Chapter 4, Problem 4.65P

Consider a long bar of square cross section (0.8 m to theside) and of thermal conductivity $2\text{W/m}\cdot \text{K}\text{.}$ Three of thesesides are maintained at a uniform temperature of $\text{300°C}\text{.}$ The fourth side is exposed to a fluid at $\text{100°C}$ for whichthe convection heat transfer coefficient is $\text{10}{\text{W/m}}^{\text{2}}\cdot \text{K}\text{.}$

1. Using an appropriate numerical technique with agrid spacing of 0.2 m, determine the midpoint temperatureand heat transfer rate between the bar andthe fluid per unit length of the bar.
2. Reducing the grid spacing by a factor of 2,determine the midpoint temperature and heattransfer rate. Plot the correspondingtemperaturedistribution across the surface exposed to the fluid.Also, plot the 200 and $\text{250°C}$ isotherms.