Heat Transfer Handbook part 24. The Heat Transfer Handbook provides succinct hard data, formulas, and specifications for the critical aspects of heat transfer, offering a reliable, hands-on resource for solving day-to-day issues across a variety of applications. | TWO-DIMENSIONAL STEADY CONDUCTION 221 Figure Hemispherical droplet condensing on an isothermal surface. Adapted from Poulikakos 1994. Method of Superposition The configuration considered in the preceding section involved one nonhomogeneous boundary condition either eq. or . When two or more nonhomogeneous boundary conditions occur the analysis can be split into two subanalyses each containing one nonhomogeneous boundary condition. Each subanalysis can then be solved using the method of separation of the aariahlcs. add the sum of the solutions to the two subanalyses will provide the solution to the overall problem. This approach is illustrated in Fig. for a rectangular plate with two homogeneous boundary conditions. The mathematical description ofthe problem is 0 where 9 T T3. The boundary conditions are 9 0 y 91 Ti T3 9 x 0 92 T2 T3 9 L y 0 9 x H 0 222 CONDUCTION HEAT TRANSFER 0 0 T L t2 Figure Rectangular plate with two nonhomogeneous boundary conditions. x 2 Figure Splitting the problem of Fig. into two subproblems with known solutions. 2 The problem is split into two subproblems as indicated in Fig. and the two solutions can be obtained from eq. with appropriate adjustment to account for the definition of 9 and the coordinates x and y. The sum of the two solutions is sinh 2n 1 nL H 2n 1 401 sinh 2n 1 n L - x H sin 2n 1 ny H 0 n n 0 È n n 0 sinh 2n 1 n H - y L sin 2n 1 nx L sinh 2n 1 nH L 2n 1 Conduction Shape Factor Method Although the conduction shape factor method does not give the temperature distribution it provides a simple equation for the rate of heat transfer TWO-DIMENSIONAL STEADY CONDUCTION 223 q kS AT where k is the thermal conductivity of the conducting medium AT the temperature difference driving the heat flow and S the conduction shape factor. Table provides expressions for the conduction shape factor for various two-dimensional .
