In the lumped capacitance model of transient conduction heat...

in the lumped capacitance model of transient conduction heat transfer, the system was assumed to be at a uniform temperature. Consider what would happen for an object cooled from an initial high temeprature by convection with a cold fluid. If the biot number was large, the temperature would change more or less quickly than the lumped capacitance model predicted? explain wht?

A long cylinder of 30-mm diameter, initially at a uniform temperature of 700 K, is suddenly quenched in a large, constant-temperature oil bath at 350 K. The cylinder properties are k = 1.7 W/m·K, c = 1600 J/kg·K, and ρ = 400 kg/m³, while the convection coefficient is 59 W/m²·K. Step 1 When deciding if the lumped capacitance method can be used, what is the value of the Biot number? Bi_c = 0.26 Step 2 When using the one-term approximation for transient 1-D conduction, what is the value of the applicable Biot number? Use Table 5.1. Bi = .52 Step 3 Using the one-term approximation, if Bi in Table 5.1 were equal to 1.0, what would be the value of C1 for this problem? C_1 = 1.207 Step 4 Use the one-term approximation method to solve for the Fourier number for reaching the surface temperature of 500 K. F_0 = Step 5 Solve for the time required for the surface of the cylinder to reach 500 K, in sec. t = sec

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