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8.30 A fin is an extended surface used to transfer heat from a base material (at x = 0) to an ambient. Heat flows from the base material through the base of the fin, through its outer surface, and through the tip. Measurement of the temperature distribution along a pin fin gives the following data: x (cm) 1 0 2 3 4 5 6 7 8 9 10 473 446.3 422.6 401.2 382 364.3 348.0 332.7 318.1 304.0 290.1 T(K) The fin has a length L = 10 cm, constant cross-sectional area of 1.6× 105 m², and thermal conductivity k = 240 W/m/K. The heat flux L (W/m²) is given by qx=-k dx TA (a) Determine the heat flux at x = 0. Use the three-point forward differ- ence formula for calculating the derivative. Ts (b) Determine the heat flux at x = L. Use the three-point backward dif- ference formula for calculating the derivative. ТВ (c) Determine the amount of heat (in W) lost between x = 0 and x = L. (The heat flow per unit time in Watts is the heat flux multiplied by the cross-sectional area of the fin.)

8.30 A fin is an extended surface used to transfer heat from a base material (at x = 0) to an ambient. Heat flows from the base material through the base of the fin, through its outer surface, and through the tip. Measurement of the temperature distribution along a pin fin gives the following data: x (cm) 1 0 2 3 4 5 6 7 8 9 10 473 446.3 422.6 401.2 382 364.3 348.0 332.7 318.1 304.0 290.1 T(K) The fin has a length L = 10 cm, constant cross-sectional area of 1.6× 105 m², and thermal conductivity k = 240 W/m/K. The heat flux L (W/m²) is given by qx=-k dx TA (a) Determine the heat flux at x = 0. Use the three-point forward differ- ence formula for calculating the derivative. Ts (b) Determine the heat flux at x = L. Use the three-point backward dif- ference formula for calculating the derivative. ТВ (c) Determine the amount of heat (in W) lost between x = 0 and x = L. (The heat flow per unit time in Watts is the heat flux multiplied by the cross-sectional area of the fin.)

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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8.30 A fin is an extended surface used to transfer heat from a base material (at x = 0) to an ambient. Heat flows from the base material through the base of the fin, through its outer surface, and through the tip. Measurement of the temperature distribution along a pin fin gives the following data: x (cm) 1 0 2 3 4 5 6 7 8 9 10 473 446.3 422.6 401.2 382 364.3 348.0 332.7 318.1 304.0 290.1 T(K) The fin has a length L = 10 cm, constant cross-sectional area of 1.6× 105 m², and thermal conductivity k = 240 W/m/K. The heat flux L (W/m²) is given by qx=-k dx TA (a) Determine the heat flux at x = 0. Use the three-point forward differ- ence formula for calculating the derivative. Ts (b) Determine the heat flux at x = L. Use the three-point backward dif- ference formula for calculating the derivative. ТВ (c) Determine the amount of heat (in W) lost between x = 0 and x = L. (The heat flow per unit time in Watts is the heat flux multiplied by the cross-sectional area of the fin.)
Transcribed Image Text:8.30 A fin is an extended surface used to transfer heat from a base material (at x = 0) to an ambient. Heat flows from the base material through the base of the fin, through its outer surface, and through the tip. Measurement of the temperature distribution along a pin fin gives the following data: x (cm) 1 0 2 3 4 5 6 7 8 9 10 473 446.3 422.6 401.2 382 364.3 348.0 332.7 318.1 304.0 290.1 T(K) The fin has a length L = 10 cm, constant cross-sectional area of 1.6× 105 m², and thermal conductivity k = 240 W/m/K. The heat flux L (W/m²) is given by qx=-k dx TA (a) Determine the heat flux at x = 0. Use the three-point forward differ- ence formula for calculating the derivative. Ts (b) Determine the heat flux at x = L. Use the three-point backward dif- ference formula for calculating the derivative. ТВ (c) Determine the amount of heat (in W) lost between x = 0 and x = L. (The heat flow per unit time in Watts is the heat flux multiplied by the cross-sectional area of the fin.)
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