M. Subhas Abel

Study of visco-elastic fluid flow and heat transfer over a stretching sheet with variable viscosity

Abstract This paper deals with the study of boundary layer flow and heat transfer of a visco-elastic fluid immersed in a porous medium over a non-isothermal stretching sheet. The fluid viscosity is assumed to vary as a function of temperature. The presence of variable viscosity of the fluid leads to the coupling and the non-linearity in the boundary value problem. A numerical shooting algorithm for two unknown initial conditions with fourth-order Runge–Kutta integration scheme has been used to solve the coupled non-linear boundary value problem. An analysis has been carried out for two different cases namely (1) prescribed surface temperature (PST), and (2) prescribed heat flux (PHF), to get the effect of fluid viscosity, permeability parameter and visco-elastic parameter for various situations. The important finding of our study is that the effect of fluid viscosity parameter is to decrease the wall temperature profile significantly when flow is through a porous medium. Further, the effect of permeability parameter is to decrease the skin friction on the sheet.

Momentum and heat transfer in visco‐elastic fluid flow in a porous medium over a non‐isothermal stretching sheet

Visco‐elastic fluid flow and heat transfer in a porous medium over a non‐isothermal stretching sheet have been investigated. The flow is influenced by linearly stretching the sheet in the presence of suction, blowing and impermeability of the wall. Thermal conductivity is considered to vary linearly with temperature. The intricate non‐linear problem has been solved numerically by shooting technique with fourth order Runge‐Kutta algorithm after using perturbation method. The zeroth order solutions are obtained analytically in the form of Kummer’s function. An analysis has been carried out for two different cases, namely prescribed surface temperature (PST) and prescribed heat flux (PHF) to get the effect of porosity and visco‐elasticity at various physical situations. The important finding is that the effect of visco‐elasticity and porosity is to increase the wall temperature in case of blowing and to decrease in both the cases of suction and when the stretching sheet is impermeable.

Heat Transfer in MHD Visco‐elastic Fluid Flow over a Stretching Surface

An analysis has been carried out to study the effect of magnetic field on the visco-elastic fluid flow and heat transfer over a non-isothermal stretching sheet with internal heat generation. The solutions for heat transfer characteristics are evaluated numerically for different parameters such as Prandtl number, magnetic field, suction, visco-elasticity, and the temperature profile. The solutions for the temperature profile, heat transfer characteristics, and their asymptotic limits for large and small Prandtl numbers are obtained in terms of Kummers function. The important finding is that the effect of visco-elasticity is to decrease temperature profile in the flow field for small values of Prandil number. The temperature profile decreases with the increase of magnetic field.

Convective heat and mass transfer in a visco‐elastic fluid flow through a porous medium over a stretching sheet

Presents a numerical solution of the two‐dimensional laminar boundary layer problem on free and forced convection of an incompressible visco‐elastic fluid immersed in a porous medium over a stretching sheet. Here, the driving force for the flow is provided by an impermeable sheet stretched with a velocity proportional to the distance from a slit and buoyancy effects due to both temperature and concentration gradients. The resultant governing boundary layer equations are highly non‐linear and coupled form of partial differential equations, and they have been solved by employing a numerical shooting technique with fourth order Runge‐Kutta integration scheme. Numerical computations are carried out for the non‐dimensional physical parameters. The results are analyzed for the effect of different physical parameters like visco‐elasticity, permeability of the porous medium, Grashof number, Schmidt number and Prandtl number on the flow, heat and mass transfer characteristics. One of the several important observations is that the combined effect of thermal diffusion and diffusion of species is to increase the horizontal velocity profile and to decrease the temperature and concentration profiles in the boundary layer flow field.

HEAT TRANSFER DUE TO MHD SLIP FLOW OF A SECOND-GRADE LIQUID OVER A STRETCHING SHEET THROUGH A POROUS MEDIUM WITH NONUNIFORM HEAT SOURCE/SINK

An analysis is carried out to study the heat transfer characteristics of a second-grade non-Newtonian liquid due to a stretching sheet through a porous medium under the influence of external magnetic field. The stretching sheet is assumed to be impermeable. Partial slip condition is used to study the flow behavior of the liquid. The effects of viscous dissipation, nonuniform heat source/sink on the heat transfer are addressed. The nonlinear partial differential equations governing momentum and heat transfer in the boundary layer are converted into nonlinear ordinary differential equations using similarity transformation. Analytical solutions are obtained for the resulting boundary value problems in the case of two types of boundary heating, namely, constant surface temperature (CST) and prescribed surface temperature (PST). The effects of slip parameter, second-grade liquid parameter, combined (magnetic and porous) parameter, Prandtl number, Eckert number, and nonuniform heat source/sink parameters on the heat transfer are shown in several plots. Analytical expressions for the wall frictional drag coefficient and wall temperature gradient are obtained.

The Effects of MHD Flow and Heat Transfer for the UCM Fluid over a Stretching Surface in Presence of Thermal Radiation

An analysis is performed to investigate the effect of MHD and thermal radiation on the two-dimensional steady flow of an incompressible, upper-convected Maxwells (UCM) fluid in presence of external magnetic field. The governing system of partial differential equations are transformed into a system of coupled nonlinear ordinary differential equations and is solved numerically by efficient shooting technique. Velocity and temperature fields have been computed and shown graphically for various values of physical parameters. For a Maxwell fluid, a thinning of the boundary layer and a drop in wall skin friction coefficient is predicted to occur for the higher elastic number which agrees with the results of Hayat et al. 2007 and Sadeghy et al. 2006. The objective of the present work is to investigate the effect of elastic parameter β, magnetic parameter Mn, Eckert number Ec, Radiation parameter N, and Prandtl number Pr on flow and heat transfer charecteristics.

Numerical solution of the momentum and heat transfer equations for a hydromagnetic flow due to a stretching sheet of a non-uniform property micropolar liquid

A study of the hydromagnetic flow due to a stretching sheet and heat transfer in an incompressible micropolar liquid is made. Temperature-dependent thermal conductivity and a non-uniform heat source/sink render the problem analytically intractable and hence a numerical study is made using the shooting method based on Runge-Kutta and Newton-Raphson methods. The two problems of horizontal and vertical stretching are considered to implement the numerical method. The former problem involves one-way coupling between linear momentum and heat transport equations and the latter involves two-way coupling. Further, both the problems involve two-way coupling between the non-linear equations of conservation of linear and angular momentums. A similarity transformation arrived at for the problem using the Lie group method facilitates the reduction of coupled, non-linear partial differential equations into coupled, non-linear ordinary differential equations. The algorithm for solving the resulting coupled, two-point, non-linear boundary value problem is presented in great detail in the paper. Extensive computation on velocity and temperature profiles is presented for a wide range of values of the parameters, for prescribed surface temperature (PST) and prescribed heat flux (PHF) boundary conditions.

HYDROMAGNETIC BOUNDARY LAYER FLOW AND HEAT TRANSFER IN VISCOELASTIC FLUID OVER A CONTINUOUSLY MOVING PERMEABLE STRETCHING SURFACE WITH NONUNIFORM HEAT SOURCE/SINK EMBEDDED IN FLUID-SATURATED POROUS MEDIUM

Analytical study for the problem of flow and heat transfer of electrically conducting viscoelastic fluid over a continuously moving permeable stretching surface with nonuniform heat source/sink in a fluid-saturated porous medium has been undertaken. The momentum and thermal boundary layer equations, which are partial differential equations, are converted into ordinary differential equations, by using suitable similarity transformation. The resulting nonlinear ordinary differential equations of momentum are solved analytically assuming exponential solution, and similarly thermal boundary layer equations are solved exactly by using power series method, with the solution obtained in terms of Kummers function. The results are shown with graphs and tables. The effect of various physical parameters like viscoelastic parameter, porosity parameter, Eckert number, space, and temperature-dependent heat source/sink parameters enhances the temperature profile, whereas increasing the values of the suction parameter and Prandtl number decreases the temperature profile. The results have technological applications in liquid-based system involving stretchable materials.

HEAT TRANSFER IN MHD VISCOELASTIC FLUID FLOW ON STRETCHING SHEET WITH HEAT SOURCE/SINK, VISCOUS DISSIPATION, STRESS WORK, AND RADIATION FOR THE CASE OF LARGE PRANDTL NUMBER

An analysis is carried out to study the magnetohydrodynamic boundary layer flow behavior and heat transfer characteristics of a viscoelastic fluid flow over a stretching sheet with radiation and for the case of large Prandtl numbers. The basic boundary layer equations of momentum and heat transfer, which are nonlinear partial differential equations, are converted into nonlinear ordinary differential equations by means of similarity transformation. The resulting nonlinear ordinary differential equations of momentum are solved exactly. Similarly, the energy equation is transformed to a confluent hypergeometric differential equation using a new variable and Rosseland approximation for radiation. The analytic solutions for temperature profile and heat transfer characteristics are obtained in terms of Kummers function, and their asymptotic limits for large Prandtl numbers are also obtained. The effects of magnetic field, viscoelastic parameter, viscous dissipation, heat generation/absorption, work done due to deformation, and radiation on flow and heat transfer characteristics are discussed through several graphs. To assess the validity and accuracy of the present work, heat transfer results were compared to those of previously published work of Nataraja et al. (1977). This comparison shows excellent agreement between the results.

HEAT TRANSFER THROUGH A POROUS MEDIUM OVER A STRETCHING SHEET WITH EFFECT OF VISCOUS DISSIPATION

An analysis was carried out to study the flow and heat transfer characteristics in a second-grade fluid through a porous medium over a linear stretching surface with two general cases, namely PST and PHF, including the effect of viscous dissipation. The partial differential equations governing the flow and heat transfer are converted into nonlinear ordinary differential equations and boundary conditions by using suitable similarity transformation. The proposed problem was solved analytically by the power series method (using Kummers function). The graphical results for velocity, skin-friction coefficient, and temperature (for PST and PHF cases) are presented and discussed. The numerical values of wall friction coefficient , wall temperature gradient θη(0), and wall temperature θ(0) are also calculated, tabulated, and discussed.