Sujit Kumar Khan

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.

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.

Atmospheric diffusion model of secondary pollutants with settling

A time-dependent mathematical model of chemically reactive atmospheric primary pollutants and their byproduct in a protected zone above the surface layer has been developed to study the impact of removal of larger particles when the heavy admixture is present. The different meteorological and source parameters in the surface layer (SL), including a settling velocity term, have been taken into account through appropriate boundary conditions. The variation of surface layer and mixing layer heights on atmospheric stability, geostrophic drag by terrain and several other meteorological parameters are also treated. The results have been analysed for stable and neutral atmospheric conditions. It is shown that the effect of settling velocity on concentration of secondary pollutants is significant in a stable layer compared to the neutral case. Further, the effect of chemical reaction of a primary pollutant is to increase the concentration of secondary pollutant throughout the protected zone for all values of chemical reaction rate and the effect of settling is to increase the concentration in the lower part of the protected zone for certain ranges of settling velocity. In the upper part, the effect of settling is to decrease the concentration for all values of settling velocity. It is interesting to note that the effect of chemical reaction rate has virtually no impact on the formation of secondary pollutant at short travel time but has significant effect at large travel time.