Chapter 4, Problem 4.76P

The shape factor for conduction through the edge of adjoining walls for which $D>L/5,$ where D and L are the wall depth and thickness, respectively. is shown in Table 4.1. The two-dimensional symmetrical element of the edge. which is represented by inset (a), is bounded by the diagonal symmetry adiabat and a section of the wall thickness over which the temperature distribution is assumed to be linear between $T_1$ and $T_2$ .

1. Using the nodal network of inset (a) with $L=40\text{mm,}$ determine the temperature distribution in the element for $T_1=100°\text{C}$ and $T_2=0°\text{C}\text{.}$ Evaluate the heat rate per unit depth $\left(D=1\text{m}\right)$ if $k=1\text{W/m}\cdot \text{K}\text{.}$Determine the corresponding shape factor for the edge. and compare your result with that from Table 4.1.
2. Choosing a value of $n=1$ or $n=1.5,$ establish a nodal network for the trapezoid of inset (b) and determine the corresponding temperature field. Assess the validity of assuming linear temperature distributions across sections a—a and b—b.