Chapter 4, Problem 4.67P

A common arrangement for heating a large surface area is to move warm air through rectangular ducts below the surface. The ducts are square and located midway between the top and bottom surfaces that are exposed to room air and insulated, respectively.

For the condition when the floor and duct temperatures are 30 and 80°C, respectively, and the thermal conductivity of concrete is $1.4\text{W/m}\cdot \text{K,}$ calculate the heat rate from each duct, per unit length of duct. Use a grid spacing with $\Delta x=2\Delta y,$ where $\Delta y=0.125L$ and $L=150\text{mm}\text{.}$