Chapter 3, Problem 3.4P

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

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