Explanation Given data: The temperature distribution along the fin is given by, T − T ambient = ( T base − T ambient ) e − m x (1) Where, m = h p k A (2) Here, h is the heat transfer coefficient, p is the perimeter of the fin, A is the cross sectional area of the fin, k is the thermal conductivity of the fin material. The base temperature ( T base ) is 100 ° C . The ambient temperature ( T ambient ) is 20 ° C . Refer to the Problem 18.8 Figure in the textbook. k = 180 W m ⋅ K h = 15 W m 2 ⋅ K a = 0.05 m b = 0.015 m The value of x vary from 0 to 0 .015 m . The value of k vary from 180 to 350 W m ⋅ K . Formula used: Formula to calculate the perimeter of the fin is, p = 2 ( a + b ) (3) Here, a is the length, b is the breadth. Formula to calculate the area of the fin is, A = a ⋅ b (4) Calculation: From equation (1), x is the independent variable, T is the dependent variable. When, the value of x changes in equation (1) the value of temperature also changes. Therefore, T is dependent variable and x is independent variable. Let the sample calculation: Substitute 0.05 m for a , and 0.015 m for b in equation (3), p = 2 ( 0.05 m + 0.015 m ) = 0.13 m Substitute 0.05 m for a , and 0.015 m for b in equation (4), A = ( 0.05 m ) ( 0.015 m ) = 7.5 × 10 − 4 m 2 Substitute 15 W m 2 ⋅ K for h , 180 W m ⋅ K for k , 0.13 m for p , and 7.5 × 10 − 4 m 2 for A in equation (2), m = ( 15 W m 2 ⋅ K ) ( 0.13 m ) ( 180 W m ⋅ K ) ( 7.5 × 10 − 4 m 2 ) = 14.4 m − 2 = 3.8 m − 1 Reduce the equation (1) to find T . T = ( T base − T ambient ) e − m x + T ambient (5) Substitute 100 ° C for T base , 20 ° C for T ambient , 3.8 m − 1 for m in equation (5), T = ( 100 ° C − 20 ° C ) e − ( 3.8 m − 1 ) x + 20 ° C =8 0 ° C e − ( 3.8 m − 1 ) x + 20 ° C (6) Example calculation: Substitute 0.001 m for x in equation (6), T =8 0 ° C e − ( 3

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ISBN: 9780357126592

Author: MOAVENI

Publisher: CENGAGE CO

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Chapter 18, Problem 8P

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Plot the temperature distribution along the fin by varying x and temperature of the tip of the fin as a function of k, also name the dependent and independent variables.

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Chapter 18, Problem 7P

Chapter 18, Problem 9P

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Chapter 18 Solutions

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Ch. 18.2 - Prob. 1BYG Ch. 18.2 - Prob. 2BYG Ch. 18.2 - Prob. 3BYG Ch. 18.2 - Prob. 4BYG Ch. 18.2 - Prob. BYGV Ch. 18.3 - Prob. 1BYG Ch. 18.3 - Prob. 2BYG Ch. 18.3 - Prob. 3BYG Ch. 18.3 - Prob. BYGV Ch. 18.4 - Prob. 1BYG

Ch. 18.4 - Prob. 2BYG Ch. 18.4 - Prob. 3BYG Ch. 18.4 - Prob. 4BYG Ch. 18.4 - Prob. BYGV Ch. 18.5 - Prob. 1BYG Ch. 18.5 - Prob. 2BYG Ch. 18.5 - Prob. 3BYG Ch. 18.5 - Prob. 4BYG Ch. 18.5 - Prob. BYGV Ch. 18.6 - Prob. 1BYG Ch. 18.6 - Prob. 2BYG Ch. 18.6 - Prob. 3BYG Ch. 18.6 - Prob. 4BYG Ch. 18.6 - Prob. BYGV Ch. 18.7 - Prob. 1BYG Ch. 18.7 - Prob. 2BYG Ch. 18.7 - Prob. BYGV Ch. 18 - Prob. 1P Ch. 18 - Prob. 2P Ch. 18 - Prob. 3P Ch. 18 - In Chapter 12, we explained that the electric...Ch. 18 - The deflection of a cantilevered beam supporting...Ch. 18 - Prob. 6P Ch. 18 - Prob. 7P Ch. 18 - Prob. 8P Ch. 18 - Prob. 9P Ch. 18 - Prob. 10P Ch. 18 - Prob. 11P Ch. 18 - Prob. 12P Ch. 18 - Prob. 13P Ch. 18 - Prob. 14P Ch. 18 - A jet plane taking off creates a noise with a...Ch. 18 - Prob. 16P Ch. 18 - Prob. 17P Ch. 18 - Prob. 18P Ch. 18 - Prob. 19P Ch. 18 - Prob. 20P Ch. 18 - Prob. 21P Ch. 18 - Prob. 22P Ch. 18 - Prob. 23P Ch. 18 - Prob. 24P Ch. 18 - Prob. 25P Ch. 18 - Prob. 26P Ch. 18 - Prob. 27P Ch. 18 - Prob. 28P Ch. 18 - Prob. 29P Ch. 18 - Prob. 30P Ch. 18 - Prob. 31P Ch. 18 - Prob. 32P Ch. 18 - Prob. 33P Ch. 18 - Prob. 34P Ch. 18 - Prob. 35P Ch. 18 - Prob. 36P Ch. 18 - Prob. 37P Ch. 18 - Prob. 38P Ch. 18 - Prob. 39P Ch. 18 - Prob. 40P Ch. 18 - Prob. 41P Ch. 18 - Prob. 42P Ch. 18 - Prob. 43P Ch. 18 - Prob. 44P Ch. 18 - Prob. 45P

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Plot the temperature distribution along the fin by varying x and temperature of the tip of the fin as a function of k , also name the dependent and independent variables.

Plot the temperature distribution along the fin by varying x and temperature of the tip of the fin as a function of k, also name the dependent and independent variables.

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Chapter 18 Solutions