ENGINEERINGA pan is used to boil water by placing it on a stove, from which heat is transferred at a fixed rate $q_{o}$. There are two stages to the process. In Stage 1, the water is taken from its initial (room) temperature $T_{i}$ to the boiling point, as heat is transferred from the pan by natural convection. During this stage, a constant value of the convection coefficient h may be assumed, while the bulk temperature of the water increases with time, $T_{\infty}=T_{\infty}(t)$. In Stage 2, the water has come to a boil, and its temperature remains at a fixed value, $T_{\infty}=T_{b}$, as heating continues. Consider a pan bottom of thickness L and diameter D, with a coordinate system corresponding to x=0 and x=L for the surfaces in contact with the stove and water, respectively. (a) Write the form of the heat equation and the boundary/initial conditions that determine the variation of temperature with position and time, T(x, t), in the pan bottom during Stage 1. Express your result in terms of the parameters $q_{o}$, D, L, h, and $T_{\infty}$, as well as appropriate properties of the pan material. (b) During Stage 2, the surface of the pan in contact with the water is at a fixed temperature, T(L, t)=$T_{L}>T_{b}$. Write the form of the heat equation and boundary conditions that determine the temperature distribution T(x) in the pan bottom. Express your result in terms of the parameters $q_{o}$, D, L, and $T_{L}$, as well as appropriate properties of the pan material. 1st EditionDavid Besanko, Mark Shanley, Scott Schaefer215 solutions

3rd EditionOctave Levenspiel228 solutions

10th EditionErwin Kreyszig4,134 solutions

9th EditionAlan T. McDonald, John W Mitchell, Philip J. Pritchard, Robert W Fox1,024 solutions