HEAT TRANSFER - EXAMPLE 5.3 : In a cylinder with a hollow, let a is outside radius and b is the inside radius. In a steady state temperature distribution with no heat generation, the differential equation is (d / dr) (r dT / dr) = 0 where r is for radius and T is for temperature. (a) Integrate the heat equation above into T(r) in term of r. (b) At r = a, T = c; at r = b, T = d. Find the heat equation of T(r) in term of r, a, b, c, d.
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HEAT TRANSFER - ANSWER 5.3 : Let r (dT / dr) = e, then dT / dr = e / r. T(r) = e ln r + f by integrating both sides where e and f are constants. (b) Let c = e ln a + f and d = e ln b + f. Subtracting both equations gives c - d = e (ln a - ln b) = e ln (a / b). Then e = (c - d) / [ ln (a / b) ] and f = d - e ln b. T(r) = e ln r + d - e ln b = e ln (r / b) + d = (c - d) [ ln (a / b) ] ln (r / b) + d. The answer is given by Kang Chuen Tat; PO Box 6263, Dandenong, Victoria VIC 3175, Australia; SMS +61405421706; chuentat@hotmail.com; http://kangchuentat.wordpress.com.
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