Chapter 4, Problem 4.12P

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

1. Determine the two-dimensional shape factor for theobject for $a=10\text{mm,}b=12\text{mm}\text{.}$ Determine the two-dimensional shape factor for theobject for $a=10\text{mm,}b=15\text{mm}\text{.}$ Use the alternative conduction analysis of Section3.2 to estimate the shape factor for parts (a) and(b). Compare the values of the approximate shapefactors of the alternative conduction analysis to thetwo-dimensional shape factors of parts (a) and (b).
2. For $T_1=100°\text{C}$ and $T_2=60°\text{C,}$ determine the heattransfer rate per unit depth for $k=15\text{W/m}\cdot \text{K}$ forparts (a) and (b).