Thermodynamics HW Solutions 481

Thermodynamics HW Solutions 481 - Chapter 5 Numerical...

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Chapter 5 Numerical Methods in Heat Conduction The upper limit of the time step Δ t is determined from the stability criteria that requires the coefficient of in the T expression (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 T in 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 T m i m i + 1 i 3 T i 3 1 + 14 4 0 1 41 4 1 2 −− ≥ → + →≤ + ττ τ α hl kh l k t l hl k (/ ) ) Δ since . Substituting the given quantities, the maximum allowable value of the time step is determined to be τα tl / 2 s 3 . 16 C)] W/m. 15 /( m) 015 . 0 )( C . W/m 80 ( 1 /s)[ m 10 2 . 3 ( 4 ) m 015 . 0 ( 2 2 6 2 = ° ° + × 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.

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