Consider the one-dimensional wall shown in the sketch, which is initially at a uniform temperature T i and is suddenly subjected to the convection boundary condition with a fluid at T ∞ . For a...

Consider the one-dimensional wall shown in the sketch, which is initially at a uniform temperature T_i
and is suddenly subjected to the convection boundary condition with a fluid at T_∞.

For a particular wall, case 1, the temperature at x = L₁
after t₁
= 100 s is T₁(L₁, t₁) 315°C. Another wall, case 2, has different thickness and thermal conditions as shown.

How long will it take for the second wall to reach 28.5°C at the position x = L₂? Use as the basis for analysis, the dimensionless functional dependence for the transient temperature distribution expressed in Equation 5.41.

Copper-coated, epoxy-filled fiberglass circuit boards are treated by heating a stack of them under high pressure, as shown in the sketch. The purpose of the pressing–heating operation is to cure the epoxy that bonds the fiberglass sheets, imparting stiffness to the boards. The stack, referred to as a book, is comprised of 10 boards and 11 pressing plates, which prevent epoxy from flowing between the boards and impart a smooth finish to the cured boards. In order to perform simplified thermal analyses, it is reasonable to approximate the book as having an effective thermal conductivity (k) and an effective thermal capacitance (ρc_p). Calculate the effective properties if each of the boards and plates has a thickness of 2.36 mm and the following thermophysical properties: board

Circuit boards are treated by heating a stack of them under high pressure, as illustrated in Problem 5.45. The platens at the top and bottom of the stack are maintained at a uniform temperature by a circulating fluid. The purpose of the pressing–heating operation is to cure the epoxy, which bonds the fiberglass sheets, and impart stiffness to the boards. The cure condition is achieved when the epoxy has been maintained at or above 170°C for at least 5 min. The effective thermophysical properties of the stack or book (boards and metal pressing plates) are k 0.613 W/m ∙ K and ρc_p
= 2.73 × 10⁶
J/m³
∙ K.

(a) If the book is initially at 15°C and, following application of pressure, the platens are suddenly brought  to a uniform temperature of 190°C, calculate the elapsed time t_e
required for the midplane of the book to reach the cure temperature of 170°C.

(b) If, at this instant of time, t - t_e, the platen temperature were reduced suddenly to 15°C, how much energy would have to be removed from the book by the coolant circulating in the platen, in order to return the stack to its initial uniform temperature?