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Problem ( 2 ) : A semi - infinite solid domain is shown that extends to in the + x direction. Heat conduction occurs only

Problem (2): A semi-infinite solid domain is shown that extends to in the +x direction. Heat conduction occurs only in the x direction. Originally, the temperature in the solid is uniform at T0. At time t=0, the solid is suddenly exposed to or immersed in a large mass of ambient fluid at temperature T1, which is constant. The convection coefficient h is present and is constant; that is a surface resistant is present. Hence, the temperature TS at the surface is not the same as T1. Show that the temperature distribution within the solid domain is given by
T-T0T1-T0=erfc(x2t2)-exp[ht2k(xt2+ht2k)]erfc(x2t2+ht2k)
where k is the thermal conductivity of solid domain, =kcp, and erfc is the complementary error function. Hint: Use Laplace Transform.
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