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This work explores the heat transfer flow characteristics of an incompressible non-Newtonian Jeffrey fluid over a stretching/shrinking surface with thermal radiation and heat source. The sheet is linearly stretched in the presence of a transverse magnetic field with convective boundary conditions. Appropriate similarity variables are used to transform the basic governing equations (PDEs) into ODEs. The resulting equations are solved by utilizing MATLAB bvp4c. The impact of distinctive physical parameters and dimensionless numbers on the flow field and heat transfer is analysed graphically. It is noticed that the measure of heat raised with increasing the Biot number and opposite effect with the rise of the suction parameter.

The current research work is devoted to study the exploration of dissipation and chemical reaction on MHD radiative Casson nanoliquid thin film flow generated due to the sheet stretching. Brownian motion, viscous dissipation, radiation and chemical reactions are considered, respectively, in energy and concentration equations. The popularly used similarity variables are utilized to remodel the nonlinear partial differential equations to a system of ordinary differential equations. The computational results are obtained for this system by adopting shooting technique. The impressions of significant flow variables on liquid stream are obtained through diagrams and tables. The outcomes of current work conclude that the thickness of thin film decreases with the rise of unsteady, magnetic and Casson parameters. Also, for higher estimates of non-Newtonian parameter a reduction in the coefficient of wall friction is noticed. The outcomes are matched with the viscous fluid flow and the results are in better agreement as a limiting case.

This work examines the effects of non-linear thermal radiation and Joule heating on MHD three-dimensional visco-elastic nanofluid flow due to a surface stretching in lateral directions. A coupled nonlinear differential system is generated from the boundary layer equations by using self-similarity variables and is then solved numerically by using most powerful shooting technique with Runge Kutta method of fourth order. The computational results for the flow variables are plotted graphically and are discussed in detail for various governing parameters that emerged in the analysis. It is observed that the momentum of the visco elastic nanofluid is better than that of a viscous fluid. Thicker thermal and concentration boundary layers are formed for increasing nonlinear thermal radiation and temperature ratio parameters. Also the results are in very good agreement with the outcomes available in the literature as a particular case. This model may play a significant role in the field of manufacturing and engineering applications.

The importance of thermophoresis and its essential role in particle migration have led to many published reports (i.e. aim and objectives). However, there exists no report on thermo-migration of tiny/nano-sized particles in the motion of various fluids. A meta-analysis on the significance of either nano or tiny particles exposed to thermophoretic force owing to temperature gradient during the dynamics of liquid substances is deliberated upon in this report. The method of slope linear regression through the data point was adopted to scrutinize sixty (60) published reports in which the effects of thermophoresis (thermodiffusion) is deliberated upon. The outcome of the study shows that different responses to the force of a temperature gradient are sufficient enough to enhance the temperature distribution and the concentration of non-Newtonian fluid due to an increase in thermophoresis. Thermophoretic effect increases the concentration of fluids in which the relationship between the shear stress and shear strain is non-linear. Skin friction coefficients is a decreasing function of thermophoresis. Increase in thermophoretic deposition is achievable due to an increase in thermophoresis. The effect of haphazard motion of nanoparticles should be investigated when it increases negligibly and considerably large. Thermal radiation strongly influences the significance of thermo-migration of tiny particles on fluid flow.

A mathematical model for hybrid nanofluid is proposed to study the influence of oblique magnetic field and thermal radiation on an exponentially elongated sheet. A comparison of the thermal characteristics of the hybrid nanofluid and the mono nanofluids (Al2O3 /water and TiO2/water) is made. The governing flow equations are transformed into a system of ODEs with the assistance of similarity variables and are then computationally addressed using bvp4c.The graphs are displayed for velocity, heat measure, and reduced frictional coefficients for selected flow parameters. Hybrid nanofluid has 1–4% growth in the rate of heat transfer when compared to mono nanofluid while it is 1–4.5% in comparison to viscous fluid for increasing radiation parameter. The outcomes of this work revealed that the heat transfer as a consequence of the dispersion of dual nanomaterials is more promising than the mono nanofluid. To accomplish very effective cooling/heating in industrial and engineering applications, hybrid nanofluids can substitute mono nanofluids.

The present research explores the features of thermal and solutal transport of a 3D micropolar liquid stream on an elongated convectively heated inclined sheet taking Soret effect. Mathematical modelling is designed with the aid of suitable scaling analysis on the governing PDEs conceiving the small magnetic Reynolds number. The resultant set of coupled nonlinear ODEs are derived with MATLAB to obtain computational solutions. Impression of the emerged flow parameters on the three boundary layers is graphically traced and deliberated. The parameters of magnetic field and stretching ratio and power law index diminished frictional drag. Hike in rate of thermal diffusion is prevailed with stronger surface heat convective and Prandtl numbers. Outcomes are collated with the data available in the literature and found to agree very closely as a limiting case.

In this report, the effects of homogeneous-heterogeneous autocatalytic chemical reaction together with the variable thermal conductivity in the Maxwell fluid flow due to nonlinear surface of variable thickness are investigated. Thermal radiation and heat generation / absorption effects are also incorporated in the analysis. Appropriate scaling analysis is implemented to reduce the mathematical model describing the physics of the problem in to a set of nonlinear differential equations and are subsequently solved computationally. Graphical illustrations indicating the effect of pertinent parameters on momentum, thermal and solutal boundary layers are presented and discussed. The study reveals that velocity distribution shows a decreasing (increasing) tendency for larger values of wall thickness parameter when the velocity power law index is less (greater) than unity. The concentration of the homogeneous bulk fluid with catalyst at the surface decreases with increasing chemical reaction rate parameters.

The intent of this study is to analyse the influence of nonlinear thermal radiation, thermophoresis, second order slip and magnetic field on the doubly stratified flow of a non-Newtonian micropolar fluid induced by a stretched sheet along with transport of thermal energy and mass species. The radiative heat flux term is modified using the non-linear Rosseland diffusion approximation. The partial differential equations governing the physics of the problem are recast into a set of coupled non-linear ordinary differential equations by using appropriate similarity transformations and later they are solved numerically using RKF-45 algorithm along with shooting technique. Results of the numerical solution are illustrated graphically for several sets of values of the governing parameters. Comparison of our results with the available results in literature for some special cases reveals close agreements. The results indicate that material parameter boosts the velocity and micro-rotation. The temperature ratio parameters that arise due to non-linear thermal radiation are seen to have opposite effect on temperature. It is seen that for strong thermal stratification reverse flow takes place accompanied by an undershoot in temperature. Excessive mass stratification and weaker molecular diffusivity resulted in a significant undershoot of species concentration. Keywords: Dual stratification, Double diffusion, Nonlinear thermal radiation, Second order velocity, Micropolar fluid

In the present work, dynamical aspects of boundary layer flow of hydromagnetic fluid (suspended with microorganisms) are investigated near the stagnation region over a stretchable heated permeable sheet. Viscosity is taken as a linear function of temperature where the flow field accommodates diffusion processes due to temperature and concentration gradients (Soret/Dufour numbers). A system of partial differential equations is set up for the mathematical description of the related bio-physical phenomenon. Unit free conversions and analysis of symmetry are implemented to obtain nonlinear dimensional free differential equations setup which can be solved numerically via the Runge–Kutta–Fehlberg scheme. Results in the form of pictorial and tabulation representation reveal that velocity profile increases when viscosity is a function of temperature difference, but the velocity profile influences the fluid temperature in the opposite direction.

This analysis pertains to the non-Newtonian nanofluid impinging the surface of stretching obliquely. The base fluid under discussion obeys the constitutive equation of a UCM fluid. Use of similarity variables and RKF 45 numerical method along with shooting technique enabled us to obtain the solution of the problem. The effects of physical parameters associated with nanofluids on the flow variables are discussed in detail through graphs. The streamlines are skewed towards right of the stagnation point when the stagnation flow parameter is negative and towards left for positive values. Due to Brownian motion, thermophoresis and nonlinear thermal radiation temperature is enhanced. Brownian motion and chemical reaction have an increasing influence on Sherwood number while a reversal effect is noticed with thermophoresis. The results of this study are compared with those available in the existing literature and are found to be in good agreement. Keywords: Maxwell fluid, Nanofluid, Non-orthogonal flow, Non-linear thermal radiation, Streamlines

The candid objective of this study is to simulate stagnation point flow of the MHD chemically reactive Maxwell based nanofluid under the action of Arrhenius activation energy function with radiative thermal energy and frictional heating. Application of scaling analysis followed by the RKF-45 method to the governing flow equations yield the computational solution. Maxwell parameter results in abatement of flow. Higher the Eckert number greater is the temperature with a overshoot in the vicinity of the stretched surface Nanoparticle concentration enhances proportionally with activation energy and temperature difference parameter.

In this paper we discuss the MHD unsteady flow of a micropolar nanofluid through a vertical channel with expanding/contracting walls under the influence of nonlinear thermal radiation considering weak permeability. The PDEs of the governing problem are reduced into a set of ODEs by using self-similar transformations and are then solved numerically. Influence of flow parameters such as wall dilation ratio, permeability Reynolds number, micropolar parameters, thermal radiation parameter, nanofluid parameters etc. on the flow, thermal energy and volume fraction of nanoparticles has been discussed in detail. We trust that the results of this study are not only useful for industrial applications but also present a basic understanding of the physical model.

A mathematical model is established to examine the influence of viscous dissipation and joule heating on magnetohydrodynamic (MHD) flow of an incompressible viscoelastic nanofluid over a convectively heated stretching sheet. Brownian motion and thermophoresis effects have been introduced in this nanofluid model. The governing equations are transformed into ODE’s by using suitable similarity conversions and are then solved numerically by the most robust shooting technique. The significance of numerous physical flow constraints is performed for, and distributions through graphs. It is noticed that, the increases for higher values of and reduces for rising values of heat source and Biot numbers. An outstanding contract was found between our numerical results and previously publicised results.

The present study discusses two dimensional Darcy-Forchheimer steady flow of a doubly stratified Maxwell nanofluid over a sheet of continuous stretching. Analysis of thermal energy and species concentration is carried out incorporating radiative heat, thermal and solutal stratifications, Brownian motion and thermophoresis. By introducing suitable transformations the system of equations of the flow are recast into a set of nonlinear ODEs which are then solved numerically by using the RKF-45 method. Flow characteristics are deliberated for different variations of governing parameters. Surface drag force, thermal energy and mass transfer rates are computed and discussed. Favourable comparisons with published work in the literature for different special cases of the problem are examined.

An analysis illustrating the flow of an Ostwald-de-Waele liquid film on an unsteady stretching sheet under the influence of thermocapillary force, magnetic field and viscous dissipation is carried out. In this study, thermal conductivity is assumed to be a function of fluid temperature. Numerical solutions for the partial differential equations governing the flow are obtained by employing the elegant Runge-Kutta-Fehlberg method for certain representative values of controlling parameters, such as thermocapillarity number, magnetic field parameter, etc. Film thickness is calculated for various values of flow parameters. Film thickness of shear thinning fluids is found to be smaller than that of a Newtonian fluid and a converse trend holds true for shear thickening fluids. Thicker films are noticed for increasing values of thermocapillarity number. In the presence of thermocapillary force, an initial decrease in the velocity of a shear thinning fluid occurs before fluid velocity experiences a significant increase towards the free surface. Stronger magnetic field strengths are seen to increase the free surface velocity. Themocapillary force on temperature in a shear thinning fluid is more prominent.

In this study we analyze the effects of thermal radiation and surface mass transfer on the flow generated by a shrinking sheet. Homotopy analysis method (HAM) is employed to obtain analytical solutions for the flow, temperature and mass concentration fields. The plots for the velocity, temperature and concentration fields are presented and their behavior is discussed for several sets of values of the governing parameters. Dual solutions are observed to exist for the shrinking sheet problem. Surface drag coefficient of the stable solution is enhanced for increasing values of the magnetic parameter and suction parameter. Also, thermal radiation parameter and Eckert number increase the rate of heat transfer in the case of stable solution. However, mass transfer rate of the stable solution is noticed to be a decreasing function of Schmidt number and chemical reaction parameter. We expect that the results obtained will not only provide useful information for industrial applications but also complement the existing literature.

Entropy generation is inherently affiliated with transport of thermal energy. However, not much attention has been paid to the study of entropy generation in liquid thin film flows. Hence, in this paper an analysis is carried out to study the entropy generation in a thin viscous fluid film on a stretching sheet embedded in a porous medium subject to a magnetic field and thermocapillarity force taking thermal radiation and internal heating/absorption into account. The numerical solution of the equations of momentum and energy governing the flow is obtained. Influence of various parameters emerged in the analysis on the velocity, temperature, surface drag, Nusselt number, entropy generation number and the Bejan number are graphically illustrated and discussed. Thermocapillarity number shows an enhancement of velocity at the free surface. Film thickness is found to increase with increasing thermocapillary force. Thinner films are noticed for stronger magnetic field strengths. It is found that in the absence of thermocapillary force, the effect of magnetic field on entropy generation number near the stretching surface is prominent. Thermocapillarity is seen to have a stronger effect on the entropy generation number near the stretching surface as well as at the free surface.

The partial derivative DOW is missing in Eqs. (3–5) in the original publication. The corrected equations are shown below.

Study of thermal radiative heat transport is relevant in several industrial applications. Analysis of radiative heat transfer in Newtonian fluids under different conditions has been studied extensively. However, not much attention has been paid to analyze the non-linear thermal radiative heat transfer in non-Darcy Casson fluid flows over stretching surfaces. Hence, in this paper an attempt is made to study the combined effect of non-linear thermal radiation and Navier slip in a magnetohydrodynamically and chemically reactive Casson fluid flow on a stretching surface immersed in a non-Darcy porous medium in the presence of thermo-diffusion. The physics of the problem is delineated by a set of partial differential equations. To solve these equations numerically scaling analysis and Runge–Kutta–Fehlberg method are sequentially applied. Computational results of the investigation are analyzed through graphs and tables. It is noted that the non-Newtonian rheology parameter, inertial and Lorentz forces are seen to suppress the flow while thermal and solutal buoyancy forces have an opposite effect. Parameters of temperature ratio and thermal radiation enhanced the temperature.

Analysis of nonlinear radiative heat transfer on the MHD Maxwell fluid flow in the boundary layers adjacent to a sheet with continuous stretching is discussed. Numerical solution of the PDEs governing the flow is obtained by the successive application of suitable similarity variables and BVP4c method. The flow variables, surface frictional coefficient, and local gradients of temperature and concentration are discussed through the graphs and tables. Results of the present analysis are compared with the previously published work and are found to be in close agreement.

This study addresses the thermal energy transport in a slippery sheet-driven flow of a micropolar fluid analysing the effect of radiative heat flux. The solution of PDEs of the governing the flow is derived numerically by the application of self-similarity transformations and Runge-Kutta Fehlberg algorithm along with shooting method. The computational results are discussed graphically for several selected flow parameters. Results of this analysis are compared with the published results and are seen to tally very closely.

The aim of this investigation is to analyze the effectiveness of Lorentz force, viscous dissipation and internal heating on the heat and flow characteristics of a non-Newtonian Casson fluid thin film resting on a stretching surface under the influence of a magnetic field. Employing suitable similarity variables and shooting technique and integrating scheme numerical solutions for velocity and temperature are obtained. The results of this analysis are compared with the published work and are found to be in good agreement. The thickness of the thin film is evaluated and is observed that Lorentz force and the non-Newtonian nature of the fluid have a thinning influence on the film. Velocity and temperature distributions in the thin film are discussed for various flow parameters.

The flows of non-Newtonian fluid over upper horizontal surfaces of rockets, over bonnets of cars, and pointed surfaces of aircraft are of great importance to the experts in the field of space sciences, automobile construction, and aerodynamic industry where efficiency is dependent on the thickness of paraboloid of revolution, buoyancy, and autocatalysis. The purpose of this study is to present not only the nonlinear governing equation which models the transport phenomenon, but also to analyze the non-Newtonian Erying–Powell fluid flow within a thin layer formed on an object which is neither a perfect horizontal nor a vertical, and neither an inclined surface nor a cone/wedge. The governing equation suitable to model the transport phenomenon above for the case of equal diffusivity during quartic autocatalytic kind of chemical reaction was non-dimensionalized and solved numerically. The velocity of the flow along x − direction can be enhanced when thickness increases negligible but buoyancy forces increase significantly. The rate of increase in the velocity of the flow along the y − direction from the wall to the free stream is optimal when the thickness of the paraboloid of revolution is zero (objects with a uniform thickness) and buoyancy force is sufficiently large. The concentration of Erying–Powell fluid at the wall G ( 0 ) is a decreasing function of Prandtl number but an increasing property of Schmidt number.

The objective of the present analysis is to understand the effects of Hall currents and chemical reaction on the unsteady flow of a viscous incompressible fluid past an exponentially stretching sheet in the presence of temperature dependent heat source and thermal radiation with slip effects.

The unsteady dispersion of a solute in blood flow modeling blood as a Newtonian fluid under the influence of a body acceleration is studied using the generalized dispersion model proposed by Gill and Sankarasubramanian [13]. As a result, the total process of dispersion can be described in terms of a simple diffusion process with the effective diffusion coefficient as a function of time. The model brings out mainly the effect of body acceleration and radius of the artery on the overall dispersion process. In the absence of body acceleration, the dispersion coefficient is found to increase rapidly and maintains a steady value in aorta while in other arteries it oscillates about a mean value after reaching it. Body acceleration is observed to enhance the value of the dispersion coefficient in all arteries. The effective diffusivity is found to depend on body acceleration. In the presence of body acceleration, it is noticed that there is a decrease in the effective diffusivity in aorta, femoral, and carotid while in coronary it is increased.

The combined effect of annular gap, yield stress and irreversible boundary reaction on the dispersion process in a Casson fluid flow is studied using generalized dispersion model. The study describes the development of dispersive transport following the injection of a tracer in terms of the three effective transport coefficients viz. absorption, convection and dispersion coefficients. The combined effect of annular gap, yield stress and wall absorption parameter on the above three effective transport coefficients is discussed. It is observed that the absorption coefficient is independent of the yield stress of the fluid and depends on the annular gap and wall absorption parameter. It is also observed that the asymptotic convection, dispersion coefficients are dependent on the yield stress of the fluid, annular gap and wall absorption parameter. The effect of the flow parameters on the mean concentration is studied. Application of this model for understanding the dispersion of solute in blood in a catheterized artery is discussed.

Peristaltic motion of a non-Newtonian, incompressible power law fluid with suspension of small particles in a two-dimensional channel is analyzed. A perturbation method has been employed to obtain the solution of the problem under the long wavelength approximation. The formation and growth of trapping zone are explained for variations in amplitude ratio and volume flow rate. The phenomenon of reflux has been studied. The behaviour of the axial velocity of fluid and solid particles has been discussed. The speed of the suspended particles is observed to be less than that of the fluid particles.

An analysis is carried out to investigate the effect of magnetic field and heat source on the steady boundary layer flow and heat transfer of a Casson nanofluid over a vertical cylinder stretching exponentially along its radial direction. Using a similarity transformation, the governing mathematical equations, with the boundary conditions are reduced to a system of coupled, non –linear ordinary differential equations. The resulting system is solved numerically by the fourth order Runge – Kutta scheme with shooting technique. The influence of various physical parameters such as Reynolds number, Prandtl number, magnetic field, Brownian motion parameter, thermophoresis parameter, Lewis number and the natural convection parameter are presented graphically and discussed for non – dimensional velocity, temperature and nanoparticle volume fraction. Numerical data for the skin – friction coefficient, local Nusselt number and the local Sherwood number have been tabulated for various parametric conditions. It is found that the local Nusselt number is a decreasing function of Brownian motion parameter Nb and the thermophoresis parameter Nt., {"references":["Lin, C. R., and Shih, Y. P., \"Laminar boundary layer heat transfer along\nstatic and moving cylinder\", J. Chin. Inst. Eng., vol. 3, 1980, pp. 73 –\n79.","Lin, C. R., and Shih, Y. P., \"Buoyancy effects on the laminar boundary\nlayer heat transfer along vertically moving cylinder\", J. Chin. Inst. Eng.,\nvol. 4, 1981, pp. 45 – 51.","Wang, C. Y., \"Fluid flow due to a stretching cylinder\", Phys Fluids. ,\n1988, 31: pp. 466 – 468.","Ishak, A., Nazar,R., Pop,I., \"Magnetohydrodynamic (MHD) flow and\nheat transfer due to a stretching cylinder\", Energy Convers Manag ,\n2008, 49:pp. 3265 – 3269.","Elbashbeshy, E. M. A., Emam, T. G., El – Azab, M. S., Abdelgaber, K.\nM., \"Laminar boundary layer flow along a stretching horizontal cylinder\nembedded in a porous medium in the presence of a heat source or sink\nwith suction/injection\", International Journal of Energy & Technology ,\n2012, 4 (28) pp. 1 – 6.","Fredrickson, A.G. \"Principles and Applications of Rheology\", Prentice –\nHall, Englewood Cliffs, NJ, USA, 1964.","Nagarani, P., Sarojamma, G., \"Flow of a Casson fluid through a\nstenosed artery subject to periodic body acceleration\", Proc. Of the 9th\nWSEAS Int. Conf. On Mathematical and Computational Methods in\nScience and Engineering, Trinidad and Tobago, 2007, pp. 237 – 244.","Sarojamma, G., Vishali, B., Ramana, B., \"Flow of blood through a\nstenosed catheterized artery under the influence of a body acceleration\nmodeling blood as a Casson fluid\", Int. J. Of Appl. Math and Mech ,\n2012, 8(11): pp. 1 – 17.","Penkavova, V., Tihon, J., Wein, O., \"Stability and rheology of dilute tio2\n– water nanoflids, Nanoscale Res Lett\", vol. 6, 2011, pp. 273.\n[10] Namburua, PK., Kulkarni, DP., Misrab, D., Das, DK., \"Viscosity of\ncopper oxide nanoparticles dispersed in ethylene glycol and water\nmixture\", Exp Therm Fluid Sci, Vol. 32, 2007, pp. 397.\n[11] Kulkarni, DP., Das, DK., Chukwu, GA., \"Temperature dependent\nrheological property of copper oxide nanoparticles suspension\n(nanofluid)\", J Nanosci Nanotechno, vol. 6,2006, pp. 1150.\n[12] Duan, F., Kwek, D., Crivoi, A., \"Viscosity affected by nanoparticle\naggregation in Al2O3 – water nanofluids\", Nanoscale Res Lett, vol. 6,\n2011, pp. 248.\n[13] Chen, H., Ding, Y., Tan, C., \"Rheological behavior of nanofluids\", New\nJ Phys, vol. 9, 2007, pp. 367.\n[14] Buongiarno, J. \"Convective transport in nanofluids\", J. Heat Transfer,\n2006, 128, pp. 240 – 250.\n[15] Malik., M. Y,Naseer M,Nadeem S, Rehman,A., \"The boundary layer\nflow of Casson nanofluid over a vertical exponentially stretching\ncylinder\", Appl Nanosci, 2013, 4:869–873."]}

The dispersion of a solute in the flow of a Casson fluid in an annulus is studied. The generalized dispersion model is employed to study the dispersion process. The effective diffusion coefficient, which describes the whole dispersion process in terms of a simple diffusion process, is obtained as a function of time, in addition to its dependence on the yield stress of the fluid and on the annular gap between the two cylinders. It is observed that the dispersion coefficient changes very rapidly for small values of time and becomes essentially constant as time takes large values. In non–Newtonian fluids the steady state is reached at earlier instants of time when compared to the Newtonian case and the time taken to reach the steady state is seen to depend on the values of the yield stress. It is observed that a decrease in the annular gap inhibits the dispersion process for all times both in Newtonian as well as in non–Newtonian fluids. When the yield stress is 0.05, depending upon the size of the annular gap (0.9–0.7) the reduction factor in the dispersion coefficient varies in the range 0.58–0.08. The application of this study for understanding the dispersion of an indicator in a catheterized artery is discussed.

The combined effect of yield stress and irreversible boundary reaction on dispersion process in a Casson fluid flowing in a conduit (pipe/channel) is studied using the generalized dispersion model proposed by Sankarasubramanian and Gill (Sankarasubramanian, R., and W. N. Gill. Proc. R. Soc. London, Ser. A 333:115-132, 1973). The study describes the development of dispersive transport following the injection of a tracer in terms of the three effective transport coefficients, viz., exchange, convection, and dispersion coefficients. The exchange coefficient does not depend on yield stress but the convection and dispersion coefficients depend on yield stress or equivalently plug flow region. For large times, when the plug flow radius is one-tenth of pipe radius, the convective coefficient is reduced by 0.41 times of the corresponding value for a Newtonian fluid at equivalent wall absorption parameter; in channel case the reduction is by 39%. It is seen that the asymptotic dispersion coefficient decreases with increase in wall absorption parameter and yield stress of the fluid. When the plug radius in pipe (channel) is 0.1, depending upon the values of wall absorption parameter, say (0.01-100) the reduction factor in dispersion coefficient is in the range (0.1-0.3) in comparison to the values of the Newtonian case. The results reduce to those of Sankarasubramanian and Gill (Sankarasubramanian, R., and W. N. Gill. Proc. R. Soc. London, Ser. A 333:115-132, 1973) when there is no yield stress for the pipe flow analysis and to those of Dash et al. (Dash, R. K., G. Jayaraman, and K. N. Mehta. Ann. Biomed. Eng. 28:373-385, 2000) when there is no interphase mass transfer. The study can be used as a starting first approximation solution for studying the dispersion in the cardiovascular system.

In this paper, diffusion of solute in a Newtonian fluid flowing in a pipe/channel under the influence of transverse magnetic field with interphase mass transfer at the boundaries is analysed using the generalized dispersion model. The study describes the development of dispersive transport following the injection of a tracer in terms of the three effective transport coefficients viz. the absorption, the convection and the dispersion coefficients. The absorption coefficient does not depend on magnetic field but the convection and dispersion coefficients are influenced by the magnetic field. The effect of magnetic field on the mean concentration has also been discussed

We discuss the combined free and forced convection flow of a viscous incompressible fluid in a vertical pipe of variable cross-section. The governing nonlinear equations are solved in terms of the stream function and temperature. The behaviour of the velocity, temperature and heat transfer coefficient is discussed numerically in detail.

The paper studies the combined free and forced convection in a rotating, viscous, incompressible fluid confined between two parallel porous plates. Assuming that the temperature varies linearly along the plates and the pressure gradient maintained uniform over the planes parallel to the plates, the velocity, temperature and the stresses are calculated analytically. Their behaviours for different values of the parameters viz., the Hartmann number, the Grashoff number and the suction parameter etc., are discussed graphically giving out the interplay between the various forces.

In this study the unsteady flow of a viscous incompressible fluid past a stretching wedge under the influence of a transverse magnetic field, viscous dissipation, and wall slip is investigated. The governing partial differential equations of the flow are solved numerically. The point of flow separation is observed to occur at small times and for smaller values of wedge angle. The temperature is found to be an increasing function of Eckert and Biot numbers and a decreasing function of wedge angle.

The peristaltic transport of a Casson fluid in a two — dimensional asymmetric channel is studied under long- wavelength and low-Reynolds number assumption. The asymmetry in the channel is created by considering the peristaltic waves imposed on the boundary walls to possess different amplitude and phase. The analysis of the flow is carried out in a wave frame of reference moving with the velocity of the wave. Due to the asymmetry in the channel two yield planes exist and they are calculated by solving the transcendental equation in terms of the core width. In an asymmetric channel the yield planes are skewed towards the boundary with higher amplitude or a phase difference in relation to the other boundary. While in a symmetric channel the yield planes are located symmetrically on either side of the axis of the channel. The phenomena of trapping and reflux have been discussed in the symmetric case of the channel. It is noticed that trapping of fluid occurs and the trapping zone extends for an increase in the time average flux. It is found that reflux occurs for higher values of amplitude of the peristaltic wave and the reflux zone extends for increased amplitudes.