ON THERMAL-BOUNDARY LAYERS ON A FLAT-PLATE SUBJECTED TO A VARIABLE HEAT-FLUX

The problem of a steady forced convection thermal boundary-layer past a flat plate with a prescribed surface heat flux proportional to (1 x(2))(m) (m a constant) is investigated both analytically and numerica lly. In view of the present formulation, the governing equations reduc e to the well-known Blasius similarity equation and to the full bounda ry-layer energy equation with two parameters: the wall flux exponent n z and Prandtl number Pr. The range of existence of solutions is consid ered, it being shown that solutions for both x small and x large exist only for in > -1/2. However, for m less than or equal to -1/2 the asy mptotic structure for x large is found to be different for m < -1/2 an d m = -1/2, respectively. These asymptotic solutions for large x are d erived and compared with numerical solutions of the full boundary-laye r equation. A very good agreement between these asymptotic solutions a nd numerical simulations are found in the range of Prandtl numbers con sidered, (C) 1998 Elsevier Science Inc. All rights reserved.