Consider the oven of Problem 1.54. The walls of the oven consist of L = 30-mm-thick layers of insulation characterized by k_ins = 0.03 W/m · K that are sandwiched between two thin layers of sheet metal. The exterior surface of the oven is exposed to air at 23°C with h_ext = 2 W/m² · K. The interior oven air temperature is 180°C. Neglecting radiation heat transfer, determine the steady-state heat flux through the oven walls when the convection mode is disabled and the free convection coefficient at the inner oven surface is h_fr = 3 W/m² · K. Determine the heat flux through the oven walls when the convection mode is activated, in which case the forced convection coefficient at the inner oven surface is h_fo = 27 W/m² · K. Does operation of the oven in its convection mode result in significantly increased heat losses from the oven to the kitchen? Would your conclusion change if radiation were included in your analysis?

Data From Problem 1.54

Convection ovens operate on the principle of inducing forced convection inside the oven chamber with a fan. A small cake is to be baked in an oven when the convection feature is disabled. For this situation, the free convection coefficient associated with the cake and its pan is h_fr = 3 W/m² · K. The oven air and wall are at temperatures T_∞ T_sur = 180°C. Determine the heat flux delivered to the cake pan and cake batter when they are initially inserted into the oven and are at a temperature of T_i =
24°C. If the convection feature is activated, the forced convection heat transfer coefficient is h_fo = 27 W/m² · K. What is the heat flux at the batter or pan surface when the oven is operated in the convection mode? Assume a value of 0.97 for the emissivity of the cake batter and pan.