Chapter 7, Problem 7.35P

One hundred electrical components, each dissipating 25 W, are attached to one surface of a square $\left(0.2\text{m}\times 0.2\text{m}\right)$ copper plate, and all the dissipated energy is transferred to water in parallel flow over the opposite surface. A protuberance at the leading edge of the plate acts to trip the boundary layer, and the plate itself may be assumed to be isothermal. The water velocity and temperature are $u_{\infty }=2\text{m/s}$ and $T_{\infty }=17°\text{C,}$ and the water's thermophysical properties may be approximated as $v=0.96\times {10}^{-6}{\text{m}}^{\text{2}}\text{/s,}k=0.620\text{W/m}\cdot \text{K,}$ and $\mathrm{Pr}=\mathrm{5.2.}$

1. What is the temperature of the copper plate?
2. If each component has a plate contact surface area of $1{\text{cm}}^{\text{2}}$ and the corresponding contact resistance is $2\times {10}^{-4}{\text{m}}^{\text{2}}\cdot \text{K/W,}$ what is the component temperature? Neglect the temperature variation across the thickness of the copper plate.