Summer2022-VM335 Homework 1
机械工程学代写ASSIGNMEN An aluminum plate 4 mm thick is mounted in ahorizontal position,and its bottom surface is well insu-lated.
The concrete slab of a basement is 13 m long, 10 m wide.and 0.30 m thick. During the winter,temperatures arenominally 17°C and 10°C at the top and bottom surfaces.respectively. lf the concrete has a thermal conductivityof 1.4 W/m·K, what is the rate of heat loss through theslab? If the basement is heated by a gas furnace operat-ing at an efficiency of ηf= 0.90 and natural gas is priced at C= $0.02/MJ, what is the daily cost of the heat loss?
1.26 A square isothermal chip is of width w = 5 mm on aside and is mounted in a substrate such that its side andback surfaces are well insulated; the front surface isexposed to the flow of a coolant at T∞ = 15°C. Fromreliability considerations, the chip temperature must notexceed T=85°C.
If the coolant is air and the corresponding convectioncoefficient is h=200 W/m2·K, what is the maximumallowable chip power? If the coolant is a dielectricliquid for which h = 3000 W/m2K, what is the maxi-mum allowable power?
An aluminum plate 4 mm thick is mounted in ahorizontal position,and its bottom surface is well insu-lated. A special, thin coating is applied to the topsurface such that it absorbs 80% of any incident solarradiation, while having an emissivity of 0.25. Thedensity p and specific heat c of aluminum are known tobe 2700 kg/m3 and 900 J/kg·K,respectively.
(a) Consider conditions for which the plate is at a tem-perature of 25°C and its top surface is suddenlyexposed to ambient air at T= 20C and to solarradiation that provides an incident flux of 900 W/mThe convection heat transfer coefficient between thesurface and the air is h = 20 W/m2.K. What is theinitial rate of change of the plate temperature? 机械工程学代写ASSIGNMEN
(b) What will be the equilibrium temperature of theplate when steady-state conditions are reached?
(c) The surface radiative properties depend on the spe-cific nature of the applied coating. Compute and plotthe steady-state temperature as a function of theemissivity for 0.05 ≤ ε ≤ 1, with all other conditionsremaining as prescribed. Repeat your calculations forvalues of αs= 0.5 and 1.0, and plot the results withthose obtained for αs= 0.8. If the intent is to maxi-mize the plate temperature, what is the mostdesirable combination of the plate emissivity and itsabsorptiyilsolar radiation?
Electronic power devices are mounted to a heat sink hav-ing an exposed surface area of 0.045 m2 and an emissiv-ity of 0.80. When the devices dissipate a total power of 20W and the air and surroundings are at 27°C, the aver-age sink temperature is 42°C.What average temperaturewill the heat sink reach when the devices dissipate 30 Wfor the same environmental condition?
1.76 The wall of an oven used to cure plastic parts is ofthickness L = 0.05 m and is exposed to large surround-ings and air at its outer surface. The air and the sur-roundings are at 300 K.
(a) If the temperature of the outer surface is 400 Kand its convection coefficient and emissivity areh = 20 W/m2·K and e = 0.8, respectively, what isthe temperature of the inner surface if the wall has athermal conductivity of k = 0.7 W/m2·K?