Chapter 5 Numerical Methods in Heat Conduction The upper limit of the time step Δtis determined from the stability criteria that requires the coefficient of in the Texpression (the primary coefficient) be greater than or equal to zero for all nodes. The smallest primary coefficient in the 8 equations above is the coefficient of Tin the expression since it is exposed to most convection per unit volume (this can be verified), and thus the stability criteria for this problem can be expressed as Tmimi+1i3Ti31+14 401414 12−−≥ →≤+→≤+ττταhlkhlktlhl k(/))Δsince . Substituting the given quantities, the maximum allowable value of the time step is determined to be τα=Δtl/2s3.16C)]W/m.15/(m)015.0)(C.W/m80(1/s)[m102.3(4)m015.0(2262=°°+×≤Δ
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This note was uploaded on 01/22/2012 for the course PHY 4803 taught by Professor Dr.danielarenas during the Fall '10 term at UNF.