The shield of a nuclear reactor can be idealized by a large 10 in. thick flat plate having a thermal conductivity of 2 Btu/(h ft ?F). Radiation from the interior of the reactor penetrates the shield and produces heat generation in the shield which decreases exponentially from a value of 10 Btu/(h in3). at the inner surface to a value of 1.0 Btu/(h in3) at a distance of 5 in. from the interior surface. If the exterior surface is kept at 100?F by forced convection, determine the temperature at the inner surface of the shield.GIVENLarge flat plate with non-uniform internal heat generationThickness (L) = 10 in.Thermal conductivity (k) = 2 Btu/(h ft ?F)Exterior surface temperature (To) = 100?FHeat generation is exponential with values of10 Btu/(h in3) at the inner surface1.0 Btu/(h in3) at 5 in. from the inner surfaceASSUMPTIONSOne dimensional, steady state conductionThe thermal conductivity is constantNo heat transfer at the inner surface of theshield

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E L= 10 In – Internal Heat Generation vs Distance x 10 T, = ? T.-100° F x) = g(0)e -a 8- 4- 31 21