Consider a short cylinder of 10.0cm diameter and 5.0cm length with a thermal conductivity of k = 10 W/m.K This cylindrical solid piece is now placed in a perfectly insulating ceramic material in a way that only one of the circular end-surfaces is facing the outside air; the cylindrical surface and the buried end of the short cylinder are insulated with no heat transfer. The outside air is at 20oC and is flowing in a way to create a combined convective heat transfer coefficient of h = 20 W/m2K over the exposed surface. This short cylinder has a uniform internal heat generation at a rate of 50000 W/m3 (50 kW/m3). a. What is the rate of heat generation within the cylinder in Watts? b. What is the temperature of the cylinder surface that is exposed to the outside air? c. What and where is the highest temperature?
Consider a short cylinder of 10.0cm diameter and 5.0cm length with a thermal conductivity of k = 10 W/m.K This cylindrical solid piece is now placed in a perfectly insulating ceramic material in a way that only one of the circular end-surfaces is facing the outside air; the cylindrical surface and the buried end of the short cylinder are insulated with no heat transfer. The outside air is at 20oC and is flowing in a way to create a combined convective heat transfer coefficient of h = 20 W/m2K over the exposed surface. This short cylinder has a uniform internal heat generation at a rate of 50000 W/m3 (50 kW/m3).
a. What is the rate of heat generation within the cylinder in Watts?
b. What is the temperature of the cylinder surface that is exposed to the outside air?
c. What and where is the highest temperature?
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