hw04-hints - ABE 484/584 CHOI HW4 1. [Self-cleaning Oven]...

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ABE 484/584 CHOI HW4 1. [ Self-cleaning Oven ] An engineer at a leading manufacturer of household appliances has newly proposed a self-cleaning oven that involves the use of a composite window separating the oven cavity from the room air. The composite is to consist of two high A = 2L B and thermal conductivities are k A = 0.15 W/m K and k B = 0.08 W/m K. During the self-cleaning process, the oven wall and air temperatures, T w and T a , are 400 o C, while the room air temperature, T , is 25 o C. The inside convection and radiation heat transfer coefficients, h i and h r , as well as the outside convection coefficient, h , are approximately 25 W/m 2 K. What is the minimum window thickness, L = L A + L B , needed to ensure a temperature that is 50 o C or less at the outer surface of the window (for safety reasons)? Estimate L when ignoring the radiative effect. Discuss the results. Department of Agricultural and Biosystems Engineering, The University of Arizona Material A k A = 0.15 Material B k B = 0.08 W/m K L A T s,o < 50 o C AIR T = 25 o C h = 25 W/m 2 K L B AIR T a = 400 o C h i = 25 W/m 2 K T w = 400 o C h r = 25 W/m 2 K
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ABE 484/584 CHOI Department of Agricultural and Biosystems Engineering, The University of Arizona
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ABE 484/584 CHOI 2. [ Microwave Oven ] A microwave oven operates on the principle that the application of a high frequency field causes electrically-polarized molecules in food to oscillate. The net effect is a uniform generation of thermal energy within the food, which enables it to be heated from refrigeration temperatures (0 o C) to 90 o C in as short a time as 30 seconds. Consider the process of cooking a slab of beef of thickness 2L in a microwave oven and compare it with cooking in a conventional oven, where each side of the slab is heated by radiation for a period of approximately 30 min. In each case, the meat is to be heated from 0 o C to a minimum temperature of 90 o C. Sketch the temperature distribution at selected times for each of the cooking processes. In particular, consider the time t o at which heating is initiated, a time t 1 during the heating process, the time t 2 corresponding to the conclusion of heating, and a time t 3 well into the subsequent cooling process. Assume: (1) 1D in x, (2) uniform internal heat generation for the microwave, and (3) uniform surface heating for the radiant oven. Department of Agricultural and Biosystems Engineering, The University of Arizona +x +L -L T(t) 90 o C 45 o C 0 o C +x +L -L T(t) 90 o C 45 o C 0 o C +x +L -L Slab of beef of thickness 2L with microwave (uniform internal) heating or radiant (uniform surface) heating
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ABE 484/584 CHOI 3. [ Conduction/Convection/Heat Generation/Energy Balance ] A plane wall is a composite of two materials, A and B. The wall of material A has uniform heat generation q''' = 1.5 x 10 6 W/m 3 , k A = 75 W/m K, and thickness L A = 50 mm. The wall material has no heat generation with k
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hw04-hints - ABE 484/584 CHOI HW4 1. [Self-cleaning Oven]...

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