Solution Methodology for One-Dimensional Transient Conduction There are several different methods for solving 1-D, transient conduction problems that begin as a uniform temperature and are suddenly exposed to convection. Lumped Capacitance Method (LCM) A solid body changes temperature with time in a spatially uniform manner p bt i VC hA b e T T T t T ρ = = − − − ∞ ∞ ) ( The density, ρ , and the specific heat, C p , are of the solid body. The Biot number is a non-dimensional number that expresses the ratio of convection away from a solid body to the conduction within the solid body. Criteria for LCM : Biot Number based on volume to surface area ratio must be less than 0.1 A V L k hL Bi c c = ≤ = 1 .0 Looking a little more closely at the exponent of the solution: Number Fourier , where 2 c p c c c p L t Fo C k BiFo t L L k L h t VC hA bt α = = = = = The Fourier number is a non-dimensional time. If LCM is not valid
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