A 10- cm high and 20 -cm wide circuit board houses on its...

A $10-$ cm high and 20 -cm wide circuit board houses on its surface 100 closely spaced chips, each generating heat at a rate of $0.08 \mathrm{W}$ and transferring it by convection to the surrounding air at $25^{\circ} \mathrm{C}$. Heat transfer from the back surface of the board is negligible. If the convection heat transfer coefficient on the surface of the board is $10 \mathrm{W} / \mathrm{m}^{2} \cdot^{\circ} \mathrm{C}$ and radiation heat transfer is negligible, the average surface temperature of the chips is $(a) 26^{\circ} \mathrm{C}$ $(b)45^{\circ} \mathrm{C}$ $(c) 15^{\circ} \mathrm{C}$ $(d) 80^{\circ} \mathrm{C}$ $(e) 65^{\circ} \mathrm{C}$

A $10-$ cm high and 20 -cm wide circuit board houses on its surface 100 closely spaced chips, each generating heat at a rate of $0.08 \mathrm{W}$ and transferring it by convection to the surrounding air at $25^{\circ} \mathrm{C}$. Heat transfer from the back surface of the board is negligible. If the convection heat transfer coefficient on the surface of the board is $10 \mathrm{W} / \mathrm{m}^{2} \cdot^{\circ} \mathrm{C}$ and radiation heat transfer is negligible, the average surface temperature of the chips is
$(a) 26^{\circ} \mathrm{C}$
$(b)45^{\circ} \mathrm{C}$
$(c) 15^{\circ} \mathrm{C}$
$(d) 80^{\circ} \mathrm{C}$
$(e) 65^{\circ} \mathrm{C}$

Key Concepts

Convection Heat Transfer

This concept refers to the mechanism by which heat is transferred from a surface to a fluid (in this case, air) through the movement of the fluid. It is quantitatively described using the convection heat transfer coefficient, which relates the heat flux to the temperature difference between the surface and the ambient environment.

Heat Generation and Energy Balance

In thermal analysis, the heat generated within a system, such as by electrical components, must be balanced by the heat dissipated to maintain a steady state. This energy balance is key to determining the temperature rise of a component when the internal heat generation is known and the mode of heat transfer to the surroundings is identified.

Surface Area Calculation

The effective area through which heat is transferred plays a critical role in thermal management. In problems like these, calculating the correct surface area available for convection directly affects the estimated temperature rise since the heat transfer rate is proportional to the area.

Heat Transfer Coefficient

The heat transfer coefficient is an essential parameter in convective heat transfer that quantifies the efficiency with which heat is removed from a surface by the surrounding fluid. It directly influences the magnitude of the temperature difference required to dissipate a given amount of heat.

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