Thermodynamics HW Solutions 482

Thermodynamics HW Solutions 482 - Chapter 5 Numerical...

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Chapter 5 Numerical Methods in Heat Conduction 5-88 "!PROBLEM 5-88" "GIVEN" T_i=140 "[C]" k=15 "[W/m-C]" alpha=3.2E-6 "[m^2/s]" g_dot=2E7 "[W/m^3]" T_bottom=140 "[C]" T_infinity=25 "[C]" h=80 "[W/m^2-C]" q_dot_L=8000 "[W/m^2]" DELTAx=0.015 "[m]" DELTAy=0.015 "[m]" "time=120 [s], parameter to be varied" "ANALYSIS" l=DELTAx DELTAt=15 "[s]" tau=(alpha*DELTAt)/l^2 RhoC=k/alpha "RhoC=rho*C" "The technique is to store the temperatures in the parametric table and recover them (as old temperatures) using the variable ROW. The first row contains the initial values so Solve Table must begin at row 2. Use the DUPLICATE statement to reduce the number of equations that need to be typed. Column 1 contains the time, column 2 the value of T[1], column 3, the value of T[2], etc., and column 10 the Row." Time=TableValue('Table 1',Row-1,#Time)+DELTAt Duplicate i=1,8 T_old[i]=TableValue('Table 1',Row-1,#T[i]) end "Using the explicit finite difference approach, the eight equations for the eight unknown temperatures are determined to be"
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