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A tall, wide, thin plate has a thermal conductivity ofk=45mKW, a density of=2250m3kg, and a heat capacity ofc=235kgKJ. The plate is much taller and wider than it is thick and it is exposed to a convective environment withh=150m2Kwon both sides. The plate is initially at a uniform temperature ofTi=12Cwhen it is introduced into the convective environment atT=350C. The thickness of the wall is 45 centimeters. Find: (a) Write down the appropriate governing equation including all boundary and initial conditions. (b) Perform a separation of variables to generate a solution. (c) Show a characteristic equation (but do not solve it), giving system eigenvalues. (d) Establish a relation (but do not solve it) which would give all the necessary constants in the solution.

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