By John H Lienhard

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Don Quixote, M. 1 The heat diffusion equation Objective We must now develop some ideas that will be needed for the design of heat exchangers. The most important of these is the notion of an overall heat transfer coefficient. This is a measure of the general resistance of a heat exchanger to the flow of heat, and usually it must be built up from analyses of component resistances. In particular, we must know how to predict h and how to evaluate the conductive resistance of bodies more complicated than plane passive walls.

This statement suggests that energy is flowing from the body. 3 is constantly replenished, the body temperature need not change. Then with the help of eqn. 3) we get, from eqn. 17) This is the steady-state form of Newton’s law of cooling, as it is usually quoted, although Newton never wrote such an expression. The constant h is the film coefficient or heat transfer coefficient. The bar over h indicates that it is an average over the surface of the body. Without the bar, h denotes the “local” value of the heat transfer coefficient at a point on the surface.

1 51 These are: ∇T q =− |q| |∇T | This says that q and ∇T are exactly opposite one another in direction |q| ∝ |∇T | This says that the magnitude of the heat flux is directly proportional to the temperature gradient and Notice that the heat flux is now written as a quantity that has a specified direction as well as a specified magnitude. 3) Fortunately, most materials (though not all of them) are very nearly homogeneous. Thus we can usually write k = k(T ). The assumption that we really want to make is that k is constant.

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