Chapter 3: Conduction: One-dimensional transient and two-dimensional steady state
Abstract
This chapter discusses the analytical approaches to solving one-dimensional transient and two-dimensional steady state problems. We show that the pertinent nondimensional parameters for transient conduction are the Biot number (Bi) and Fourier number (Fo) and discuss their physical meaning. This is followed by a search for simpler solutions to the asymptotic variants of the problem. These are (1) lumped capacitance method and (2) semi-infinite approximation. We discuss the physical and mathematical conditions necessary for these approximations to be valid. The problem in its full strength is then solved using the method of separation of variables, which ...
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