Similarity Theory for Forced Convection over Horizontal Plates Subho Samanta * and Abhijit Guha † Indian Institute of Technology Kharagpur, Kharagpur 721 302, India DOI: 10.2514/1.T4033 A similarity analysis is performed to study the fluid flow and heat transfer characteristics for the steady laminar forced convection boundary-layer flow past a semi-infinite horizontal plate in the presence of mass transfer, i.e., suction or blowing. The plate is subjected either to a nonuniform heat flux or nonuniform wall temperature. The heat flux q w   x is assumed to vary in the following form q w   x a  x m , whereas the wall temperature  T w   x is assumed to vary as  T w   x −  T ∞  b  x n . Numerical results are obtained for various values of Prandtl number, suction or injection parameter ξ s , as well as for various levels of heating m or n. The effects of various values of Prandtl number Pr, suction or injection parameter ξ s , and the index m or n on velocity profiles, temperature profiles, skin-friction coefficients, and local Nusselt number are presented. The results of the present general theory agree well with previously published results for the case of constant wall temperature (the only case with quantitative solutions that were available in the literature). Subtle new flow physics, such as a sharp reduction in the Nusselt number with increasing Prandtl number when mass injection is present and the Prandtl number is large, has been elucidated. Nomenclature a = dimensional constant in the power-law variation of wall heat flux b = dimensional constant in the power-law variation of wall temperature c f  x = local skin-friction coefficient F = reduced nondimensional stream function G, g = reduced nondimensional temperatures h = local heat transfer coefficient, q w   x∕  T w   x −  T ∞  k = thermal conductivity of the fluid L = reference length of the plate in  x direction m = exponent in the power-law variation of wall heat flux n = exponent in the power-law variation of wall temperature Nu  x = local Nusselt number, h  x∕k Pr = Prandtl number, ν∕α Re  x = local Reynolds number, u ∞ L∕ν  T ∞ = temperature of the fluid u = nondimensional axial velocity component defined as, u   u∕  u ∞   u = axial velocity component  u ∞ = freestream velocity  v = normal velocity component  v w   x = transpiration velocity through the permeable wall ~ v, v = nondimensional normal velocity component defined as ~ v   v∕  u ∞  and v  ~ v  Re p , respectively x = nondimensional horizontal coordinate defined as x   x∕L  x = horizontal coordinate  y = vertical coordinate ~ y, y = nondimensional vertical coordinate defined as ~ y   y∕L and y  ~ y  Re p , respectively Greek symbols α = thermal diffusivity η = similarity variable θ, θ wt = nondimensional temperatures μ = dynamic viscosity ν = kinematic viscosity ξ s = dimensionless suction or injection parameter ψ = nondimensional stream function Subscripts w = condition at the wall wt = for the case when wall temperature is fixed ∞ = condition in freestream Superscripts 0 = differentiation with respect to η I. Introduction E XTERNAL forced convection is of theoretical as well as engineering importance. It is a fundamental topic in viscous fluid flow and heat transfer. It arises in many engineering applica- tions involving heat exchangers, turbine blades, aircrafts and automobiles, electronic devices, etc. Hence, the phenomenon has been extensively studied experimentally, analytically, and numeri- cally. As an example, the pioneering work of Prandtl and Blasius laid the foundation of the fluid dynamic studies of boundary layers over a solid surface. In this article, a similarity theory has been developed for forced convection over a horizontal flat plate with suction and blowing when the wall temperature or wall heat flux exhibits power- law variation. Flows with suction and blowing may arise in applications involving mass transfer, transpiration cooling, and boundary-layer control. The analysis of forced convection heat transfer from semi-infinite flat plates with uniform wall temperature or uniform wall heat flux is standard and can be found in [1–3]. Sartori [4] presented a comparison among various existing correlations for external forced convection flow over horizontal surfaces. Laminar transient forced convection heat transfer from an isothermal horizontal flat plate has Received 11 September 2012; revision received 24 December 2012; accepted for publication 26 January 2013; published online 23 May 2013. Copyright © 2013 by the authors. Published by the American Institute of Aeronautics and Astronautics, Inc., with permission. Copies of this paper may be made for personal or internal use, on condition that the copier pay the $10.00 per-copy fee to the Copyright Clearance Center, Inc., 222 Rosewood Drive, Danvers, MA 01923; include the code 1533-6808/13 and $10.00 in correspondence with the CCC. *Research Scholar, Mechanical Engineering Department; subhosamanta@ iitkgp.ac.in. † Professor, Mechanical Engineering Department; a.guha@mech.iitkgp .ernet.in (Corresponding Author). 506 JOURNAL OF THERMOPHYSICS AND HEAT TRANSFER Vol. 27, No. 3, July–September 2013 Downloaded by UNIVERSITY OF CALIFORNIA on August 18, 2013 | http://arc.aiaa.org | DOI: 10.2514/1.T4033