applied in the real world? Because it would have to run infinitely slowly, which is not useful.
PHSX 446 FINAL EXAM Spring 25 First, soe basic knowledge questions You need not show work here; just give the answer More than one answer ight apply Don t waste tie transcribing answers; just write on
More informationDimensions and Units
Civil Engineering Hydraulics Mechanics of Fluids and Modeling Diensions and Units You already know how iportant using the correct diensions can be in the analysis of a proble in fluid echanics If you don
More informationCHEMICALLY REACTING ON MHD BOUNDARY-LAYER FLOW OF NANOFLUIDS OVER A NON-LINEAR STRETCHING SHEET WITH HEAT SOURCE/SINK AND THERMAL RADIATION
akinde, O. D., et al.: Cheically eacting on HD Boundary-Layer Flow o... THEAL SCIENCE: Year 8, Vol., No. B, pp. 495-56 495 CHEICALLY EACTING ON HD BOUNDAY-LAYE FLOW OF NANOFLUIDS OVE A NON-LINEA STETCHING
More informationU V. r In Uniform Field the Potential Difference is V Ed
SPHI/W nit 7.8 Electric Potential Page of 5 Notes Physics Tool box Electric Potential Energy the electric potential energy stored in a syste k of two charges and is E r k Coulobs Constant is N C 9 9. E
More informationProblem T1. Main sequence stars (11 points)
Proble T1. Main sequence stars 11 points Part. Lifetie of Sun points i..7 pts Since the Sun behaves as a perfectly black body it s total radiation power can be expressed fro the Stefan- Boltzann law as
More information26 Impulse and Momentum
6 Ipulse and Moentu First, a Few More Words on Work and Energy, for Coparison Purposes Iagine a gigantic air hockey table with a whole bunch of pucks of various asses, none of which experiences any friction
More informationCFD SIMULATION OF PRESSURE LOSS IN HVDC TRANSFORMER WINDING
Journal of Energy VOLUME 63 2014 journal hoepage: http://journalofenergy.co/ Ralf Wittaack Sieens AG, Nürnberg, Gerany Ralf.Wittaack@Sieens.co CFD SIMULATION OF PRESSURE LOSS IN HVDC TRANSFORMER WINDING
More informationSolutions to the problems in Chapter 6 and 7
Solutions to the probles in Chapter 6 and 7 6.3 Pressure of a Feri gas at zero teperature The nuber of electrons N and the internal energy U, inthevoluev,are N = V D(ε)f(ε)dε, U = V εd(ε)f(ε)dε, () The
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 informationModelling diabatic atmospheric boundary layer using a RANS-CFD code with a k-ε turbulence closure F. VENDEL
Modelling diabatic atospheric boundary layer using a RANS-CFD code with a k-ε turbulence closure F. VENDEL Florian Vendel 1, Guillevic Laaison 1, Lionel Soulhac 1, Ludovic Donnat 2, Olivier Duclaux 2,
More informationProjectile Motion with Air Resistance (Numerical Modeling, Euler s Method)
Projectile Motion with Air Resistance (Nuerical Modeling, Euler s Method) Theory Euler s ethod is a siple way to approxiate the solution of ordinary differential equations (ode s) nuerically. Specifically,
More informationAnnouncement. Grader s name: Qian Qi. Office number: Phys Office hours: Thursday 4:00-5:00pm in Room 134
Lecture 3 1 Announceent Grader s nae: Qian Qi Office nuber: Phys. 134 -ail: qiang@purdue.edu Office hours: Thursday 4:00-5:00p in Roo 134 2 Millikan s oil Drop xperient Consider an air gap capacitor which
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 informationModel Fitting. CURM Background Material, Fall 2014 Dr. Doreen De Leon
Model Fitting CURM Background Material, Fall 014 Dr. Doreen De Leon 1 Introduction Given a set of data points, we often want to fit a selected odel or type to the data (e.g., we suspect an exponential
More informationCouncil for Innovative Research
ISSN 347-3487 Turbulent fil condensation in a vertical tube in presence of non condensable gas Y. Belkassi, K. Gueraoui, N. Hassanain, A. Elbouzidi Tea of vapour gas in fluid echanics and environent, LPT,
More informationSIMULATION OF SOIL TEMPERATURE VARIATION FOR GEOTHERMAL APPLICATIONS
International Journal of Mechanical Engineering and Technology (IJMET) Volue 8, Issue 2, February 2017, pp. 167 175 Article ID: IJMET_08_02_020 Available online at http://www.iaee.co/ijmet/issues.asp?jtype=ijmet&vtype=8&itype=2
More informationEffects of Viscous Dissipation on Unsteady Free Convection in a Fluid past a Vertical Plate Immersed in a Porous Medium
Transport in Porous Media (2006) 64: 1 14 Springer 2006 DOI 10.1007/s11242-005-1126-6 Effects of Viscous Dissipation on Unsteady Free Convection in a Fluid past a Vertical Plate Immersed in a Porous Medium
More informationAvailable online at ScienceDirect. Procedia Materials Science 10 (2015 )
Available online at www.sciencedirect.com ScienceDirect Procedia Materials Science 10 (2015 ) 563 571 2nd International Conference on Nanomaterials and Technologies (CNT 2014) Effect of viscous dissipation,
More informationThe Thermal Conductivity Theory of Non-uniform Granular Flow and the Mechanism Analysis
Coun. Theor. Phys. Beijing, China) 40 00) pp. 49 498 c International Acadeic Publishers Vol. 40, No. 4, October 5, 00 The Theral Conductivity Theory of Non-unifor Granular Flow and the Mechanis Analysis
More informationLecture #8-3 Oscillations, Simple Harmonic Motion
Lecture #8-3 Oscillations Siple Haronic Motion So far we have considered two basic types of otion: translation and rotation. But these are not the only two types of otion we can observe in every day life.
More information1 Brownian motion and the Langevin equation
Figure 1: The robust appearance of Robert Brown (1773 1858) 1 Brownian otion and the Langevin equation In 1827, while exaining pollen grains and the spores of osses suspended in water under a icroscope,
More informationQuestion 1. [14 Marks]
6 Question 1. [14 Marks] R r T! A string is attached to the dru (radius r) of a spool (radius R) as shown in side and end views here. (A spool is device for storing string, thread etc.) A tension T is
More informationHEAT TRANSFER IN ELECTROCONDUCTIVE FLUIDS. A HIGHLY SIMPLIFIED MARK & CELL SIMULATION
HEAT TRANSFER IN ELECTROCONDUCTIVE FLUIDS. A HIGHLY SIMPLIFIED MARK & CELL SIMULATION HIDEO KAWAHARA 1, ALEXANDRU MIHAIL MOREGA 2, MIHAELA MOREGA 3 Key words: Electroconductive fluids, Convection heat
More informationABSTRACT. A new scaling technique based on the hypothesis that flows in a compartment fire are
ABSTRACT Title of Thesis: SCALE MODELING OF THE TRANSIENT BEHAVIOR OF HEAT FLUX IN ENCLOSURE FIRES Peter Surendran Veloo, Master of Science, 26 Directed By: John L. Bryan Chair Professor Jaes G. Quintiere
More informationNational 5 Summary Notes
North Berwick High School Departent of Physics National 5 Suary Notes Unit 3 Energy National 5 Physics: Electricity and Energy 1 Throughout the Course, appropriate attention should be given to units, prefixes
More informationINFLUENCE OF THERMOPHORESIS AND JOULE HEATING ON THE RADIATIVE FLOW OF JEFFREY FLUID WITH MIXED CONVECTION
Brazilian Journal of Cheical Engineering ISSN 4-663 Printed in Brazil www.abeq.org.br/bjche Vol. 3 No. 4 pp. 897-98 October - Deceber 3 INFLUENCE OF THERMOPHORESIS AND JOULE HEATING ON THE RADIATIVE FLOW
More informationSome Perspective. Forces and Newton s Laws
Soe Perspective The language of Kineatics provides us with an efficient ethod for describing the otion of aterial objects, and we ll continue to ake refineents to it as we introduce additional types of
More informationTime Dependent Pressure Gradient Effect on Unsteady MHD Couette Flow and Heat Transfer of a Casson Fluid
Engineering, 011, 3, 38-49 doi:10.436/eng.011.31005 Published Online January 011 (http://www.scirp.org/journal/eng) Tie ependent Pressure Gradient Effect on Unsteady MH Couette Flow and Heat Transfer of
More informationFLOW OF A WILLIAMSON FLUID OVER A STRETCHING SHEET
Brazilian Journal of Cheical Engineering ISSN 4-66 Printed in Brazil www.abeq.org.br/bjche Vol., No., pp. 69-65, July - Septeber, FLOW OF A WILLIAMSON FLUID OVER A STRETCHING SHEET S. Nadee *, S. T. Hussain
More informationMeasuring Temperature with a Silicon Diode
Measuring Teperature with a Silicon Diode Due to the high sensitivity, nearly linear response, and easy availability, we will use a 1N4148 diode for the teperature transducer in our easureents 10 Analysis
More informationSimulation of Geomechanical Behavior during SAGD Process using COMSOL Multiphysics
Siulation of Geoechanical Behavior during SAGD Process using COMSOL Multiphysics X. Gong 1, R.Wan *2 Departent of Civil Engineering, University of Calgary, Calgary, Alberta, Canada. *Corresponding author:
More informationRana, P, Shukla, N, Beg, OA, Kadir, A and Singh, B
Unsteady electroagnetic radiative nanofluid stagnation point flow fro a stretching sheet with cheically reactive nanoparticles, Stefan blowing effect and entropy generation Rana, P, Shukla, N, Beg, OA,
More informationNUMERICAL ANALYSIS OF A NANOFLUID FORCED CONVECTION IN A POROUS CHANNEL: A NEW HEAT FLUX MODEL IN LTNE CONDITION
Journal of Porous Media, 17 (7): 637 646 (2014) NUMERICAL ANALYSIS OF A NANOFLUID FORCED CONVECTION IN A POROUS CHANNEL: A NEW HEAT FLUX MODEL IN LTNE CONDITION T. Armaghani, 1 Ali J. Chamkha, 2, M. J.
More informationViscosity and Fluid Suction/Injection Effects on Free Convection Flow from a Vertical Plate in a Porous Medium Saturated with a Pseudoplastic Fluid
ISSN 749-3889 (print), 749-3897 (online) International Journal of Nonlinear Science Vol.8(4) No.,pp.7-38 Viscosity and Fluid Suction/Injection Effects on Free Convection Flow from a Vertical Plate in a
More information2 Q 10. Likewise, in case of multiple particles, the corresponding density in 2 must be averaged over all
Lecture 6 Introduction to kinetic theory of plasa waves Introduction to kinetic theory So far we have been odeling plasa dynaics using fluid equations. The assuption has been that the pressure can be either
More informationFree convection modeling over a vertical flat plate embedded in saturated porous medium with a variable heat source and radiation flux
ISSN 1 746-7233, England, UK World Journal of Modelling and Simulation Vol. 9 (2013) No. 3, pp. 163-172 Free convection modeling over a vertical flat plate embedded in saturated porous medium with a variable
More informationThe accelerated expansion of the universe is explained by quantum field theory.
The accelerated expansion of the universe is explained by quantu field theory. Abstract. Forulas describing interactions, in fact, use the liiting speed of inforation transfer, and not the speed of light.
More informationSPATIAL AND TEMPORAL DISTRIBUTIONS OF MIGRATION IN BIO-RETENTION SYSTEMS
Li, Y.-Q., et al.: Spatial and Teporal Distributions of Moisture THERMAL SCIENCE, Year 04, Vol. 8, No. 5, pp. 557-56 557 SPATIAL AND TEMPORAL DISTRIBUTIONS OF MIGRATION IN BIO-RETENTION SYSTEMS by Yu-Qi
More informationHALF-LIFE TIME FOR VOC EMISSION AND SORPTION OF POROUS BUILDING MATERIALS
HAF-IFE TIME FOR VOC EMISSION AND SORPTION OF POROUS BUIDING MATERIAS C.-S. ee is Ph.D. Candidate, Departent of Building, Civil, and Environental Engineering; F. Haghighat is Professor, Departent of Building,
More informationCONTINUOUS THERMODYNAMICS FINITE DIFFUSION MODEL FOR MULTICOMPONENT FUEL SPRAY EVAPORATION
CONTINUOUS THERMODYNAMICS FINITE DIFFUSION MODEL FOR MULTICOMPONENT FUEL SPRAY EVAPORATION Dongyao Wang 1 and Chia-fon F. Lee Departent of Theoretical and Applied Mechanics 1 Departent of Mechanical and
More informationIII.H Zeroth Order Hydrodynamics
III.H Zeroth Order Hydrodynaics As a first approxiation, we shall assue that in local equilibriu, the density f 1 at each point in space can be represented as in eq.iii.56, i.e. f 0 1 p, q, t = n q, t
More informationMATHEMATICAL MODELING OF LARGE FOREST FIRE INITIATION
. INTODUCTION MATHEMATICAL MODELING OF LAGE FOEST FIE INITIATION Valeri A.Perinov * Belovo Branch of Keerovo State University Belovo Keerovo region ussia A large technogeneous or space catastrophe as a
More informationMODIFIED SERIES RESISTANCE MODEL - DETERMINATION OF MEAN CONCENTRATION BY INTEGRAL TRANSFORMATION
MODIFIED SERIES RESISTANCE MODEL - DETERMINATION OF MEAN CONCENTRATION BY INTEGRAL TRANSFORMATION A. L. Venezuela a, R. F. Cantão a, R. S. Ongaratto b, and R. N. Haneda c a Universidade Federal de São
More information1 Analysis of heat transfer in a single-phase transformer
Assignent -7 Analysis of heat transr in a single-phase transforer The goal of the first assignent is to study the ipleentation of equivalent circuit ethod (ECM) and finite eleent ethod (FEM) for an electroagnetic
More informationInternational Journal of Basic & Applied Sciences IJBAS-IJENS Vol:15 No:01 11
International Journal of Basic & Applied Sciences IJBAS-IJENS Vol:5 No: An Analytical Solution for MD Micro Polar Fluid Transport Phenoena over a Stretching Pereable Sheet A. Majidian a, M. Parvizi Oran
More information