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A plate of thickness 2L surface area As mass M and specific heat cp initially at a uniform temperature Ti is suddenly heated on both surfaces by a convection process


A plate of thickness 2L, surface area As, mass M, and specific heat cp, initially at a uniform temperature Ti, is suddenly heated on both surfaces by a convection process (T, h) for a period of time to, following which the plate is insulated. Assume that the midplane temperature does not reach T within this period of time.

 

(a) Assuming Bi ≫ 1 for the heating process, sketch and label, on T–x coordinates, the following temperature distributions: initial, steady-state (t →∞), T(x, to), and at two intermediate times between t to and t →∞.

(b) Sketch and label, on T – t coordinates, the midplane and exposed surface temperature distributions. (c) Repeat parts (a) and (b) assuming Bi ≪ 1 for the plate.

(d) Derive an expression for the steady-state temperature T(x, ∞) Tf, leaving your result in terms of plate parameters (M, cp), thermal conditions (Ti, T, h), the surface temperature T(L, t), and the heating time to.

Jun 27 2020 View more View Less

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