## Heat transfer 101

"Why else would it be so infrequently addressed in the engineering trade press?" asks David Dearth, consulting engineer and president of To reacquaint readers with its terms and calculations, here is a heat-transfer problem that will be solved two ways. One way, by hand, will provide a review of heat-transfer phenomena. The second way encourages readers to repeat the problem in their FEA programs and compare results with the hand calculation. It's not surprising that finite-element methods are often applied to investigate the cooling performance of fans and heat sinks. FEA also allows investigating the effects of temperature changes on stress and deflections in a structure. For simplicity, this article considers only steady-state conditions and leaves transients for another time. "Before any finite-element work, I recommend doing a few sample or warm-up problems with known solutions," says Dearth. The sample problem is a cooling fin idealized as a uniform rod. The cylindrical fin has a heat source at the base with temperature, T A first step finds an average heat-transfer film coefficient, Differential equations for a conduction-convection system for the model are in the Holman text ( "You can solve most heat-transfer problems for simple geometry using classical equations," says Dearth. "However, in real life, geometries are not simple and temperature distributions are not always uniform," he says. One problem with real life is that heat-transfer characteristics of the selected material are often a function of temperature, or may not be the same in orthogonal directions, or both. When material properties are independent of direction along which they are measured, the material is called isotropic. When material properties differ in two or more orthogonal directions, the material is called orthotropic. |