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Plane wall of thickness 2L 40 mm and thermal con- uctivity k 5 W/m K experiences uniform volumetric generation at a rate à, while convection heat transfer occurs at both of its surfaces (x=-L, +L), each of which is exposed to a fluid of temperature T, 20°C. Under steady-state conditions, the temperature distribu- tion in the wall is of the form T(x) = a + bx + cx2 where a = 82.0°C, b=-210°C/n, c=-2x104°C/m2, and x is in meters. The origin of the x-coordinate is at the midplane of the wall. (a) Sketch the temperature distribution and identify (b) What is the volumetric rate of heat generation q in (c) Determine the surface heat fluxes, q:(-L) and significant physical features. the wall? q+ L). How are these fluxes related to the heat generation rate? (d) What are the convection coefficients for the sur- faces at x =-L and x = +L?
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