Chapter 3, Problem 3.65P

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 $\left(\rho c_p\right)$. Calculate the effective properties if each of the boards and plates has a thickness of 2.36 mm and the following thermophysical properties: board (b) $\rho =1000kg/m^3,c_{p,b}=1500J/kg\cdot K,k_b=0.30W/m\cdot K$; plate (p ) ${\rho }_p=8000kg/m^3,c_{p,p}=480J/kg\cdot K,k_p=12W/m\cdot K$.