Chapter 3, Problem 3.4P

The rear window of an automobile is defogged by attachinga thin, transparent, film-type heating element to itsinner surface. By electrically heating this element, a uniformheat flux may be established at the inner surface.

1. For 4-mm-thick window glass, determine the electricalpower required per unit window area to maintain aninner surface temperature of $15°\text{C}$ when the interior airtemperature and convection coefficient are $T_{\infty ,i}=25°\text{C}$ and $h_i=10{\text{W/m}}^2\cdot \text{K,}$ while the exterior (ambient) airtemperature and convection coefficient are $T_{\infty ,o}=-10°\text{C}$ and $h_o=65{\text{W/m}}^2\cdot \text{K}\text{.}$ In practice $T_{\infty ,o}$ and $h_o$ vary according to weatherconditions and car speed. For values of $h_o=2,20,65,$ and $100{\text{W/m}}^2\cdot \text{K,}$ determine and plot theelectrical power requirement as a function of $T_{\infty ,o}$ for $-30\le T_{\infty ,o}\le 0°\text{C}\text{.}$ From your results, what can youconclude about the need for heater operation at lowvalues of $h_o?$ How is this conclusion affected by thevalue of $T_{\infty ,o}?$ If $h\infty V^n,$ where V is the vehicle speedand n is a positive exponent, how does the vehiclespeed affect the need for heater operation?