EXPLICIT, RIGOROUS SOLUTIONS TO 2-DIMENSIONAL HEAT-TRANSFER - 2-COMPONENT MEDIA AND OPTIMIZATION OF COOLING FINS

New analytical solutions to the problem of steady heat conduction from the wall with longitudinal fins to the environment are derived. Withi n the two media two temperature fields are harmonic functions with rig orous conjugation of temperature and normal flux along the interface b etween the two components. First, for high values of the ratio e = k(1 )/k(2), with k(1) and k(2) being thermal conductivities of the grooved wall and environment, respectively, we derive the optimal fin contour providing extreme heat flux (total heat dissipation) from the fin sur face at prescribed fin cross-sectional area. This optimizer is found i n the class of arbitrary curves and both necessary and sufficient extr emum conditions are satisfied. The extreme line coincides with the con tour of constant hydraulic gradient calculated by Polubarinova-Kochina for a seepage how under a concrete dam. At arbitrary e the same isope rimetric problem is solved in the class of elliptic fins assuming fin spacing large enough to consider an isolated profile. Two non-trivial local extrema exist depending on e. For arbitrary e the case of long r ectangular fins with arbitrary direction of the outer field is studied . Streamline refraction illustrates non-trivial fluxes near the finger tips and roots. Copyright (C) 1996 Elsevier Science Ltd.