Question

. A leading manufacturer of household appliances is proposing a self-cleaning oven design that involves use of a composite window separating the oven cavity from the room air. The composite is to consist of two high-temperature plastics (A and B) of thickness LA = 2LB and thermal conductivities kA = 0.15 W/mK and kB = 0.08 W/mK. During the self-cleaning process, the oven wall and inside air temperatures, Tw and Ta are 400 ºC, while the room air temperature is 25 ºC. The inside convection and radiation heat transfer coefficients hi and hr as well as the outside convection coefficient ho, are each 25 W/m2K.

(a) Define and sketch the system and identify heat entering and leaving the system on the sketch.

(b) Write the conservation of energy equation (or energy balance) for this system.

(c) Construct a thermal resistance circuit for the system defined in part (a).

(d) Write an expression for the total resistances entering the system.

(e) What is the minimum window thickness, L = LA + LB, needed to ensure a temperature that is 50 ºC or less at the outer surface of the window? This temperature must not be exceeded for safety reasons

Answer 1

The thermal circuit can be constructed by recognizing that resistance to heat flow is associated with convection at the outer surface, conduction in the plastics, and convection and radiation at the inner surface. Accordingly, the circuit and the resistances are of the following form:

Since the outer surface temperature of the window, T_s,o is prescribed, the required window thickness may be obtained by applying an energy balance at this surface.

The total thermal resistance between the oven cavity and the outer surface of the window includes an effective resistance associated with convection and radiation, which act in parallel at the inner surface of the window, and the conduction resistances of the window materials. Hence,

substituting into the energy balance, it follows that

since L_B = L_A/2 = 0.0209 m,

L = L_A+ L_B= 0.0627 m = 62.7 mm