A plate of thickness 2L, surface area As, mass M,
Chapter 5, Problem 5.4(choose chapter or problem)
A plate of thickness 2L, surface area As, mass M, andspecific heat cp, initially at a uniform temperature Ti, issuddenly heated on both surfaces by a convectionprocess (T?, h) for a period of time to, following whichthe plate is insulated. Assume that the midplane tem-perature does not reach T?within this period of time.(a) Assuming Bi?1 for the heating process, sketch andlabel, on Txcoordinates, the following temperaturedistributions: initial, steady-state (t l?), T(x,to), andat two intermediate times between t?toand t l ?.(b) Sketch and label, on T tcoordinates, the midplaneand exposed surface temperature distributions.(c) Repeat parts (a) and (b) assuming Bi?1 for the plate.(d) Derive an expression for the steady-state tempera-ture T(x,?)?Tf, leaving your result in terms ofplate parameters (M, cp), thermal conditions (Ti, T?,h), the surface temperature T(L, t), and the heatingtime to.
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