S. Rawat

Numerical study of heat transfer of a third grade viscoelastic fluid in non-Darcy porous media with thermophysical effects

A numerical solution is presented for the natural convective dissipative heat transfer of an incompressible, third grade, non-Newtonian fluid flowing past an infinite porous plate embedded in a Darcy–Forchheimer porous medium. The mathematical model is developed in an (x,y) coordinate system. Using a set of transformations, the momentum equation is rendered one-dimensional and a partly linearized heat conservation equation is derived. The viscoelastic formulation presented by Akyildiz (2001 Int. J. Non-Linear Mechanics 36 349–52) is adopted, which generates lateral mass and viscoelastic terms in the heat conservation equation, as well as in the momentum equation. A number of special cases of the general transformed model are discussed. A finite element method is implemented to solve, with appropriate boundary conditions, the coupled third-order, second degree ordinary differential equation for momentum and the second-order, fourth degree heat conservation equation. We study the influence of the third grade viscoelastic parameter (β3), Darcian parameter (inversely proportional to permeability (kp)), the Forchheimer inertial parameter (b), transpiration velocity (Vo), the transpiration parameter in the heat equation (R) and the thermal conductivity parameter (S) on momentum and heat transfer. Additionally, we study the influence of the Forchheimer inertial parameter (b) on second-order viscoelastic non-Darcy free convection flow and also the effects of the third grade parameter (β3) on Darcian free convection. Velocities increase with rising permeability (Darcian parameter) for both second and third grade viscoelastic free convection regimes and decrease with rising Forchheimer parameter. The effects of the other parameters are described at length. The flow scenario is important in chemical engineering processes.

Heat and Mass Transfer of a Chemically Reacting Micropolar Fluid Over a Linear Streaching Sheet in Darcy Forchheimer Porous Medium

In the present study, an analysis is carried out to study twodimensional, laminar boundary layer flow and mass transfer of a micropolar chemically-reacting fluid past a linearly stretching surface embedded in a porous medium. Such a study finds important applications in geochemical systems and also chemical reactor process engineering. The non-linear partial boundary layer differential equations, governing the problem under consideration, have been transformed by a similarity transformation into a system of ordinary differential equations, which is solved numerically by using the galerkin finite element method. The numerical outcomes thus obtained are depicted graphically to illustrate the effect of different controlling parameters on the dimensionless velocity, temperature and concentration profiles. Comparisons of finite element method and finite difference method is also presented in order to test the accuracy of the methods and the results obtained are found to have an excellent agreement. Finally, the numerical values for quantities of physical interest like local Nusselt number and skin friction are also presented in tabular form.

FINITE ELEMENT STUDY OF TRANSIENT PULSATILE MAGNETO-HEMODYNAMIC NON-NEWTONIAN FLOW AND DRUG DIFFUSION IN A POROUS MEDIUM CHANNEL

A numerical study of pulsatile hydromagnetic flow and mass transfer of a non-Newtonian biofluid through a porous channel containing a non-Darcian porous material is undertaken. An extensively-validated biofluid dynamics variational finite element code, BIOFLOW, is employed to obtain comprehensive computational solutions for the flow regime which is described using a spatially two-dimensional momentum equation and a spatially one-dimensional mass transport equation, under appropriate boundary conditions. The Nakamura-Sawada rheological model is employed which provides a higher yield stress than the Casson model. A non-Newtonian model is justified on the basis that blood exhibits deviation from Newtonian behavior at low shear rates. The conduit considered is rigid with a pulsatile pressure applied via an appropriate pressure gradient term. One hundred two-noded line elements have been employed in the computations. The influence of magnetic field on the flow is studied via the magnetohydrodynamic body force ...