A plane wall of thickness 2L = 50 mm and constant thermal conductivity k = 8 W/m · K experiences uniform heat generation at a rate ėgen. Under steady conditions, the temperature distribution in the wall is of the form T(x) = a-bx2, where a = 80°C and b = 2 × 104 °C/m2, and x is in meters. The origin of the x coordinate is at the midplane of the wall.
(a) Determine the surface temperatures and sketch the temperature distribution in the wall.
(b) What is the Volumetrie rate of heat generation, egen?
(c) Determine the surface heat fluxes qs (−L.) and qs (L) .
(d) What is the relationship between these fluxes, the heat generation rate and the geometry of the wall?
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