Radiation-conduction interaction of steady streamwise surface temperature variation on vertical free convection

Abstract

We examine how the steady free convective boundary-layer flow induced by a vertical healed surface is affected by the presence of sinusoidal surface temperature variations about a constant mean value with the effect of radiation. Besides this, we have also analyze the effect of radiation of steady slreamwise surface temperature variation of a vertical cone. The problem is studied using fully numerical techniques. The surface rate of heat transfer eventually alternates in sign with distance from the leading edge, but no separation occurs unless the amplitude of the thermal modulation is sufficiently high. Numerical results are obtained for different values of the physical parameters, the radiation parameter Rd,Prandll number Pr and the surface temperature wave amplitude a. Important aspects of the overall behavior of our analysis by observing that the boundary layer is thinner when the surface temperature is relatively high and thicker when it is low. This arises because relatively high surface temperatures induce relatively large upward fluid velocities with the consequent increase in the rate of entrainment into the boundary layer. This causes, in turn, a thinning of the boundary layer. Thus, we should expect high shear stresses and rates of heat transfer at, or perhaps just beyond, where the surface temperature allains its maximum values. As x increases, the amplitude of osdltation of the rate of heat transfer curves increases gradually, and tile amplitude of oscillation of the shear stress curve decreases slowly, with x. The most interesting part of this analysis is that, when radiation parameter R.Jis increasing, both the shear stress and the rate of heat transfer are also increasing but when Rd=0. the result of rate of heat transfer is exactly the same, which was found by Rees [14]. In our study we have found that rate of 0'. ~ , heat lransfer is increasing as Rd is increasing but at a decreasing rale. That is, when R.; =1 then rate of heallransfer increased more in respect of Rd =10.