Question

Consider a heat sink with optimum fin spacing. Explain how heat transfer from this heat sink will be affected by \((a)\) removing some of the fins on the heat sink and (b) doubling the number of fins on the heat sink by reducing the fin spacing. The base area of the heat sink remains unchanged at all times.

Short answer

#tag_title#Conclusion#tag_content#In summary, altering the fin spacing from its optimal value will generally result in a decrease in the overall heat transfer rate from the heat sink. Removing some fins will reduce the total surface area available for heat transfer, while doubling the number of fins by reducing the fin spacing will increase the surface area but decrease the airflow over the fins. In both cases, the negative effects of these changes outweigh the positive effects, leading to reduced heat transfer efficiency. To maintain the maximum rate of heat removal, it is essential to use the heat sink with the optimum fin spacing as designed.

Step-by-step solution

Introduction to Heat Sink and Fins

A heat sink is a passive heat exchanger that transfers heat from an electronic or mechanical device to the surrounding air or liquid. Fins are extended surfaces attached to the heat sink which helps to increase the surface area for better heat transfer. The spacing between fins is an important parameter in determining the rate of heat transfer.

Factors affecting Heat Transfer in Fins

The rate of heat transfer in fins is influenced by the following factors: 1. Thermal conductivity of the fin material 2. Fin geometry (length, thickness, and shape) 3. Fin spacing 4. Airflow over the fins For any given heat sink, there will be an optimum fin spacing that maximizes the rate of heat removal. This is a balance between providing the largest surface area for heat transfer while maintaining adequate space for air to flow over the fins.

Effect of Removing Some Fins on the Heat Sink

If some of the fins are removed from the heat sink, this will create two primary effects: 1. The total surface area available for heat transfer will be reduced, which will decrease the overall heat transfer rate. 2. The spacing between the remaining fins will be increased, which can improve the airflow over the fins, potentially increasing the heat transfer coefficient (dependent on the existing optimal spacing). In most cases, the reduction in the total surface area will have a more significant impact on the rate of heat transfer than the increase in airflow, leading to a drop in the overall heat transfer from the heat sink.

Effect of Doubling the Number of Fins by Reducing the Fin Spacing

In this scenario, the number of fins on the heat sink will be doubled by reducing the fin spacing, while keeping the base area constant. This will have two primary effects: 1. The total surface area available for heat transfer will be increased, which will increase the overall heat transfer rate. 2. The decreased spacing between the fins will result in reduced airflow over the fins, potentially causing a drop in the heat transfer coefficient. Since the heat sink was originally at the optimal fin spacing for the rate of heat removal, doubling the number of fins will likely reduce the overall rate of heat transfer. In this case, the negative effect of decreased airflow will outweigh the positive effect of increased surface area.