Thermodynamics HW Solutions 327

Thermodynamics HW Solutions 327 - V=4/3*pi*r_o^3 m=rho*V

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Chapter 4 Transient Heat Conduction 4-51 "!PROBLEM 4-51" "GIVEN" T_infinity=-15 "[C]" "T_i=20 [C], parameter to be varied" h=8 "[W/m^2-C]" r_o=0.09/2 "[m]" time=1*3600 "[s]" "PROPERTIES" k=0.513 "[W/m-C]" rho=840 "[kg/m^3]" C_p=3.6 "[kJ/kg-C]" alpha=1.3E-7 "[m^2/s]" "ANALYSIS" Bi=(h*r_o)/k "From Table 4-1 corresponding to this Bi number, we read" lambda_1=1.3525 A_1=1.1978 tau=(alpha*time)/r_o^2 (T_o-T_infinity)/(T_i-T_infinity)=A_1*exp(-lambda_1^2*tau) (T_r-T_infinity)/(T_i-T_infinity)=A_1*exp(- lambda_1^2*tau)*Sin(lambda_1*r_o/r_o)/(lambda_1*r_o/r_o)
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Unformatted text preview: V=4/3*pi*r_o^3 m=rho*V Q_max=m*C_p*(T_i-T_infinity) Q/Q_max=1-3*(T_o-T_infinity)/(T_i-T_infinity)*(Sin(lambda_1)-lambda_1*Cos(lambda_1))/lambda_1^3 T i [C] T o [C] T r [C] Q [kJ] 2 -1.658 -5.369 6.861 4 -0.08803 -4.236 7.668 6 1.482 -3.103 8.476 8 3.051 -1.97 9.283 10 4.621 -0.8371 10.09 12 6.191 0.296 10.9 14 7.76 1.429 11.7 16 9.33 2.562 12.51 18 10.9 3.695 13.32 20 12.47 4.828 14.13 22 14.04 5.961 14.93 24 15.61 7.094 15.74 26 17.18 8.227 16.55 28 18.75 9.36 17.35 30 20.32 10.49 18.16 4-38...
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