Thermodynamics HW Solutions 441

Thermodynamics HW Solutions 441 -...

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Chapter 5 Numerical Methods in Heat Conduction 5-51 "!PROBLEM 5-51" "GIVEN" k=180 "[W/m-C], parameter to be varied" g_dot=1E7 "[W/m^3], parameter to be varied" DELTAx=0.10 "[m]" DELTAy=0.10 "[m]" d=1 "[m], depth" "Temperatures at the selected nodes are also given in the figure" "ANALYSIS" "(a)" l=DELTAx T_1=T_2 "due to symmetry" T_3=T_4 "due to symmetry" "Using the finite difference method, the two equations for the two unknown temperatures are determined to be" 120+120+T_2+T_3-4*T_1+(g_dot*l^2)/k=0 150+200+T_1+T_4-4*T_3+(g_dot*l^2)/k=0 "(b)" "The rate of heat loss from the top surface can be determined from an energy balance on a volume element whose height is l/2, length 3*l, and depth d=1 m"
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Unformatted text preview: -Q_dot_top+g_dot*(3*l*d*l/2)+2*(k*(l*d)/2*(120-100)/l+k*l*d*(T_1-100)/l)=0 k [W/m.C] T 1 [C] T 3 [C] Q top [W] 10 5134 5161 250875 30.53 1772 1799 252671 51.05 1113 1141 254467 71.58 832.3 859.8 256263 92.11 676.6 704.1 258059 112.6 577.7 605.2 259855 133.2 509.2 536.7 261651 153.7 459.1 486.6 263447 174.2 420.8 448.3 265243 194.7 390.5 418 267039 215.3 366 393.5 268836 235.8 345.8 373.3 270632 256.3 328.8 356.3 272428 276.8 314.4 341.9 274224 297.4 301.9 329.4 276020 317.9 291 318.5 277816 338.4 281.5 309 279612 358.9 273 300.5 281408 379.5 265.5 293 283204 400 258.8 286.3 285000 5-44...
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