Heat and Mass Transfer Effects of Peristaltic Transport of a Nano Fluid in Peripheral layer

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1 Available at Appl. Appl. Math. ISSN: Vol. 2, Issue 2 (December 207, pp Applications and Applied Mathematics: An International Journal (AAM Heat and Mass Transfer Effects of Peristaltic Transport of a Nano Fluid in Peripheral layer K. Maruthi Prasad, 2* N. Subadra and 3 M. A. S. Srinivas Department of Engineering Mathematics School of Technology GITAM University - Hyderabad Campus Hyderabad Telangana India kaipa_maruthi@yahoo.com *2 Department of Mathematics Geethanjali College of Engg. & Tech Cheeryal (V, Keesara (M, Medchal Dist. Telangana India nemani.subhadra@gmail.com 3 Department of Mathematics JNTUH, Kukatpally Hyderabad Telangana India massrinivas@gmail.com * Corresponding editor Abstract Received: August, 206; Accepted: October, 207 This paper deals with a theoretical investigation of heat and mass transfer effects of peristaltic transport of a nanofluid in peripheral layer. By using appropriate methods, the velocity in the core region as well as in the peripheral region, pressure drop, time averaged flux, frictional force, temperature profile, nanoparticle phenomenon, heat transfer coefficient and mass transfer coefficient of the fluid are investigated, using lubrication theory. Effects of different physical parameters like viscosity ratio, mean radius of the central layer, Brownian motion parameter, thermophoresis parameter, local temperature Grashof number as well as local nanoparticle Grashof number on pressure rise characteristics, frictional force, heat transfer coefficient, mass transfer coefficient, velocity profiles and streamline patterns of the fluid are studied. The computational results are presented in graphical form. Keywords: Peristalsis; Nano fluid; Homotopy perturbation method; Peripheral Layer; Heat transfer coefficient; Mass transfer coefficient MSC 200 No.: 92C0, 76Z05 968

2 AAM: Intern. J., Vol. 2, Issue 2 (December Introduction Peristaltic transport is an important mechanism used to describe a progressive wave of contraction along the tube whose cross sectional area consequently varies. Peristalsis is an inherent property of many tubular organs of the human body. The peristaltic transport is also exploited for industrial applications like transport of corrosive and noxious fluids, blood pumps in heart lung machine, sanitary fluid transport. In view of its importance, the study of peristaltic transport of Newtonian and non-newtonian fluids under different conditions have been investigated by several authors [Latham (966, Fung and Yih (968, Shapiro et al. (969, Devi & Devanathan (975, Meijing et al. (993, Prasad & Radhakrishnamacharya (2009, Pincombe et al. (999, Prasad et. al. (205, Santhosh et al. (205]. It is realized that the materials of nanometer dimensions have shown remarkable physical and chemical properties which paved the way for the immense contribution of Nanotechnology in the industry. Ethylene glycol, oil and water are the general base fluids used for the nanofluid phenomenon. The wider applications of nano fluids in heat transfer are Microelectronics, fuel cells, pharmaceutical processes, hybrid-powered engines, domestic refrigerator, chiller, nuclear reactor coolant, grinding and space technology, etc. They explore increased thermal conductivity, counterbalancing the convective heat transfer coefficient to the base fluid. Several researchers attention has been drawn by the wide-ranging thermal properties of nano fluids for new production of heat transfer fluids in automotive cooling significations, heat exchangers, and implants. Extensive literature is available on the study of nanofluid and its applications. Choi (995 was the pioneer of study of nano fluid technology. Peristaltic flow of nano fluid in a non-uniform tube was studied by Akbar (202. Mathematical model for the peristaltic flow of nano fluid through eccentric tubes comprising porous medium was investigated by Nadeem et al. (204. Nadeem et al. (204 studied effects of heat and mass transfer on peristaltic flow of a nano fluid between eccentric cylinders. Study of peristaltic transport of nanoparticles of micropolar fluid with heat and mass transfer effect in an inclined tube was investigated by Prasad et al. (205. Maruthi Prasad et al. (205 also studied Peristaltic transport of a nano fluid in an inclined tube. It is well known that in many physiological flows, the nature of the fluid at the core region of the tube is different compared to that near the wall. So several researches have done work on the effect of peripheral layer on peristaltic flow of fluids with particular reference to physiological systems. Effects of peripheral layer on peristaltic transport of a bio-fluid was studied by Shukla et al. (980. Srivastava and Srivastava (982 investigated peristaltic transport of a two-layered model of physiological fluid. Brasseur et al. (987 studied the influence of a peripheral layer of different viscosity on peristaltic pumping with Newtonian fluids. Rao and Usha (995 studied

3 970 N. Subadra et al. peristaltic transport of two immiscible viscous fluids in a circular tube. Prasad & Radhakrishnamacharya (2009 investigated the effect of peripheral layer on peristaltic transport of a couple-stress fluid. Effect of peripheral layer on peristaltic transport of a micropolar fluid was studied by Prasad and Radhakrishnamacharya (2009. However, the study of effect of peripheral layer on peristaltic transport of a nano fluid was not studied. Motivated by these studies, the study of effect of peripheral layer on peristaltic transport of a nano fluid, under the assumption of long wavelength and low Reynolds number has been done. To solve the resulting equations of the temperature profile and nanoparticle phenomena, Homotopy perturbation method has been used. The analytical solutions of velocity, pressure drop, frictional force and effect of heat and mass transfer are obtained. The effects of various parameters on these flow variables are investigated and graphically displayed. 2. Mathematical Formulation Consider the peristaltic transport of a nano fluid which is surrounded by Newtonian fluid in an axisymmetric tube of radius a, with core radius a. Choosing the polar coordinate system (R, θ, Z, the wall deformation due to propagation of an infinite train of peristaltic waves is given by R = H(Z, t = a + b sin 2π λ (Z ct, ( where, b is the amplitude, λ is the wave length, c is the speed of the wave. Following Prasad et al. (2009 the geometry of the interface between the peripheral layer and core region is R = H (Z, t = a + b sin 2π λ (Z ct, (2 where, a is the mean radius and b is the amplitude of the central layer. We use the transformation z = Z ct, r = R, θ = θ, w = W c, u = U. (3 From a stationary to moving frame of reference, the equations of motion in two regions are given as follows: (a Peripheral region (H (z r H(z: p = μ z p 2 w, (4 p r = 0, ` (5

4 AAM: Intern. J., Vol. 2, Issue 2 (December where, 2 = , w r 2 r r z 2 is the component velocity in z-direction, p is the pressure and μ p is the constant viscosity of Newtonian fluid in the peripheral region. (b Core Region(0 r H (z: The law of conservation of mass, momentum, energy and nanoparticle concentration for an incompressible nanofluid are described by Nadeem et al. (204 as (r u r r ρ [u u r ρ [u w r [u T r [u C r + w z = 0, (6 + w u ] = P + μ z r c [ 2 u + u + 2 u r 2 r r u z 2 r 2 ], (7 + w w ] = P + μ z z c [ 2 w + w + 2 w ] + ρgβ(t T r 2 r r z 2 o + ρgβ(c C, o (8 + w T ] = β [ 2 T + T + 2 T ] + τ {D z r 2 r r B [ C T z 2 r r + w C ] = D z B [ 2 C + C + 2 C r 2 r r z 2 ] + D T + C z T T [ 2 + T o r 2 r r T z ] + D T T o [( T r 2 + ( T 2 ]}, (9 z + 2 T ], (0 z 2 where u and w represent the radial and axial velocity components in the wave frame, μ c is the viscosity of the nano fluid in the core region, d represents the material time derivative, p is the dt pressure, C is the nanoparticle phenomena, τ = (ρc P is the ratio between the effective heat (ρc f capacity of the nanoparticle material and heat capacity of the fluid, D B is the Brownian diffusion coefficient and D T is the thermophoretic diffusion coefficient. The ambient values of T and C as r tend to h are denoted by T o andc o. We introduce the following non-dimensional quantities r = r a, z z = λ λu, w =, u = w c ac, w = w c, p = a2 p cλμ c, θ t = T T o T o, t = ct λ, δ = a λ, R e = 2ρca, σ = C C o, μ c C o β = K (ρc f, N b = (ρc PD B C o, N (ρc t = (ρc PD T T o f (ρc f β, N t = (ρc PD T T o (ρc f β, G r = gβa3 T o φ 2, B r = gβa3 C o φ 2, φ 2 = μ c ρ,

5 972 N. Subadra et al. in which N b, N t, G r and B r are the Brownian motion parameter, the Thermophoresis parameter, local temperature Grashof number and local nanoparticle Grashof number. Using the non-dimensional quantities and applying the long wavelength and low Reynolds number approximations, Equations (4 - (0 are converted to p z = r P r r (μ r r w, ( = 0, (2 u + u + w = 0, (3 r r z P = z r r 0 = r 0 = r (r w r + G rθ t + B r σ, (4 r (r θ t r + N b r (r σ r + N t σ r θ t r + N t ( θ t r 2, (5 ( (r θ t N b r r r, (6 where, μ = μ p μ c is the viscosity ratio. The non-dimensional boundary conditions are w = 0 at r = h = + ε sin 2πz, (7 w = 0, θ t = 0, σ = 0 at r = 0, (8 r r r θ t = 0, σ = 0 at r = h (z = δ + ε sin 2πz, (9 w = w at r = h (z, (20 μ w r = w r + r 2 (G rθ t + B r σ at r = h (z. (2 Following the analysis of Shukla et al. (980 it is taken that h = δh and ε = δε 3. Solution of the Problem Solving Equation (, using the boundary condition (7, the expression for w is w = r2 h 2 4μ dp + c log dz μ (r. (22 h

6 AAM: Intern. J., Vol. 2, Issue 2 (December By applying homotopy technique for Equations (5 and (6, the equations become H(ζ, θ t = ( ζ[l(θ t L(θ t 0 ] + ζ [L(θ t + N b σ H(ζ, σ = ( ζ[l(σ L(σ 0 ] + ζ [L(σ + N t where L = r Consider r (r r r ( (r θ t N b r r r is taken as linear operator for convenience. θ t r + N t ( θ t r 2 ], (23 ], (24 θ 0 (r, z = ( r2 h 2, σ 0 (r, z = ( r2 h 2, (25 4 as initial guesses which satisfy the boundary conditions. Define 4 θ t (r, z = θ t 0 + ζθ t + ζ2 θ t +, (26 2 σ(r, z = σ 0 + ζσ + ζ 2 σ 2 +. (27 Following the same procedure as done by Maruthi Prasad et al. (205 the solution for temperature profile and nanoparticle phenomena can be written for ζ = as θ t (r, z = ( r4 h 4 σ(r, z = ( r2 h 2 64 (N b N t, (28 4 N t N b. (29 Substituting the Equations (28 and (29 into Equation (4 and applying boundary conditions (8 - (2, the closed form solution for velocity in the core region is obtained as where and w = r2 dp G r (N 4 dz 64 b N t ( r6 c 4 = dp 2 dz (h h 2 4μ r2 4 h 36 + B 4 r ( N t ( r4 N b r2 2 h 6 h 2 4 G r 288 (N b N t h 6 + 3B r 64 (N t N b h 4 + c μ log (h h, 4 + c 4, (30

7 974 N. Subadra et al. c = G r (N b N t ( h 6 B 92 r ( N t ( h 4. N b 4 The dimensionless flux in the moving frame is given as q = h 0 2rwdr h + 2rw dr. (3 h Substituting Equations (22 and (30 into Equation (3, the flux is where q = dp S + G dz r(n b N t [ 5h 8 S = h 4 + h B r ( N t 8μ + h4 The pressure gradient dp dz [ h 6 N b h2 6 h + h 8 92μ 768μ + h2 4 h h μ + h2 2 h. 8μ 2μ 6μ log (h 768μ + log (h 6 h (h is obtained from Equation (32 and is ( h 8 h2 6 h ] h 92μ 388μ + h2 4 h 4μ 8μ ], (32 dp = q + G r (N b N t dz S S + B r S (N t N b [ h [ 5h 8 h2 6 h + h 8 92μ 768μ 6 + h2 4 h h μ 768μ + log (h 6μ log (h The pressure drop over the wavelength P λ is defined as ( h 8 h2 6 h ] h 92μ 388μ 6 h (h + h2 4 h 4μ 8μ ]. (33 P λ = dp 0 dz. dz (34 Substituting the expression dp dz where in Equation (34, the pressure drop is P λ = ql + L 2, (35 L = 0 dz, S L 2 = G r (N b N t ( 0 8 5h + h2 6 h h 8 92μ 768μ B r ( N t ( N b 0 768μ log (h S ( h 8 h h h2 h 4 6μ h 6 6μ log(h h (h 6 4μ +h2 h 4 8μ S h2 6 h 92μ 388μ dz (36 dz. (37

8 AAM: Intern. J., Vol. 2, Issue 2 (December Following the analysis of Shapiro et al. (969 the time averaged flux over a period in the laboratory frame Q is given as Q = q. (38 Substituting Equation (38 into Equation (35, the time averaged flux is Q = P λ L L 2 L. (39 The dimensionless frictional force F at the wall is 0 F = h 2 ( dp dz 3.. Heat Transfer Coefficient dz. (40 The heat transfer coefficient at the wall is given as Z θ (r, z = ( h z ( θ t r 3.2. Mass Transfer Coefficient. (4 The mass transfer coefficient at the wall is given as Z σ (r, z = ( h z ( σ r 4. Results and Discussion. (42 The effects of various parameters on pressure rise, time averaged flux, frictional force, heat transfer coefficient and mass transfer coefficient have been computed numerically and the results are presented graphically using Mathematica 9.0 software. 4.. Pressure Rise Characteristics Effects of various parameters like viscosity ratio (μ, mean radius of the central layer (δ, Brownian motion parameter (N b, thermophoresis parameter (N t, local temperature Grashof number (G r, local nanoparticle Grashof number (B r on pressure rise ( p λ are shown in Figures It is observed from Figures. -.6 that, pressure rise ( p λ decreases with the increase of time averaged flux (Q for fixed values of viscosity ratio (μ, mean radius of the central

9 976 N. Subadra et al. layer (δ, Brownian motion parameter (N b, thermophoresis parameter (N t, local temperature Grashof number (G r and local nanoparticle Grashof number (B r. It is observed from Figures.,.4,.5 and.6 that, pressure rise ( p λ increases with the increase of viscosity ratio (μ, thermophoresis parameter (N t, local temperature Grashof number (G r and with local nanoparticle Grashof number (B r. It is also observed that, when time averaged flux (Q reaches.0, pressure rise ( p λ converges. (From Figure. From Figures.2 and.3, it is noticed that the pressure rise ( p λ decreases with the increase of mean radius of the central layer (δ and with Brownian motion parameter (N b. Figure.: Effect of Q and μ on ( p λ ( ε = 0. 2, G r = 0. 5, B r = 0. 3, N b =. 3, δ = 0. 3, N t =. 8 Figure.2: Effect of Q and δ on ( p λ ( ε = 0. 5, G r = 0. 5, B r = 0. 3, N b =. 3, μ = 0. 5, N t =. 8 Figure.3: Effect of Q and N b on ( p λ ( ε = 0. 2, G r = 0. 5, B r = 0. 3, δ = 0. 8, μ = 0. 5, N t =. 8 Figure.4: Effect of Q and N t on ( p λ ( ε = 0. 2, G r = 0. 5, B r = 0. 3, δ = 0. 9, μ = 0. 2, N b =. 3

10 AAM: Intern. J., Vol. 2, Issue 2 (December Figure.5: Effect of Q and G r on ( p λ ( ε = 0. 5, N t = 7. 8, B r = 5. 3, δ = 0. 8, μ = 0. 05, N b = 7. 3 Figure.6: Effect of Q and B r on ( p λ ( ε = 0. 5, G r = 0. 5, N t =. 8, δ = 0. 8, μ = 0. 5, N b = Frictional Force Figures show the effect of various parameters on frictional force(f. It is observed from figures that, frictional force decreases with the increase of time averaged flux (Q for fixed values of viscosity ratio (μ, mean radius of the central layer (δ, Brownian motion parameter (N b, thermophoresis parameter (N t, local temperature Grashof number (G r and local nanoparticle Grashof number (B r. It can be seen from Figures 2., 2.4, 2.5 and 2.6 that frictional force (F increases with the increase of viscosity ratio (μ, thermophoresis parameter (N t, local temperature Grashof number (G r and with local nanoparticle Grashof number (B r. From Figures 2.2 and 2.3, it is observed that the frictional force (F decreases with the increase of mean radius of the central layer (δ and with Brownian motion parameter (N b. It is interesting to observe from Figure 2.2 that, when time averaged flux (Q reaches to.0, frictional force (F converges. Figure 2.: Effect of Q and μ onf ( ε = 0., G r = 0. 5, B r = 0. 3, N b =. 3, δ = 0. 3, N t =. 8 Figure 2.2: Effect of Q and δ onf ( ε = 0., G r = 0. 5, B r = 0. 3, N b =. 3, μ = 0. 4, N t =. 8

11 978 N. Subadra et al. Figure 2.3: Effect of Q and N b on F ( ε = 0. 6, G r = 0. 5, B r = 0. 3, δ = 0. 8, μ = 0. 2, N t =. 8 Figure 2.4: Effect of Q and N t onf ( ε = 0. 6, G r = 0. 5, B r = 0. 3, δ = 0. 8, μ = 0. 2, N b =. 3 Figure 2.5: Effect of Q and G r onf ( ε = 0. 5, N t =. 8, B r = 0. 3, δ = 0. 99, μ = 0. 05, N b =. 3 Figure 2.6: Effect of Q and B r onf ( ε = 0. 3, G r = 0. 5, N t =. 8, δ = 0. 8, μ = 0. 3, N b = Temperature Profile Effects of Brownian motion parameter (N b and thermophoresis parameter (N t on temperature profile (θ t have been shown in Figures It is noticed from Figure 3. that, with the increase of Brownian motion parameter (N b, temperature profile (θ t increases in the region r [, 0.8] and in the region r [0.8, ], but decreases in the region r [ 0.8, 0.8]. However, temperature profile (θ t shows an opposite behaviour with thermophoresis parameter (N t. Figure 3.: Variation in Temperature profile with N b (Z =. 5, ε = 0. 9, N t =. 8, δ = 0. 8 Figure 3.2: Variation in Temperature profile with N t (Z = 3, ε = 0. 9, N b = 0., δ = 0. 8

12 AAM: Intern. J., Vol. 2, Issue 2 (December Nanoparticle Phenomena The nature of nanoparticle phenomena (σ for different values of Brownian motion parameter (N b and thermophoresis parameter (N t can be observed from Figures It is observed that, nanoparticle phenomena (σ decreases with the increase of Brownian motion parameter (N b in the regions r [, 0.8], r [0.8, ] and increases in the region r [ 0.8, 0.8]. It is interesting to observe that nanoparticle phenomena (σ reaches maximum at r = 0. However, it shows an opposite behaviour with thermophoresis parameter (N t. Figure 4.: Variation in Nanoparticle Phenomenon with N b (Z =, ε = 0. 5, N t =. 8, δ = 0. 8 Figure 4.2: Variation in Nanoparticle Phenomenon with N t (Z =, ε = 0. 9, N b =. 8, δ = Heat Transfer Coefficient Figures explain the variation of heat transfer coefficient (Z θ for various values of Brownian motion parameter (N b, thermophoresis parameter (N t and amplitude ratio (ε. From Figures 5.2 and 5.3, it is observed that the value of the heat transfer coefficient (Z θ increases with thermophoresis parameter (N t and amplitude ratio (ε and then decreases after attaining a constant value. However, heat transfer coefficient (Z θ shows an opposite behaviour with respect to Brownian motion parameter (N b (from Figure 5.. It is interesting to observe that there is no significant change in the heat transfer coefficient (Z θ value in the region rε[ 0.2, 0.2]. Figure 5.: Variation in heat transfer coefficient with N b (Z = 4, ε = 0. 2, N t =. 2, δ = 0. 8 Figure 5.2: Variation in heat transfer coefficient with N t (Z = 3, ε = 0. 7, N b = 2. 2, δ = 0. 8

13 980 N. Subadra et al. Figure 5.3: Variation in heat transfer coefficient with ε (Z = 4. 2, N t = 0. 8, N b = 0. 2, δ = Mass Transfer Coefficient Figures indicate the effect of various parameters on mass transfer coefficient(z σ. It is noticed that mass transfer coefficient (Z σ decreases with the increase of Brownian motion parameter (N b, thermophoresis parameter(n t and then increases after attaining a constant value r = 0. However, mass transfer coefficient(z σ shows an opposite behaviour with respect to amplitude ratio(ε. It is interesting to observe that mass transfer coefficient (Z σ converges in the region rε[, 0] and diverges in the region rε[0, ]. Figure 6.: Variation in Mass transfer coefficient with N b (Z = 3. 2, ε = 0. 9, N t =. 2, δ = 0. 8 Figure 6.2: Variation in Mass transfer coefficient with N t (Z =. 5, ε = 0. 9, N b = 2. 8, δ = 0. 8 Figure 6.3: Variation in Mass transfer coefficient with ε (Z = 3, N t = 0. 8, N b = 0. 3, δ = 0. 8

14 AAM: Intern. J., Vol. 2, Issue 2 (December Velocity Profiles The variation in velocity profiles in the core region can be observed from Figures It is observed that velocity profiles increase in the radial direction for fixed values of velocity ratio (μ, thermophoresis parameter (N t, local temperature Grashof number (G r and local nanoparticle Grashof number (B r. It is also observed that velocity profiles decrease with the increase of velocity ratio (μ, mean radius of the central layer (δ, thermophoresis parameter (N t, local temperature Grashof number (G r and local nanoparticle Grashof number (B r. Figure 7.: Variation in velocity profile w with μ ( ε = 0. 5, G r = 0. 05, B r = 0. 03, N b = 0. 03, δ = 0. 0, N t = 0. 08, Q =. 5, z = 0. 5 Figure 7.2: Variation in velocity profile w with δ ( ε = 0. 9, G r = 0. 5, B r = 0. 3, N b = 0. 3, μ = 0. 9, N t = 0. 8, Q = 3, z = 2. 5 Figure 7.3: Variation in velocity profile w with N t ( ε = 0. 2, G r = 0. 5, B r = 0. 3, δ = 0. 5, μ = 0. 06, N b = 0. 3, Q = 2, z = 2 Figure 7.4: Variation in velocity profile w with G r ( ε = 0. 5, N t =. 8, B r =. 3, δ = 0. 8, μ = 0., N b = 0. 3, Q = 2, z = 3

15 982 N. Subadra et al. Figure 7.5: Variation in velocity profile w with B r ( ε = 0. 2, N t = 0. 8, G r = 0. 3, δ = 0. 5, μ = 0. 04, N b = 0. 3, Q = 2, z = Streamline Patterns The formulation of an internally circulating bolus of the fluid by closed streamline is called trapping. This trapped bolus is pulled ahead along with the peristaltic wave. Figures explain the streamline patterns and trapping for different values of viscosity ratio, mean radius of the central layer, Brownian motion parameter, thermophoresis parameter, local temperature Grashof number, local nanoparticle Grashof number and amplitude ratio. From Figures 8., 8.2, 8.3 and 8.7, it is noticed that the volume of trapped bolus decreases with the increase of viscosity ratio, mean radius of the central layer, Brownian motion parameter (N b and with amplitude ratio (ε. From Figures 8.4, 8.5 and 8.6, it is observed that, the volume of the trapped bolus increases with the increase of thermophoresis parameter (N t, local temperature Grashof number (G r and with the local nanoparticle Grashof number (B r. Figure 8.: Stream line patterns for different values of μ (ε = 0. 2, Q = 0. 7, G r = 5, B r = 3, N b = 7, N t = 3, δ = 0. 9

16 AAM: Intern. J., Vol. 2, Issue 2 (December Figure 8.2: Stream line patterns for different values of δ (ε = 0. 2, Q = 0. 7, G r = 5, B r = 3, N b = 7, N t = 3, μ = 0. 4 Figure 8.3: Stream line patterns for different values of N b (ε = 0. 2, Q = 0. 7, G r = 5, B r = 3, δ = 0. 9, N t = 3, μ = 0. 5 Figure 8.4: Stream line patterns for different values of N t (ε = 0. 2, Q = 0. 7, G r = 5, B r = 3, δ = 0. 9, N b = 7, μ = 0. 5

17 984 N. Subadra et al. Figure 8.5: Stream line patterns for different values of G r (ε = 0. 2, Q = 0. 7, N t = 3, B r = 3, δ = 0. 9, N b = 7, μ = 0. 5 Figure 8.6: Stream line patterns for different values of B r (ε = 0. 2, Q = 0. 7, N t = 3, G r = 5, δ = 0. 9, N b = 7, μ = 0. 5 Figure 8.7: Stream line patterns for different values of ε (B r = 5, Q = 0. 7, N t = 3, G r = 5, δ = 0. 9, N b = 7, μ = Conclusion The present study deals with heat and mass transfer effects of peristaltic transport of a nanofluid in peripheral layer under the approximations of low Reynold s number and long wave length. Emphasis has been laid on investigating pressure drop, frictional force, temperature profile in the

18 AAM: Intern. J., Vol. 2, Issue 2 (December core region as well as peripheral region, nanoparticle phenomenon, heat transfer coefficient, mass transfer coefficient, velocity profiles and streamline patterns for the nano fluid for the variables like viscosity ratio, mean radius of the central layer, Brownian motion parameter, thermophoresis parameter, local temperature Grashof number and local nanoparticle Grashof number. Homotopy perturbation method has been used to solve the nonlinear coupled equations of temperature profile and nanoparticle phenomena. The main points of the analysis are as follows: a. The pressure rise increases with the increase of viscosity ratio, thermophoresis parameter, local temperature Grashof number, local nanoparticle Grashof number and decreases with the increase of mean radius of the central layer and Brownian motion parameter. b. The frictional force increases with the increase of viscosity ratio, thermophoresis parameter, local temperature Grashof number, local nanoparticle Grashof number and decreases with the increase of mean radius of the central layer and Brownian motion parameter. c. With the increase of Brownian motion parameter, temperature profile increases in the region r [, 0.8] and in the region r [0.8, ], but decreases in the region r [ 0.8, 0.8]. However, temperature profile shows opposite behaviour with thermophoresis parameter. d. Nanoparticle phenomenon decreases with the increase of Brownian motion parameter in the regions r [, 0.8], r [0.8, ] and increases in the region r [ 0.8, 0.8]. Nanoparticle phenomena reach maximum at r = 0. However, it shows an opposite behaviour with thermophoresis parameter. e. Heat transfer coefficient increases with the increase of thermophoresis parameter and amplitude ratio; and shows an opposite behaviour with the increase of Brownian motion parameter. f. Mass transfer coefficient converges in the region rε[, 0] and diverges in the region rε[0, ] with the increase of Brownian motion parameter and thermophoresis parameter and amplitude ratio. g. Velocity profiles in the core region increase in the radial direction for fixed values of velocity ratio, thermophoresis parameter, local temperature Grashof number and local nanoparticle Grashof number. h. Velocity profiles decrease with the increase of velocity ratio, mean radius of the central layer, thermophoresis parameter, local temperature Grashof number and local nanoparticle Grashof number. i. The volume of the trapped bolus increases with the increase of thermophoresis parameter, local temperature Grashof number, local nanoparticle Grashof number and decreases with

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