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Thermodynamics HW Solutions 421

Thermodynamics HW Solutions 421 - Chapter 5 Numerical...

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Chapter 5 Numerical Methods in Heat Conduction 5-34 "!PROBLEM 5-34" "GIVEN" k=15.1 "[W/m-C], parameter to be varied" "epsilon=0.6 parameter to be varied" T_0=95 "[C]" T_infinity=25 "[C]" w=0.002 "[m]" s=0.01 "[m]" L=0.18 "[m]" h=13 "[W/m^2-C]" T_surr=295 "[K]" DELTAx=0.015 "[m]" sigma=5.67E-8 "[W/m^2-K^4], Stefan-Boltzmann constant" "ANALYSIS" "(b)" M=L/DELTAx+1 "Number of nodes" A=w*s p=2*(w+s) "Using the finite difference method, the five equations for the unknown temperatures at 12 nodes are determined to be" T_0-2*T_1+T_2+h*(p*DELTAx^2)/(k*A)*(T_infinity- T_1)+epsilon*sigma*(p*DELTAx^2)/(k*A)*(T_surr^4-(T_1+273)^4)=0 "mode 1" T_1-2*T_2+T_3+h*(p*DELTAx^2)/(k*A)*(T_infinity- T_2)+epsilon*sigma*(p*DELTAx^2)/(k*A)*(T_surr^4-(T_2+273)^4)=0 "mode 2" T_2-2*T_3+T_4+h*(p*DELTAx^2)/(k*A)*(T_infinity- T_3)+epsilon*sigma*(p*DELTAx^2)/(k*A)*(T_surr^4-(T_3+273)^4)=0 "mode 3" T_3-2*T_4+T_5+h*(p*DELTAx^2)/(k*A)*(T_infinity- T_4)+epsilon*sigma*(p*DELTAx^2)/(k*A)*(T_surr^4-(T_4+273)^4)=0 "mode 4" T_4-2*T_5+T_6+h*(p*DELTAx^2)/(k*A)*(T_infinity-
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