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Thermodynamics HW Solutions 452

Thermodynamics HW Solutions 452 - Chapter 5 Numerical...

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Unformatted text preview: Chapter 5 Numerical Methods in Heat Conduction 5-57 "!PROBLEM 5-57" "GIVEN" k=1.4 "[W/m-C]" A_flow=0.20*0.40 "[m^2]" t=0.10 "[m]" T_i=280 "[C], parameter to ve varied" h_i=75 "[W/m^2-C]" T_o=15 "[C]" h_o=18 "[W/m^2-C]" epsilon=0.9 "parameter to ve varied" T_sky=250 "[K]" DELTAx=0.10 "[m]" DELTAy=0.10 "[m]" d=1 "[m], unit depth is considered" sigma=5.67E-8 "[W/m^2-K^4], Stefan-Boltzmann constant" "ANALYSIS" "(b)" l=DELTAx "We consider only one-fourth of the geometry whose nodal network consists of 10 nodes. Using the finite difference method, 10 equations for 10 unknown temperatures are determined to be" h_o*l/2*(T_o-T_1)+k*l/2*(T_2-T_1)/l+k*l/2*(T_5-T_1)/l+epsilon*sigma*l/2*(T_sky^4- (T_1+273)^4)=0 "Node 1" h_o*l*(T_o-T_2)+k*l/2*(T_1-T_2)/l+k*l/2*(T_3-T_2)/l+k*l*(T_6-T_2)/l+epsilon*sigma*l*(T_sky^4- (T_2+273)^4)=0 "Node 2" h_o*l*(T_o-T_3)+k*l/2*(T_2-T_3)/l+k*l/2*(T_4-T_3)/l+k*l*(T_7-T_3)/l+epsilon*sigma*l*(T_sky^4- (T_3+273)^4)=0 "Node 3" h_o*l*(T_o-T_4)+k*l/2*(T_3-T_4)/l+k*l/2*(T_8-T_4)/l+epsilon*sigma*l*(T_sky^4-(T_4+273)^4)=0...
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