Chapter 3, Problem 3.93P

In Section 5.2 we noted that the value of the Biot number significantly influences the nature of the temperature distribution in a solid during a transient conduction process. Reinforce your understanding of this important concept by using the ¡HT model for one-dimensional transient conduction to determine radial temperature distributions in a 30-mm-diameter, stainless steel rod $\left(k=15W/m\cdot K,\rho =8000kg/m^3,c_p=475J/kg\cdot K\right)$, as it is cooled from an initial uniform temperature of 325°C by a fluid at 25°C. For the following values of the convection coefficient and the designated times, determine the radial temperature distribution: $h=100W/m^2\cdot K$ $\left(t=0,100,500s\right)$; $h=1000W/m^2\cdot K\left(t=0,10,50s\right)$; $h=5000W/m^2\cdot K\left(t=0,1,5,25s\right)$. Prepare a separate graph for each convection coefficient, on which temperature is plotted as a function of dimensionless radius at the designated times.