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A rectangular steel (k = 58.7 W/mK) fin 25 mm thick and 150 mm long is attached to a wall that is at 250°C. The ambient air around the fin is at 20°C and the heat-transfer coefficient is 26 W/m². K. Calculate: (a) The fin efficiency. (b) The rate of heat transfer from the fin per meter of fin width.

A rectangular steel (k = 58.7 W/mK) fin 25 mm thick and 150 mm long is attached to a wall that is at 250°C. The ambient air around the fin is at 20°C and the heat-transfer coefficient is 26 W/m². K. Calculate: (a) The fin efficiency. (b) The rate of heat transfer from the fin per meter of fin width.

Introduction to Chemical Engineering Thermodynamics
Introduction to Chemical Engineering Thermodynamics
8th Edition
ISBN:9781259696527
Author:J.M. Smith Termodinamica en ingenieria quimica, Hendrick C Van Ness, Michael Abbott, Mark Swihart
Publisher:J.M. Smith Termodinamica en ingenieria quimica, Hendrick C Van Ness, Michael Abbott, Mark Swihart
Chapter1: Introduction
Section: Chapter Questions
Problem 1.1P
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(2.17) A rectangular steel (k = 58.7 W/m · K) fin 25 mm thick and 150 mm long is attached to a wall that is at 250°C. The ambient air around the fin is at 20°C and the heat-transfer coefficient is 26 W/m² · K. Calculate: . (a) The fin efficiency. (b) The rate of heat transfer from the fin per meter of fin width. Ans. (a) 77.9%. (b) 1456 W/m of width.
Transcribed Image Text:(2.17) A rectangular steel (k = 58.7 W/m · K) fin 25 mm thick and 150 mm long is attached to a wall that is at 250°C. The ambient air around the fin is at 20°C and the heat-transfer coefficient is 26 W/m² · K. Calculate: . (a) The fin efficiency. (b) The rate of heat transfer from the fin per meter of fin width. Ans. (a) 77.9%. (b) 1456 W/m of width.
Expert Solution
Step 1

Given:

Thermal conductivity of steel, k = 58.7 W/m.K

Thickness of fin, w = 25 mm ⇒0.025 m

Length of fin, l = 150 mm ⇒0.15 m

The base temperature of fin, Tb = 250∘C

The ambient temperature, T∞ = 20∘C

The heat transfer coefficient, h = 26 W/m2.K

Let width of the fin, b = 1 m

hence perimeter of the fin, P = 2 (b + w) ⇒2 (1 + 0.025) ⇒2.05 m

 

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