A 0.3-cm-thick, 12-cm-high, and 18-cm-long circuit board houses 80 closely spaced logic chips on one side, each dissipating 0.06 W. The board is impregnated with copper fillings and has an effective thermal conductivity of 16 W/m · °C. All the heat generated in the chips is conducted across the

Question

A 0.3-cm-thick, 12-cm-high, and 18-cm-long circuit board houses 80 closely spaced logic chips on one side, each dissipating 0.06 W. The board is impregnated with copper fillings and has an effective thermal conductivity of [latex] 16 W / m \cdot{ }^{\circ} C [/latex]. All the heat generated in the chips is conducted across the circuit board and is dissipated from the back side of the board to the ambient air. Determine the temperature difference between the two sides of the circuit board.

Accepted Answer

A circuit board houses 80 closely spaced logic chips on one side, each dissipating 0.06 W. All the heat generated in the chips is conducted across the circuit board. The temperature difference between the two sides of the circuit board is to be determined.

Assumptions 1 Steady operating conditions exist. 2 Thermal properties of the board are constant. 3 All the heat generated in the chips is conducted across the circuit board.

Properties The effective thermal conductivity of the board is given to be [latex] k = 16 W / m \cdot{ }^{\circ} C [/latex].

Analysis The total rate of heat dissipated by the chips is

[latex] \dot{Q} = 80 imes(0.06 W ) = 4.8 W [/latex]

Then the temperature difference between the front and back surfaces of the board is

[latex] A=(0.12 m )(0.18 m ) = 0.0216 m ^{2} [/latex]

[latex] \dot{Q}=k A \frac{\Delta T}{L} \longrightarrow \Delta T=\frac{\dot{Q} L}{k A}=\frac{(4.8 W )(0.003 m )}{\left(16 W / m \cdot{ }^{\circ} C ight)\left(0.0216 m ^{2} ight)}=0.042^{\circ} C [/latex]

Discussion Note that the circuit board is nearly isothermal.

Question 1.92: A 0.3-cm-thick, 12-cm-high, and 18-cm-long circuit board hou...

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