Heat transfer in a viscoelastic boundary layer flow through a porous medium

Abstract

This paper examines the viscoelastic fluid flow and heat transfer characteristics in a saturated porous medium over an impermeable stretching surface with frictional heating and internal heat generation or absorption. The heat transfer analysis has been carried out for two different heating processes, namely (i) with prescribed surface temperature (PST-case) and (ii) prescribed surface heat flux (PHF-case). The governing equations for the boundary layer flow problem result similar solutions. For the specified five boundary conditions, it is not possible to solve directly the resulting sixth-order nonlinear ordinary differential equation. For the present incompressible boundary layer flow problem with constant physical parameters, the momentum equation is decoupled from the energy equation. Two closed-form solutions for the momentum equation are obtained and identified the realistic solution of the physical problem. Exact solution for the velocity field and the skin-friction are obtained. Also, the solution for the temperature and the heat transfer characteristics are obtained in terms of Kummer's function. Asymptotic results for the temperature function for large Prandtl numbers are presented. The work due to deformation in the energy equation, which is essential and escaped from the attention of researchers while formulating the visco-elastic boundary layer flow problems, is considered. Drastic variation in the values of heat transfer coefficient is observed when the work due to deformation is ignored.

Heat transfer in a Walter’s liquid B fluid over an impermeable stretching sheet with non-uniform heat source/sink and elastic deformation

“…Tables 2 and 3 gives values of wall temperature gradient h g ð0Þ and wall temperature g(0) for PST and PHF cases, respectively, for various values of B Ã and these present results are compared with the existing results. From these tables it is clear that, our results on heat transfer are in excellent agreement with that of Pillai et al [22] and Subhas and Veena [29] under the limiting conditions A Ã ¼ 0:0; Pr ¼ 3:0; k 1 ¼ 0:2. Table 4 gives the values of wall temperature gradient h g ð0Þ and wall temperature g(0) in absence of elastic deformation, for various values of parameters governing the flow.…”

“…The magnitude of the non-dimensional surface velocity gradient f gg ð0Þ and 1 2 C f Re 1=2 x , increase with viscoelastic parameter k 1 . These results have good agreement with the results of Pillai et al [22] under the limiting condition k 2 ! 0 (i.e.…”

“…(5). Further Pillai et al [22] obtained a solution for fourth order differential momentum equation having porous parameter by a simple mathematical procedure, they also discussed the uniqueness of the solution of momentum equation. In view of above discussion, we choose a realistic solution proposed in above literature, for present physical situation, the solution of Eq.…”

“…Pillai et al [22] investigated the effects of work done by deformation in viscoelastic fluid in porous media with uniform heat source, Hayat et al [23] also investigated the effects of work done by deformation in second grade fluid with partial slip condition, in this no account of heat source has been taken into consideration and Khan et al [24] also investigated the effect of work done by deformation in Walter's liquid B but with uniform heat source. Mahapatra et al [35] also investigated the heat transfer analysis with two general cases (CST and PST) with stagnation point flow.…”

Effect of slip condition on viscoelastic mhd oscillatory forced convection flow in a vertical channel with heat radiation

“…Labropulu (2000) obtained another exact solution of non-Newtonian fluid flows with prescribed vorticity. Pillai et al (2004) studied the heat transfer in a viscoelastic boundary layer flow through a porous medium. Choudhury and Das (2000) K.D.Singh investigated magnetohydrodynamic boundary layer flow of a non-Newtonian fluid past a flat plate.…”