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In this work, an analytical study of the effects of Hall current and Joule heating on the entropy generation rate of couple stress fluid is performed. It is assumed that the applied pressure gradient induces fluid motion. At constant velocity, hot fluid is injected at the lower wall and sucked off at the upper wall. The obtained equations governing the flow are transformed to dimensionless form and the resulting nonlinear coupled boundary value problems for velocity and temperature profiles are solved by Adomian decomposition method. Analytical expressions for fluid velocity and temperature are used to obtain the entropy generation and the irreversibility ratio. The effects of Hall current, Joule heating, suction/injection and magnetic field parameters are presented and discussed through graphs. It is found that Hall current enhances both primary and secondary velocities and entropy generation. It is also interesting that Joule heating raises fluid temperature and encourages entropy production. On the other hand Hartman number inhibited fluid motion while increase in suction/injection parameter resulted into a shift in flow symmetry.

In this work, an analytical study of the effects of Hall current and Joule heating on the entropy generation rate of couple stress fluid is performed. It is assumed that the applied pressure gradient induces fluid motion. At constant velocity, hot fluid is injected at the lower wall and sucked off at the upper wall. The obtained equations governing the flow are transformed to dimensionless form and the resulting nonlinear coupled boundary value problems for velocity and temperature profiles are solved by Adomian decomposition method. Analytical expressions for fluid velocity and temperature are used to obtain the entropy generation and the irreversibility ratio. The effects of Hall current, Joule heating, suction/injection and magnetic field parameters are presented and discussed through graphs. It is found that Hall current enhances both primary and secondary velocities and entropy generation. It is also interesting that Joule heating raises fluid temperature and encourages entropy production. On the other hand Hartman number inhibited fluid motion while increase in suction/injection parameter resulted into a shift in flow symmetry.

Exact analysis of miscible dispersion of solute with interphase mass transfer in a poorly conducting couple stress fluid flowing through a rectangular channel bounded by porous layers is considered because of its application in many practical situations. The generalized dispersion model of Sankarasubramanian and Gill is used, which brings into focus the exchange coefficient, the convective coefficient and the dispersion coefficient. The exchange coefficient comes into picture due to the interphase mass transfer and independent of solvent fluid viscosity. It is observed that the convective coefficient increases with an increase in the porous parameter while it decreases with an increase in the couple stress parameter. The dispersion coefficient is plotted against wall reaction parameter for different values of porous parameter and couple stress parameter. It is noted that the dispersion coefficient decreases with an increase in the value of couple stress parameter but increases with porous parameter.

This communication reports the peristaltic transport of a fluid in a uniform channel having compliant wall in porous medium. Taking into account the equations of the deformable boundaries and the fluid, the problem is inspected under low Reynolds number and long wave length approximation. Obtaining solution for the velocity, the behaviour of various parameters including the Saffman slip parameter (β), couple stress fluid parameter (α), elastic parameters (E 1 , E 2 , E 3 ) are examined through the graphical results for time average velocity. In case of non zero elasticity parameters, we observe that the time average velocity increases as the slip parameter as well as the Darcy number.

In this note, traveling wave solutions for (3 + 1) dimensional fluid models of incompressible flow are considered. The governing partial differential equations of two models are reduced to ordinary differential equation by employing wave parameter and exact solutions are obtained. It is shown that these fluid models allow 3 + 1 dimensional solutions amongst each other. The methodology used in this work is independent of symmetric consideration and other restrictive assumption. Finally, a set of example of boundary condition is discussed for the couple stress fluid. It is observed that velocity profile strongly depends upon couple stress parameter.

This paper describes the effects of induced magnetic field and partial slip on the peristaltic flow of a couple stress fluids in an asymmetric channel. The two dimensional equation of couple stress fluid are simplified by making the assumptions of long wave length and low Reynolds number. The exact solutions of reduced momentum equation and magnetic force function have been computed in wave frame. The expressions for stream function, magnetic force function and pressure rise per wave length have been also computed. Finally, the pressure rise, pressure gradient, velocity, magnetic force function and stream lines for different physical parameters of interest are plotted.

The Couette&ndash, Poiseuille flow of couple stress fluid with magnetic field between two parallel plates was investigated. The flow was driven due to axial pressure gradient and uniform motion of the upper plate. The influence of heating at the wall in the presence of spherical and homogeneous Hafnium particles was taken into account. The temperature dependent viscosity model, namely, Reynolds&rsquo, model was utilized. The Runge&ndash, Kutta scheme with shooting was used to tackle a non-linear system of equations. It was observed that the velocity decreased by increasing the values of the Hartman number, as heating of the wall reduced the effects of viscous forces, therefore, resistance of magnetic force reduced the velocity of fluid. However, due to shear thinning effects, the velocity was increased by increasing the values of the viscosity parameter, and as a result the temperature profile also declined. The suspension of inertial particles in an incompressible turbulent flow with Newtonian and non-Newtonian base fluids can be used to analyze the biphase flows through diverse geometries that could possibly be future perspectives of proposed model.

The present study is about the pressure-driven heated bi-phase flow in two slippery walls. The non-Newtonian couple stress fluid is suspended with spherically homogenous metallic particles. The magnetic susceptibility of Hafnium allures is taken into account. The rough surface of the wall is tackled by lubrication effects. The nonlinear coupled partial differential equations along with the associated boundary conditions are first reduced into a set of ordinary differential equations by using appropriate transformations and then numerical results were obtained by engaging the blend of Runge&ndash, Kutta and shooting techniques. The sway of physical quantities are examined graphically. An excellent agreement within graphical illustration and numerical results is achieved.

The purpose of this paper is to study the non-isothermal Poiseuille flow between two heated parallel inclined plates using incompressible couple stress fluids. Reynold’s model is used for temperature dependent viscosity. We have developed highly non-linear coupled ordinary differential equations from momentum and energy equations. The Perturbation technique is used to obtain the approximate analytical expressions for velocity and temperature distributions. Expressions for velocity field, temperature distribution, dynamic pressure, volume flow rate, average velocity and shear stress on the plates are obtained. The influence of various emerging parameters on the flow problem is discussed and presented graphically.

This paper presents the theoretical study of porous inclined stepped composite bearings with couple stress fluids. The generalized Reynolds type equation is derived for porous inclined stepped composite bearings with couple stress fluids. The closed form expressions are obtained for the fluid film pressure, load carrying capacity, frictional force and coefficient of friction. These expressions can be utilized to obtain the performance characteristic of four different types of bearing systems viz; porous plane slider, porous composite tapered land bearing, porous composite tapered concave bearing. It is observed that the effect of couple stress fluid lubricant provide an enhanced load carrying capacity and reduced coefficient of friction as compared to the corresponding Newtonian case for the bearings under consideration. Further, it is found that porous inclined stepped composite bearing has the largest load carrying capacity and lowest coefficient of friction as compared to other bearing geometries under consideration.

The Soret and Dufour effects in the presence of chemical reaction on natural convection heat and mass transfer of a couple stress fluid in a vertical channel formed by two vertical parallel plates is presented. The governing non-linear partial differential equations are transformed into a system of ordinary differential equations using similarity transformations. The resulting equations are then solved using Homotopy Analysis Method (HAM). Profiles of dimensionless velocity, temperature and concentration are shown graphically for various values of Dufour number, Soret number, Couple stress parameter and chemical reaction parameter.

This paper presents the Hall and Ion-slip effects on electrically conducting couple stress fluid flow between two circular cylinders in the presence of a temperature dependent heat source. The governing non-linear partial differential equations are transformed into a system of ordinary differential equations using similarity transformations and then solved using homotopy analysis method (HAM). The effects of the magnetic parameter, Hall parameter, Ion-slip parameter and couple stress fluid parameter on velocity and temperature are discussed and shown graphically.

Stokes’ first and second problems for an incompressible couple stress fluid are considered under isothermal conditions. The problems are solved through the use of Laplace transform technique. Inversion of the Laplace transform of the velocity component in each case is carried out using a standard numerical approach. Velocity profiles are plotted and studied for different times and different values of couple stress Reynolds number. The results are presented through graphs in each case.

In this paper, we investigate the generalized Stokes’ problems for an incompressible couple stress fluid. Analytical solution of the governing equations is obtained in Laplace transform domain for each problem. A standard numerical inversion technique is used to invert the Laplace transform of the velocity in each case. The effect of various material parameters on velocity is discussed and the results are presented through graphs. It is observed that, the results are in tune with the observation of V.K.Stokes in connection with the variation of velocity in the flow between two parallel plates when the top one is moving with constant velocity and the bottom one is at rest., {"references":["V.K. Stokes, Couple stresses in fluids, 9(9) (1966), pp.1710-1715.","V.K. Stokes, Theory of fluids with microstructure-An introduction, Springer Verlag, (1984).","N.B. Naduvinamani, P.S. Hiremath, G. Gurubasavaraj, Squeeze film lubrication of a short porous journal bearing with Couple stress fluids, Tribology International, 34(11) (2001), pp. 739-747.","N.B. Naduvinamani, P.S. Hiremath, G. Gurubasavaraj, Surface roughness effects in a short porous journal bearing with a Couple stress fluid, Fluid Dynamics Research, 31(5-6) (2002), pp. 333-354.","N.B. Naduvinamani, P.S. Hiremath, G. Gurubasavaraj, Effects of surface roughness on the Couple stress squeeze film between a sphere and a flat Plate, Tribology International, 38(5) (2005), pp. 451-458.","N.B. Naduvinamani, Syeda Tasneem Fathima, P.S. Hiremath, Hydrodynamic lubrication of rough slider bearings with Couple stress fluids, Tribology International, 36(12) (2003), pp. 949-959.","N.B. Naduvinamani, Syeda Tasneem Fathima, P.S. Hiremath, Effect of surface roughness on characteristics of couplestress squeeze film between anisotropic porous rectangular plates, Fluid Dynamics Research, 32(5) (2003), pp. 217-231.","Jaw-Ren Lin, Chi-Ren Hung, Combined effects of non-Newtonian couple stresses and fluid inertia on the squeeze film characteristics between a long cylinder and an infinite plate, Fluid Dynamics Research, 39(8) (2007), pp. 616-639.","H. Schlichting, K. Gersten, Boundary Layer Theory, Springer, (2002).\n[10] P.R. Gupta, K.L. Arora, Hydromagnetic flow between two parallel planes, one is oscillating and the other fixed, Pure. Appl. Geophy., 112(2) (1974), pp.498-505.\n[11] I.A. Hassanien, M.A. Mansour, Unsteady magnetohydrodynamic flow through a porous medium between two infinite parallel plates, Astrophy. Spac. Scie., 163(2) (1990), pp.241-246.\n[12] I.A. Hassanien, Unsteady hydromagnetic flow through a porous medium between two infinite parallel porous plates with time varying suction, Astrophy. Spac. Scie., 175(1) (1991), pp.135-147.\n[13] T. Hayat, S. Asghar, A.M. Siddiqui, Some unsteady unidirectional flows of a non-Newtonian fluid, Int. J. Engg. Sci., 38(3) (2000), pp 337-346.\n[14] M.E. Erdogan, On the unsteady unidirectional flows generated by impulsive motion of a boundary or sudden application of a pressure gradient, Int. J. Non-Linear Mech., 37(6) (2002), pp.1091-1106.\n[15] T. Hayat, Masood Khan, A.M. Siddiqui, S. Asghar, Transient flows of a second grade fluid\", Int. J. Non-Linear Mech., 39(10) (2004), pp.1621-1633.\n[16] M.E. Erdogan, C.E. Imrak, On unsteady unidirectional flows of a second grade fluid, Int. J. Non-Linear Mech., 40(10) (2005), pp.1238-1251.\n[17] M.E. Erdogan, C.E. Imrak, On some unsteady flows of a non-Newtonian fluid, Appl. Math. Model., 31(2) (2007), pp.170-180.\n[18] C. Fetecau, C. Fetecau, Starting solutions for some unsteady unidirectional flows of second grade fluid, Int. J. Engg. Sci., 43(10) (2005), pp.781-789.\n[19] G. Honig, U. Hirdes, A method for the numerical inversion of Laplace Transforms, J. Comp. Appl. Math., 10(1) (1984)., pp.113-132.\n[20] M. Devakar, T.K.V. Iyengar, Stokes' problems for an incompressible couple stress fluid\". Non-Linear Anal. Mode. Contr., 13(2) (2008), pp.181-190."]}

Steady incompressible couple stress fluid flow through two dimensional symmetric channel with stenosis is investigated. The flow consisting of a core region to be a couple stress fluid and a peripheral layer of plasma (Newtonian fluid). Assuming the stenosis to be mild, the equations governing the flow of the proposed model are solved using the slip boundary condition and closed form expressions for the flow characteristics (the dimensionless resistance to flow and wall shear stress at the maximum height of stenosis) are derived. The effects of various parameters on these flow variables have been studied. It is observed that the resistance to flow as well as the wall shear stress increase with the height of stenosis, viscosity ratio and Darcy number. However, the trend is reversed as the slip and the couple stress parameter increase., {"references":["","D. F. Young, Effects of a time-dependent stenosis on flow through a tube, J. Engrg. Ind.Trans.ASME.,vol.90, pp. 248-254, 1968.","G.R.Zendehbudi and M.S.Moayeri, Comparison of physiological and simple plusatile flows through stenosed arteries, J. Biomech., vol.32, pp. 959-965,1999.","G. Radhakrishnamacharya and P. Srinivasa Rao, Flow of a magnetic fluid through a non-uniform wavy tube, Proc.Nat.Acad.Sci.India, vol.76 , pp. 241-245, 2007.","R.L.Whitmore, Rheology of the Circulation, Pergamon Press, New York ,1968.","J.H. Forrester and D.F. Young, Flow through a converging-diverging tube and its implications in occlusive vascular disease, J. Biomech., vol.3, pp. 307-316, 1970.","J. B. Shukla, R. S. Parihar and B. R. P. Rao, Effects of stenosis on non-Newtonian flow of the blood in an artery,Bull. Math. Biol., vol.42, pp. 283-294, 1980.","J.C.Misra and S.K. Ghosh S K, A mathematical model for the study of blood flow through a channel with permeable walls, Acta Mechanica, vol.12, pp. 137-153, 1997.","N.Jain , S.P.Singh and M. Gupta, Steady flow of blood through an atherosclerotic artery: A non-Newtonian model, International Journal of Applied Mathematics and Mechanics,vol.8, pp. 52-63, 2012.","S. Gupta, M. Gupta and S.P. Singh SP, Effect of radial viscosity variation on non-Newtonian flow of blood in a stenosed artery.International Journal of Applied Mathematics and Mechanics, vol.8, pp. 51-61, 2012.\n[10] V. K. Stokes, Couple Stresses in Fluids, Phys. Fluids., vol.9, pp. 1709-1715,1966.\n[11] S.C.Cowin, The theory of polar fluids, Advances in Applied Mechanics, Academic Press, New York, pp. 279-347, 1974.\n[12] G. C. Sankad and G. Radhakrishnamacharya, Effect of Magnetic field on the peristaltic transport of couple stress fluid in a channel with wall properties, Int. J. Biomath., vol.4, pp. 365-378,2011.\n[13] D. Srinivasacharya and D. Srikanth, Effect of couple stresses on the pulsatile flow through a constricted annulus,Comptus Rendus Mecanique., vol.336, pp. 820-827,2008.\n[14] R.K. Naeem, S.Younus and Dania, Inverse solutions for unsteady incompressible couple stress fluid flows, International Journal of Applied Mathematics and Mechanics, vol.6, pp.1-17, 2010.\n[15] G. Bugliarello and J.W. Hyden, Detailed characteristics of the flow of blood in vitro, Trans.Soc.Rheol., vol.7, pp. 209-230, 1963.\n[16] G.Bugliarello and J.Sevilla, Velocity distribution and other characteristics of steady and pulsatile blood flow in fine glass tubes, Biorheology, vol.7, pp. 85-107,1970.\n[17] J.B.Shukla, R.S.Parihar and B.R.P.Rao BRP, Effect of peripheral layer viscosity on blood flow through the artery with mild stenosis, Bull.Math.Biol., vol.42, pp. 797-805, 1980.\n[18] J.B. Shukla, R.S. Parihar and B.R.P.Rao, Biorheological aspects of blood flow through artery with mild stenosis: Effect of peripherial layer, Biorheology, vol.17, pp. 403-410, 1980.\n[19] P.Chaturani and P.N. Kaloni, Two-layered poiseuille flow model for blood flow through arteries of small diameter and arterioles, Biorheology, vol.13, pp. 243-250, 1976.\n[20] P. Chaturani and R.Ponalagusamy, A two-layered model for blood flow through stenosed arteries, Proc. Of 11th National Conf. on fluid mechanics and fluid power,B.H.E.L.(R and D),Hydrabad, India, pp. 6-22, 1982.\n[21] R.Ponalagusamy and R.Tamil Selvi, A study on two layered model (Casson-Newtonian) for blood through an arterial stenosis: Axially variable slip velocity at the wall, J.Franklin Inst., vol.348, pp. 2308-2321, 2011.\n[22] H. Alemayehu and G. Radhakrishnamacharya, Dispersion of solute in peristaltic motion of couple stress fluid in the presence of magnetic field, Int. J of Engineering and Appl. Sciences., vol.7, pp. 156-160, 2011.\n[23] B. S. Bhatt and N. C. Sacheti, On the analogy in slip flows, Indian Journal of Pure and Applied Mathematics., vol.10, pp. 303-306, 1979.\n[24] K. Maruthi Prasad and G.Radhakrishnamacharya, Flow of Herschel-Bulkley fluid through an inclined tube of non-uniform cross-section with multiple stenosis, Arch. Mech., vol.60, pp. 161-172, 2008."]}

The paper deals with the pulsating flow of an incompressible couple stress fluid between permeable beds. The couple stress fluid is injected into the channel from the lower permeable bed with a certain velocity and is sucked into the upper permeable bed with the same velocity. The flow between the permeable beds is assumed to be governed by couple stress fluid flow equations of V. K. Stokes and that in the permeable regions by Darcy-s law. The equations are solved analytically and the expressions for velocity and volume flux are obtained. The effects of the material parameters are studied numerically and the results are presented through graphs., {"references":["D.N.Ku, D.P.Giddens, C.K. Zairns, S. Glagov, Pulsatile flow and\natherosclerosis in human carotid bifurcation: positive correlation between\nplaque location and low and oscillating shear stress, Arteriosclerosis 5\n(1985) 293-302.","R.M.Nerem, M.J.Levesque, Hemodynamics and the arterial wall, Vasc.\nDisc. (1987) 295-317.","F.Fedele, D.Hitt, R.D.Prabhu, Revisiting the stability of pulsatile pipe\nflow, European J. of Mech. ÔÇö B/Fluids 24 (2005) 237-254.","Y.C. Wang, Pulsatile flow in a porous channel, J. Appl. Mech. 38 (1971)\n553-555.","K. Vajravelu, K. Ramesh, S. Sreenadh, P.V. Arunachalam, Pulsatile flow\nbetween permeable beds, Int. J. Non-Linear Mech. 38 (2003) 999-1005","G.S. Beavers, D.D.Joseph : Boundary conditions at a naturally permeable\nwall. J. Fluid Mech., Vol 30, (1967) 197-207.","V.K.Stokes, Couple Stresses in Fluids, Phys. Fluids., Vol 9,(1966) 1709-\n1715.","V.K.Stokes, Theories of Fluids with Microstructure, Springer-Verlag,\nBerlin 1984.","S.K.Lakshmana Rao and T.K.V.Iyengar, Analytical and computational\nstudies in couple stress fluid flows, U.G.C. Research project C-8-4/82\nSR III, (1985)\n[10] L.M.Srivastava,Flow of couple stresss fluid through stenotic blood\nvessels, J.Bio Mech., Vol 18, 479-485 (1985)\n[11] L.M.Srivastava, Perstaltic transport of a couple stresss fluid, Rheo.Acta,\nVol 25, 638-641 (1986).\n[12] N.B.Naduvinamani, P.S.Hiremath and G.Gurubasavaraj : Squeeze film\nlubrication of a short porous journal bearing with couple stress fluids,\nTribo.Inter.,Vol 34, 739-747 (2001).\n[13] N.B.Naduvinamani, P.S.Hiremath and G.Gurubasavaraj : Surface roughness\neffects in a short porous journal bearing with couple stress fluid,\nFluid Dyn. Res.,Vol 31, 333-354 (2002).\n[14] N.B.Naduvinamani,Syeda Taseem Fathima and P.S.Hiremath: Effects of\nsurface roughness on characteristics of couple stress squeeze film between\nanisotropic porous rectangular plates, Fluid Dyn. Res., Vol 32, 217-231\n(2003).\n[15] M.Devakar and T.K.V.Iyengar, Stoke-s problems for an incompressible\ncouple stress fluid, Nonlinear Analysis: Modeling and Control, Vol 1,\n181-190 (2008).\n[16] M.Devakar and T.K.V.Iyengar, Runup flow a couple stress fluid between\nparallel plates , Nonlinear Analysis: Modeling and Control, Vol 15, 29-37\n(2010).\n[17] T.S.L.Radhika and T.K.V.Iyengar, Stokes flow of an incompressible couple\nstress fluid past a porous spherical shell, Proceedings of International\nMulti conference of Engineers and Computer Scientists, Vol 3, 1634-1639\n(2010)"]}

The paper presents an analytical solution for dispersion of a solute in the peristaltic motion of a couple stress fluid through a porous medium with slip condition in the presence of both homogeneous and heterogeneous chemical reactions. The average effective dispersion coefficient has been found using Taylor-s limiting condition and long wavelength approximation. The effects of various relevant parameters on the average coefficient of dispersion have been studied. The average effective dispersion coefficient tends to increase with permeability parameter but tends to decrease with homogeneous chemical reaction rate parameter, couple stress parameter, slip parameter and heterogeneous reaction rate parameter., {"references":["G. I. Taylor, Dispersion of soluble matter in solvent flowing slowly\nthrough a tube, Proc. Roy. Soc. Lond., vol.A 219, pp.186-203, 1953.","G. I. Taylor, The dispersion of matter in turbulent flow through a pipe,\nProc. Roy. Soc. Lond., vol.A 223, pp.446-468, 1954a.","G. I. Taylor, Conditions under which dispersion of a solute in a stream\nof solvent can be used to measure molecular diffusion, Proc. Roy. Soc.\nLond., vol.A 225, pp. 473-477, 1954b.","R. Aris, On the dispersion of a solute in a fluid flowing through a tube,\nProc. Roy. Soc. Lond., vol.A 235, pp.67-77, 1956.","D. Padma and V. V. Ramana Rao, Effect of Homogeneous and heterogeneous\nreaction on the dispersion of a solute in laminar flow between two\nparallel porous plates, Indian Journal of Technology, vol.14, pp.410-412,\n1976.","P. S. Gupta and A. S. Gupta, Effect of homogeneous and heterogeneous\nreactions on the dispersion of a solute in the laminar flow between two\nplates, Proc. Roy. Soc. Lond., vol.A 330, pp.59-63, 1972.","V. V. Ramana Rao and D. Padma, Homogeneous and heterogeneous\nreaction on the dispersion of a solute in MHD Couette flow, Curr. Sci.,\nvol.44, pp.803-804, 1975.","V. V. Ramana Rao and D. Padma, Homogeneous and heterogeneous\nreaction on the dispersion of a solute in MHD Couette flow II, Curr.\nSci., vol.46, pp.42-43, 1977.","B. K. N. Dutta, N. C. Roy and A. S. Gupta, Dispersion of a solute in a\nnon-Newtonian fluid with simultaneous chemical reaction, Mathematica-\nMechanica fasc., vol.2, pp.78-82, 1974.\n[10] V. M. Soundalgekar and P. Chaturani, Effects of couple-stresses on the\ndispersion of a soluble matter in a pipe flow of blood, Rheologica Acta,\nvol.19, pp.710-715, 1980.\n[11] J. B. Shukla, R. S. Parihar and B. R. P. Rao, Dispersion in non-\nNewtonian fluids: Effects of chemical reaction, Rheologica Acta, vol.18,\npp.740-748, 1979.\n[12] Dulal Pal, Effect of chemical reaction on the dispersion of a solute in\na porous medium, Applied Mathematical Modeling, vol.23, pp.557-566,\n1999.\n[13] K. N. Mehta, and M. C. Tiwari, Dispersion in presence of slip and\nchemical reactions in porous wall tube flow, Def. Sci. J., vol.38, pp.1-11,\n1988.\n[14] J. C. Misra and S. K. Ghosh, A mathematical model for the study of\nblood flow through a channel with permeable walls, Acta Mechanica,\nvol.122, pp.137-153, 1997.\n[15] Y. C. Fung, and C. S. Yih, Peristaltic transport, J. Appl. Mech. Trans.\nASME, vol.5, pp.669-675, 1968.\n[16] A. H. Shapiro, M. Y. Jaffrin and S. L.Weinberg, Peristaltic pumping with\nwith long wavelengths at low Reynold number, J. Fluid Mech., vol.37,\npp.799-825, 1969.\n[17] J. C. Misra and S. K. Pandey, Peristaltic transport in a tapered tube,\nMathl. Comput. Modelling, vol.22, pp.137-151, 1995.\n[18] G. Radhakrishnamacharya, Long wavelength approximation to peristaltic\nmotion of a power law fluid, Rheologica Acta, vol.21, pp.30-35,\n1982.\n[19] J. C. Misra and S. K. Pandey, Peristaltic flow of a multilayered powerlaw\nfluid through a cylindrical tube, International Journal of Engineering\nScience, vol.39, pp.387-402, 2001.\n[20] A. Ramachandra Rao and Manoranjan Mishra, Peristaltic transport of\na power-law fluid in a porous tube, Journal of Non-Newtonian Fluid\nMechanics, vol.121, pp.163-174, 2004.\n[21] V.K. Stokes, Couple Stress Fluid, Physics in Fluids, vol.9, pp.1709-1715.\n1966.\n[22] S. Islam and C. Y. Zhou, Exact solutions for two dimensional flows of\ncouple stress fluids, Z. angew. Math. Phys., vol.58, pp.1035-1048, 2007.\n[23] L. M. Srivastava, Peristaltic transport of a couple-stress fluid, Rheologica\nActa, vol.25, pp.638-641, 1986.\n[24] Kh.S. Mekheimer and Y. Abd elmaboud, Peristaltic flow of a couple\nstress fluid in an annulus: Application of an endoscope, Physica A.,\nvol.387, pp.2403-2415, 2008.\n[25] Ayman Mahmoud Sobh, Interaction of Couple Stresses and Slip Flow\non Peristaltic Transport in Uniform and Nonuniform Channels, Turkish\nJ. Eng. Env. Sci., vol.32, pp.117-123, 2008.\n[26] R. M. Terrill, A note on laminar flow in a porous tube, IMA Journal of\nApplied mathematics, vol.33, pp.169-174, 1984.\n[27] W. Kwang-Hua Chua and J. Fang, Peristaltic transport in a slip flow,\nEur. Phys. J. B, vol.16, pp.543-547, 2000.\n[28] B. S. Bhatt and N. C. Sacheti, On the analogy in slip flows, Indian\nJournal of Pure and Applied Mathematics, vol.10, pp.303-306, 1979.\n[29] K. Suga, Y. Matsumura, Y. Ashitaka, S. Tominaga and M. Kaneda,\nEffects of wall permeability on turbulence, Int. J. Heat Fluid Flow,\ndoi:10.1016/ j.ijheatfluidflow.2010.02.023, 2010.\n[30] Suvadip Paul, Axial dispersion in pressure perturbed fow through an\nannular pipe oscillating around its axis, Z. angew. Math. Phys., vol.60,\n899-920, 2009."]}

An analytical solution for dispersion of a solute in the peristaltic motion of a couple stress fluid in the presence of magnetic field with both homogeneous and heterogeneous chemical reactions is presented. The average effective dispersion coefficient has been found using Taylor-s limiting condition and long wavelength approximation. The effects of various relevant parameters on the average effective coefficient of dispersion have been studied. The average effective dispersion coefficient tends to decrease with magnetic field parameter, homogeneous chemical reaction rate parameter and amplitude ratio but tends to increase with heterogeneous chemical reaction rate parameter., {"references":["G. I. Taylor, Dispersion of soluble matter in solvent flowing slowly\nthrough a tube, Proc. Roy. Soc. Lond., vol.A 219, pp.186-203, 1953.","G. I. Taylor, The dispersion of matter in turbulent flow through a pipe,\nProc. Roy. Soc. Lond., vol.A 223, pp.446-468, 1954a.","G. I. Taylor, Conditions under which dispersion of a solute in a stream\nof solvent can be used to measure molecular diffusion, Proc. Roy. Soc.\nLond., vol.A 225, pp. 473-477, 1954b.","R. Aris, On the dispersion of a solute in a fluid flowing through a tube,\nProc. Roy. Soc. Lond., vol.A 235, pp.67-77, 1956.","B. K. N. Dutta, N. C. Roy and A. S. Gupta, Dispersion of a solute in a\nnon-Newtonian fluid with simultaneous chemical reaction, Mathematica-\nMechanica fasc., vol.2, pp.78-82, 1974.","J. B. Shukla, R. S. Parihar and B. R. P. Rao, Dispersion in non-Newtonian\nfluids: Effects of chemical reaction, Rheologica Acta, vol.18, pp.740-748,\n1979.","P. Chandra and R. P. Agarwal, Dispersion in simple microfluid flows,\nInternational Journal of Engineering Science, vol.21, pp.431-442,1983.","D. Philip, and P. Chandra, Effects of heterogeneous and homogeneous\nreactions on the dispersion of a solute in simple microfluid, Indian J.\nPure Appl. Math., vol.24, pp.551-561, 1993.","V. M. Soundalgekar and P. Chaturani, Effects of couple-stresses on the\ndispersion of a soluble matter in a pipe flow of blood, Rheologica Acta,\nvol.19, pp.710-715, 1980.\n[10] P. S. Gupta and A. S. Gupta, Effect of homogeneous and heterogeneous\nreactions on the dispersion of a solute in the laminar flow between two\nplates, Proc. Roy. Soc. Lond., vol.A 330, pp.59-63, 1972.\n[11] V. V. Ramana Rao and D. Padma, Homogeneous and heterogeneous\nreaction on the dispersion of a solute in MHD Couette flow, Curr. Sci.,\nvol.44, pp.803-804, 1975.\n[12] V. V. Ramana Rao and D. Padma, Homogeneous and heterogeneous\nreaction on the dispersion of a solute in MHD Couette flow II, Curr. Sci.,\nvol.46, pp.42-43, 1977.\n[13] D. Padma and V. V. Ramana Rao, Effect of Homogeneous and heterogeneous\nreaction on the dispersion of a solute in laminar flow between two\nparallel porous plates, Indian Journal of Technology, vol.14, pp.410-412,\n1976.\n[14] A. H. Shapiro, M. Y. Jaffrin and S. 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This present investigation carried out the effects of Joule heating and Hall current on free convection flow of electrically conducting couple stress fluid in a vertical channel. The final system of ordinary differential equations is obtained from the governing non- linear partial differential equations by using the similarity transformations. Homotopy Analysis Method has been used to solve the non-linear system. The influence of the emerging parameters (Hall, magnetic, Joule heating and the couple stress parameters) on velocity and temperature profiles are presented through plots.

In this paper, we have studied the flow of incompressible fluids in a straight square duct through the porous medium. The couple stress fluid model and Jeffrey fluid model are considered separately to study the flow properties. The governing partial differential equations have been solved numerically using finite difference method in each case. In both the cases, the variation of different flow parameters on the fluid velocity is illustrated graphically and the numerical results for the volume flow rate have been presented through tables. It is observed that, the velocity and volume flow rate decrease with an increase in couple stress parameter and porosity parameter, while the velocity and volume flow rate increase with an increase in Jeffrey parameter and pressure gradient.

The unsteady three-dimensional flow of couple stress fluid over a stretched surface is investigated. Analysis has been performed in the presence of mass transfer and chemical reaction. Nonlinear flow analysis is computed by a homotopic approach. Plots are presented and analyzed for the various parameters of interest. A comparative study with existing solutions in a limiting sense is made.

The radiation and thermal diffusion effects on mixed convection flow of couple stress fluid through a channel are investigated. The governing non-linear partial differential equations are transformed into a system of ordinary differential equations using similarity transformations. The resulting equations are then solved using the Spectral Quasi-linearization Method (QLM). The results, which are discussed with the aid of the dimensionless parameters entering the problem, are seen to depend sensitively on the parameters.

In the present paper, the pulsatile flow of blood through a bifurcated artery with mild stenosis in parent artery is investigated by taking blood as couple stress fluid. The arteries pattern of bifurcation is treated to be symmetric about the axis of the parent artery and straight circular cylinders of limited length. The governing equations are made dimensionless and suitable coordinate transformation is used to convert the irregular boundary to a well designed boundary. The resulting system of equations is solved numerically using the finite difference method. The influence of physical parameters on the velocity, shear stress, flow rate and impedance near the apex is studied graphically. Further, the oscillatory nature of impedance, flow rate and shear stress against time near the apex in both parent and daughter arteries is presented. Keywords: Blood flow, Pulsatile flow, Couple stress fluid, Bifurcated artery, Impedance