Thermal mixed convection induced locally by a step change in surface temperature in a Poiseuille flow in the framework of triple deck theory

The classical Leveque solution of heat transfer induced by a small step cha nge in the surface temperature in a shear flow (u linear in y) is revisited . To obtain the shear flow we rescale the laminar channel flow of a perfect gas at a high Reynolds number in the Triple Deck scales and we investigate the retroaction of the temperature on the basic Poiseuille profile (near t he wall the profile is a linear in y). This retroaction is achieved by two means, first through the dependence of the viscosity and the density upon t emperature and second through the gravity-induced transverse pressure gradi ent gauged by the inverse of the Froude number. In the case of no transverse gradient a new self-similar solution is obtain ed showing that the skin friction at the lower wall is reduced by the heati ng while the one at the top wall is simultaneously increased. In the general case with a Lower Deck based Froude number not infinite, the case of asymptotically small wall temperature variation allows a linearize d solution which is solved with the Fourier transform method. If the Froude number I:is increased to infinity we recover the preceding self-similar so lution with small temperature variation. If Fis now decreased to zero we fi nd that the leading term in 1/F of the solution shows that the skin frictio n at the lower wall is increased while that at the upper wall is decreased. The conclusion is that the increase of temperature produces two opposite ef fects: first, the expandability of the gas causes an upward displacement of the streamlines and a pressure decrease (the preceding self-similar soluti on is recovered with small tempterature variation); second, the buoyant eff ect produces the reverse effect of a downward displacement and a pressure i ncrease which we believe may cause separation at the top wall in the non-li near case (skin friction at the lower wall is increased, whereas it is decr eased at the upper wall). These two effects qualitatively explain the flow computed with a full Navier-Stokes equation in an MOCVD reactor. (C) 1999 E lsevier Science Ltd. All rights reserved.