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Thermodynamics HW Solutions 385

# Thermodynamics HW Solutions 385 - A_1_c=1.0050...

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Chapter 4 Transient Heat Conduction 4-117E "!PROBLEM 4-117E" "GIVEN" 2*L=1/12 "[ft]" 2*r_o_c=1/12 "[ft], c stands for cylinder" 2*r_o_s=1/12 "[ft], s stands for sphere" T_i=400 "[F]" T_infinity=75 "[F]" h=7 "[Btu/h-ft^2-F]" "time=5 [min], parameter to be varied" "PROPERTIES" k=15 "[Btu/h-ft-F]" alpha=0.333*Convert(ft^2/h, ft^2/min) "[ft^2/min]" "ANALYSIS" "For plane wall" Bi_w=(h*L)/k "From Table 4-1 corresponding to this Bi number, we read" lambda_1_w=0.1410 A_1_w=1.0033 tau_w=(alpha*time)/L^2 (T_o_w-T_infinity)/(T_i-T_infinity)=A_1_w*exp(-lambda_1_w^2*tau_w) "For long cylinder" Bi_c=(h*r_o_c)/k "From Table 4-1 corresponding to this Bi number, we read" lambda_1_c=0.1995
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Unformatted text preview: A_1_c=1.0050 tau_c=(alpha*time)/r_o_c^2 (T_o_c-T_infinity)/(T_i-T_infinity)=A_1_c*exp(-lambda_1_c^2*tau_c) "For sphere" Bi_s=(h*r_o_s)/k "From Table 4-1 corresponding to this Bi number, we read" lambda_1_s=0.2445 A_1_s=1.0060 tau_s=(alpha*time)/r_o_s^2 (T_o_s-T_infinity)/(T_i-T_infinity)=A_1_s*exp(-lambda_1_s^2*tau_s) time [min] T o,w [F] T o,c [F] T o,s [F] 5 312.3 247.9 200.7 10 247.7 166.5 123.4 15 200.7 123.4 93.6 20 166.5 100.6 82.15 25 141.6 88.57 77.75 30 123.4 82.18 76.06 35 110.3 78.8 75.41 40 100.7 77.01 75.16 45 93.67 76.07 75.06 50 88.59 75.56 75.02 55 84.89 75.3 75.01 60 82.2 75.16 75 4-96...
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