Chapter 1, Problem 1.40P

Chips of width $L=15\text{mm}$ on a side are mounted to a substrate that is installed in an enclosure whose walls and air are maintained at a temperature of $T_{\text{sur}}=25°\text{C}\text{.}$ The chips have an emissivity of $\epsilon =0.60$ and a maximum allowable temperature of $T_S=85°\text{C}\text{.}$

1. If heat is rejected from the chips by radiation and natural convection, what is the maximum operating power of each chip? The convection coefficient depends on the chip-to-air temperature difference and may be approximated as $h=C{\left(T_s-T_{\infty }\right)}^{1/4},$ where $C=4.2{\text{W/m}}^{\text{2}}\cdot {\text{K}}^{5/4}.$ If a fan is used to maintain airflow through the enclosure and heat transfer is by forced convection, with $h=250{\text{W/m}}^{\text{2}}\cdot \text{K,}$ what is the maximum operating power?