Conjugate forced convection heat transfer from a flat plate by laminar plane wall jet flow

AbstractAn analytical solution is investigated for forced convection heat transfer from a laminar plane wall jet as conjugatecase. For Re 1, boundary layer theory is used for the investigation. The problem has been solved for two classic casessuch as Pr P 1 and Pr 1. The conjugate model consists of considering the full Navier–Stokes equation in the fluidmedium and coupling of energy equations in the fluid and the slab through the interface boundary conditions. Closed-form relations are found for Nusselt number (Nu), average Nusselt number ðNuÞ and conjugate interface boundary tem-perature (h b ). The effects of the Reynolds number (Re), the Prandtl number (Pr), the thermal conductivity ratio (k)between the slab and the fluid medium and the slab aspect ratio (k) are investigated on the heat transfer characteristics.The analytical results are compared with the full numerical results. 2005 Elsevier Ltd. All rights reserved. Keywords: Plane wall jet; Conjugate heat transfer; Computation 1. IntroductionA conjugate heat transfer problem occurs when thefluid regime is coupled with the conducting solid wallof finite thickness. The temperature and the heat fluxesat the solid-fluid interface are considered to be equal.This is referred to as the fourth-kind boundarycondition[1]. Conjugate heat transfer is involved in many applica-tions like high speed jet engines, electronics cooling, filmcooling of turbine blades, extrusion of materials, etc.Many publications are devoted to conjugate heattransfer on flat plate [2–6]. Chiu et al. [7] studied conju-gate heat transfer of horizontal channel both experimen-tally and numerically. They showed the effects ofconjugate heat transfer with non-conjugate results.Rao et al. [8] presented the results for laminar mixedconvection with surface radiation from a vertical platewith a heat source as conjugate case. Jilani et al. [9] havesolved conjugate heat transfer from a heat generatingvertical cylinder.Glauert [10] defined plane wall jet as a stream of fluidblown tangential along a plane wall. Similarity solutionfor plane wall jet as well as radial wall jet for both lam-inar and turbulent cases were presented with the intro-duction of Glauert constant F. Schwarz and Caswell[11] have investigated the heat transfer characteristicsof a two-dimensional laminar incompressible wall jet.They found exact solutions for both constant wall tem-perature and constant heat flux cases. In addition, theyhave solved for variable starting length of the heated

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