Thermal Jump Effects on Boundary Layer Flow of a Jeffrey Fluid Near the Stagnation Point on a Stretching/Shrinking Sheet with Variable Thermal Conductivity

A mathematical model will be analyzed in order to study the effects of thermal jump and variable thermal conductivity on flow and heat transfer near the stagnation point on a stretching/shrinking sheet in a Jeffrey fluid. The highly nonlinear partial differential equation of Jeffrey fluid flow along with the energy equation are transformed to an ordinary system using nondimensional transformations. The arising equations are solved for temperature, velocity, shear stress, and heat flux using finite difference method. The effect of the influences parameters is discussed. For nonradiation regular viscous fluid our results are as that by Nazar et al. (2002). 1. Introduction It is well known that the thermophysical properties of a fluid play an important role in the engineering applications in aerodynamics, geothermal systems, crude oil extractions, ground water pollution, thermal insulation, heat exchanger, storage of nuclear waste, and so forth, convective flows over bodies. The change in the thermal conductivity with temperature is an important property [1–5]. Prasad and Vajravelu [6] investigated the effect of variable thermal conductivity in a nonisothermal sheet stretching through power law fluids while Prasad et al. [4] reported similar studies for viscoelastic fluids. Abel et al. [7] studied combined effects of thermal buoyancy and variable thermal conductivity on a magnetohydrodynamic flow and the associated heat transfer in a power-law fluid past a vertical stretching sheet in the presence of a nonuniform heat source. The general findings of these studies were that the effects of variable thermal conductivity increase the shear stress. The temperature at wall increase with an increase in variable thermal conductivity by Seddeek et al. [8]. Prasad et al. [9] found that the variable thermal conductivity has an impact in enhancing the skin friction coefficient; hence, fluids with less thermal conductivity may be opted for effective cooling. Abel et al. [10] concluded that the variable thermal conductivity increases the temperature distribution in both prescribed surface temperature and prescribed heat flux cases. Mahanti and Gaur [11] investigated the effects of linearly varying viscosity and thermal conductivity on steady free convective flow of a viscous incompressible fluid along an isothermal vertical plate in the presence of heat sink. Deissler [12] obtained that the effects of second-order terms on the velocity and temperature jumps at a wall are by a physical derivation. The analysis used the concepts of effective mean free paths for momentum