Thermodynamics HW Solutions 477

Thermodynamics HW Solutions 477 - Chapter 5 Numerical...

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Chapter 5 Numerical Methods in Heat Conduction i i i i i i i i i i i i i i i i i i i i T T T T m T T T T m T T T T m T T T T m T T T T m 5 6 4 1 5 4 5 3 1 4 3 4 2 1 3 2 3 1 1 2 1 2 0 1 1 ) 2 1 ( ) ( : ) 5 ( 5 Node ) 2 1 ( ) ( : ) 4 ( 4 Node ) 2 1 ( ) ( : ) 3 ( 3 Node ) 2 1 ( ) ( : ) 2 ( 2 Node ) 2 1 ( ) ( : ) 1 ( 1 Node τ + + = = + + = = + + = = + + = = + + = = + + + + + Node 6 t T T C x A x T T kA q A T T A h i i i i i i i Δ Δ = Δ + + 6 1 6 6 5 solar 6 out out 2 + ) ( ρ κ & or k x q T k x h T T k x h T i i i i i Δ + Δ + Δ = + solar out out 5 6 out 1 6 2 2 2 + 2 2 1 & ττ where L = 0.30 m, k = 0.70 W/m.°C, , T α 044 10 6 . m 2 / s out and are as given in the table, & q solar = 0.76 h out = 3.4 W/m 2 . ° C, T in = 20 ° C, h in = 9.1 W/m 2 . ° C, and Δ x = 0.05 m. Next we need to determine the upper limit of the time step Δ t from the stability criteria since we are using the explicit method. This requires the identification of the smallest primary coefficient in the system. We know that the boundary nodes are more restrictive than the interior nodes, and thus we examine the formulations of the boundary nodes 0 and 6 only. The smallest and thus the most restrictive
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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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