A transformer is to be cooled via forced air convection. To increase the effectiveness of the cooling, Alloy 1095 cast aluminum fins are attached to the top of the transformer over which air is blown (negligible thermal contact resistance between the transformer and the fins). The fins are 2 cm thick and 7 cm long and span the entire length of the transformer, and the transformer is 7 cm wide and 10 cm long. Air leaves the cooling fan at 25°C . a) Decide how to model the fins before performing any real analysis. You are willing to accept some error in your analysis and so you will either model the fins as having adiabatic tips or being infinitely long. You expect the average convection coefficient over the heat transfer surfaces for this system to be around 50 W m2– K⁄ . Which tip condition should you use for the fins in your analysis? b) Modeling the transformer as being isothermal, determine the average convection coefficient over the heat transfer surfaces. Account for heat transfer from the finned and unfinned surfaces on the top of the transformer, assuming the boundary layers don’t somehow interfere with each other. Consider any other heat transfers to be negligible (e.g., from the sides and bottom of the transformer). c) What is the required air velocity to provide the necessary rate of cooling to the transformer?

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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A transformer is to be cooled via forced air convection. To increase the effectiveness of the
cooling, Alloy 1095 cast aluminum fins are attached to the top of the transformer over
which air is blown (negligible thermal contact resistance between the transformer and the
fins). The fins are 2 cm thick and 7 cm long and span the entire length of the transformer,
and the transformer is 7 cm wide and 10 cm long. Air leaves the cooling fan at 25°C

.
a) Decide how to model the fins before performing any real analysis. You
are willing to accept some error in your analysis and so you will either model the
fins as having adiabatic tips or being infinitely long. You expect the average convection
coefficient over the heat transfer surfaces for this system to be around 50 W m2– K⁄ .
Which tip condition should you use for the fins in your analysis?

b) Modeling the transformer as being isothermal, determine the average convection
coefficient over the heat transfer surfaces. Account for heat transfer from the finned
and unfinned surfaces on the top of the transformer, assuming the boundary layers
don’t somehow interfere with each other. Consider any other heat transfers to be
negligible (e.g., from the sides and bottom of the transformer).

c) What is the required air velocity to provide the necessary rate of cooling to the
transformer?

The image depicts a heat sink design for cooling a transformer:

- The transformer is rated at 20 watts.
- It has external dimensions of 10 cm by 7 cm by 7 cm.
- Multiple parallel fins are attached to the transformer.
- Each fin is 7 cm tall.
- Air at a temperature of 25°C is directed onto the fins, as indicated by arrows.
- The fins increase the surface area for heat dissipation, helping to cool the transformer effectively.

This setup is commonly used in electronics to manage heat produced by components, ensuring they operate within safe temperature ranges.

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