Question

A \(12-\mathrm{cm} \times 18-\mathrm{cm}\) circuit board houses on its surface 100 closely spaced logic chips, each dissipating \(0.06 \mathrm{~W}\) in an environment at \(40^{\circ} \mathrm{C}\). The heat transfer from the back surface of the board is negligible. If the heat transfer coefficient on the surface of the board is \(10 \mathrm{~W} / \mathrm{m}^{2} \cdot \mathrm{K}\), determine \((a)\) the heat flux on the surface of the circuit board, in W/ \(\mathrm{m}^{2}\); \((b)\) the surface temperature of the chips; and \((c)\) the thermal resistance between the surface of the circuit board and the cooling medium, in \({ }^{\circ} \mathrm{C} / \mathrm{W}\).

Short answer

\(Q_{total} = 6 \, \mathrm{W}\)#tag_title#Step 2: Calculate the heat flux on the surface of the circuit board#tag_content#Next, we'll determine the heat flux by dividing the total heat dissipation by the circuit board area. Heat flux (\(q"_{board}\)) = \(Q_{total}\) / Area of the circuit board Circuit board area = Length × Width Area = \(0.1 \, \mathrm{m} \times 0.1 \, \mathrm{m}\) Area = \(0.01 \, \mathrm{m}^2\) Now we can calculate the heat flux: \(q"_{board} = \frac{6 \, \mathrm{W}}{0.01 \, \mathrm{m}^2}\)

Step-by-step solution

Determine the total heat generated by the chips

To find the total heat generated, we will multiply the number of chips by the heat dissipation per chip. Total heat dissipation (\(Q_{total}\)) = Number of chips × Heat dissipation per chip \(Q_{total} = 100 \times 0.06 \, \mathrm{W}\)