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Calculating Heat Flow The temperature at any point (x, 37,2) of a east-iron is given by T(x, y, z) = (x2 + y2)z. Compare the heat ows across the boundary of the four solid given below, by assuming that all are oriented outward and are built with the cast-iron with the thermal conductivity of 55. What are the minimum and maximum heat ows and why? (a) A cylinder given by inequalities x2 + 3/2 S 1, 1 S 2 S 4. (b) A sphere given by inequalities 0 S x2 + y2 + z2 5 1. (c) A shell given by inequalities 1 S x2 + y2 + z2 5 4. (d) A cone given by the inequalities 22 = x2 + 312,0 5 z S 4