Chapter 1, Problem 1.17P

For a boiling process such as shown in Figure 1.5c, the ambient temperature $T_{\infty }$ in Newton’s law of cooling is replaced by the saturation temperature of the fluid $T_{\text{sat}}.$ Consider a situation where the heat flux from the hot plate is $q"=20\times {10}^5{\text{W/m}}^{\text{2}}.$ If the fluid is water at atmospheric pressure and the convection heat transfer coefficient is $h_w=20\times {10}^3{\text{W/m}}^{\text{2}}\cdot \text{K,}$ determine the upper surface temperature of the plate, $T_{s,w}.$ In an effort to minimize the surface temperature, a technician proposes replacing the water with a dielectric fluid whose saturation temperature is $T_{\text{sat,d}}=52°\text{C}\text{.}$ If the heat transfer coefficient associated with the dielectric fluid is $h_d=3\times {10}^3{\text{W/m}}^{\text{2}}\cdot \text{K,}$ will the technician’s plan work?