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?

Refrigeration and Air Conditioning Technology (MindTap Course List)

8th Edition

ISBN:9781305578296

Author:John Tomczyk, Eugene Silberstein, Bill Whitman, Bill Johnson

Publisher:John Tomczyk, Eugene Silberstein, Bill Whitman, Bill Johnson

Chapter1: Heat, Temperature, And Pressure

Section: Chapter Questions

Problem 17RQ: Convert 22C to Fahrenheit.

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Question

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?

Air
25°C
*****
10 cm
www.
ANN
Transformer
20 W
7 cm
-Fins
7 cm

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