Thermodynamics HW Solutions 430

Thermodynamics HW Solutions 430 - are determined to...

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Chapter 5 Numerical Methods in Heat Conduction 5-39 "!PROBLEM 5-39" "GIVEN" t_pipe=0.004 "[m]" k=52 "[W/m-C]" epsilon=0.8 D_o_pipe=0.10 "[m]" t_flange=0.01 "[m]" D_o_flange=0.20 "[m]" T_steam=200 "[C], parameter to be varied" h_i=180 "[W/m^2-C]" T_infinity=8 "[C]" "h=25 [W/m^2-C], parameter to be varied" T_surr=290 "[K]" DELTAx=0.01 "[m]" sigma=5.67E-8 "[W/m^2-K^4], Stefan-Boltzmann constant" "ANALYSIS" "(b)" DELTAx_1=t_pipe "the distance between nodes 0 and 1" DELTAx_2=t_flange "nodal spacing along the flange" L=(D_o_flange-D_o_pipe)/2 M=L/DELTAx_2+2 "Number of nodes" t=2*t_flange "total thixkness of the flange" "The values of radii at the nodes and between the nodes /-(the midpoints) are" r_0=0.046 "[m]" r_1=0.05 "[m]" r_2=0.06 "[m]" r_3=0.07 "[m]" r_4=0.08 "[m]" r_5=0.09 "[m]" r_6=0.10 "[m]" r_01=0.048 "[m]" r_12=0.055 "[m]" r_23=0.065 "[m]" r_34=0.075 "[m]" r_45=0.085 "[m]" r_56=0.095 "[m]" "Using the finite difference method, the five equations for the unknown temperatures at 7 nodes
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Unformatted text preview: are determined to be" h_i*(2*pi*t*r_0)*(T_steam-T_0)+k*(2*pi*t*r_01)*(T_1-T_0)/DELTAx_1=0 "node 0" k*(2*pi*t*r_01)*(T_0-T_1)/DELTAx_1+k*(2*pi*t*r_12)*(T_2-T_1)/DELTAx_2+2*2*pi*t*(r_1+r_12)/2*(DELTAx_2/2)*(h*(T_infinity-T_1)+epsilon*sigma*(T_surr^4-(T_1+273)^4))=0 "node 1" k*(2*pi*t*r_12)*(T_1-T_2)/DELTAx_2+k*(2*pi*t*r_23)*(T_3-T_2)/DELTAx_2+2*2*pi*t*r_2*DELTAx_2*(h*(T_infinity-T_2)+epsilon*sigma*(T_surr^4-(T_2+273)^4))=0 "node 2" k*(2*pi*t*r_23)*(T_2-T_3)/DELTAx_2+k*(2*pi*t*r_34)*(T_4-T_3)/DELTAx_2+2*2*pi*t*r_3*DELTAx_2*(h*(T_infinity-T_3)+epsilon*sigma*(T_surr^4-(T_3+273)^4))=0 "node 3" k*(2*pi*t*r_34)*(T_3-T_4)/DELTAx_2+k*(2*pi*t*r_45)*(T_5-T_4)/DELTAx_2+2*2*pi*t*r_4*DELTAx_2*(h*(T_infinity-T_4)+epsilon*sigma*(T_surr^4-(T_4+273)^4))=0 "node 4" k*(2*pi*t*r_45)*(T_4-T_5)/DELTAx_2+k*(2*pi*t*r_56)*(T_6-T_5)/DELTAx_2+2*2*pi*t*r_5*DELTAx_2*(h*(T_infinity-T_5)+epsilon*sigma*(T_surr^4-(T_5+273)^4))=0 "node 5" 5-33...
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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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