a) Simplify the differential equation for energy transfer for the general case of steady state, no flow, and no heat generation, leaving it in general 3D form. Note briefly but explicitly your reasoning for eliminating a term. pcCE +v.VT) = D.KOT +" + at b) Simplify the equation in a) further by assuming a constant thermal conductivity (but leave it in 3D form). c) As part of an experimental apparatus, a cylindrical thin-walled glass cylinder has been cut along its axis such that its geometry is in a cross-section as shown. The inner and outer radial surfaces are coated with an insulating epoxy (gray areas in the schematic). However, the cut surfaces are left exposed at 0 = 0 and 0 = + (i.e., 180 for a half-circle). The temperature at To and T. are different but temperature varies only in the O-direction. Integrate the differential equation obtained from the differential equation for energy transfer to obtain an equation that describes the variation of temperature in the o direction in a general form applicable regardless of boundary condition(s). d) Define reasonable boundary conditions based on the black and white illustration. e) Evaluate the integration constant(s), and present an equation that could be used to find the temperature in the half-cylinder at any angle o. T. 11 ro TE