Chapter 4, Problem 4.12P

A two-dimensional object is subjected to isothermal conditions at its left and right surfaces, as shown in the schematic. Both diagonal surfaces are adiabatic and the depth of the object is $L=100\text{mm}\text{.}$

1. Determine the two-dimensional shape factor for the object for $a=10\text{mm,}b=12\text{mm}\text{.}$
2. Determine the two-dimensional shape factor for the object for $a=10\text{mm,}b=15\text{mm}\text{.}$
3. Use the alternative conduction analysis of Section 3.2 to estimate the shape factor for parts (a) and (b). Compare the values of the approximate shape factors of the alternative conduction analysis to the two-dimensional shape factors of parts (a) and (b).
4. For $T_1=100°\text{C}$ and $T_2=60°\text{C,}$ determine the heat transfer rate per unit depth for $k=15\text{W/m}\cdot \text{K}$for parts (a) and (b).