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Problem: A straight rectangular fin of uniform cross section is connected to a base with constant temperature of 100°C (T¿). The fin is made of copper (k = 400 W/mK) with thickness (t) of 1 mm, width (w) of 3 cm, and length (L) of 5 cm. The system is exposed to the ambient air with temperatu of 30 °C and heat transfer coefficient of 30 [W/m?K]. If the temperature at the tip is known as 40° (T (x = L)), determine the following: 1. Temperature at the middle of the fin (i.e., at x = 2.5cm). 2. The fin efficiency T,h Tp L

Problem: A straight rectangular fin of uniform cross section is connected to a base with constant temperature of 100°C (T¿). The fin is made of copper (k = 400 W/mK) with thickness (t) of 1 mm, width (w) of 3 cm, and length (L) of 5 cm. The system is exposed to the ambient air with temperatu of 30 °C and heat transfer coefficient of 30 [W/m?K]. If the temperature at the tip is known as 40° (T (x = L)), determine the following: 1. Temperature at the middle of the fin (i.e., at x = 2.5cm). 2. The fin efficiency T,h Tp L

Elements Of Electromagnetics
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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### Problem: A straight rectangular fin of uniform cross-section is connected to a base with a constant temperature of 100°C (\(T_b\)). The fin is made of copper (\(k = 400 \, W/mK\)) with a thickness (\(t\)) of 1 mm, width (\(w\)) of 3 cm, and length (\(L\)) of 5 cm. The system is exposed to ambient air with a temperature of 30°C and a heat transfer coefficient of 30 [\(W/m^2K\)]. If the temperature at the tip is known to be 40°C (\(T(x = L)\)), determine the following: 1. Temperature at the middle of the fin (i.e., at \(x = 2.5 \, cm\)). 2. The fin efficiency ### Diagram Explanation: A schematic diagram of the fin is provided, illustrating the setup. The diagram shows a rectangular fin connected to a base: - The base has a constant temperature \(T_b\). - The fin has a length \(L\), thickness \(t\), and width \(w\). - The fin extends from the base into the ambient air. - The diagram also indicates parameters \(T_{\infty}\) (ambient temperature) and \(h\) (heat transfer coefficient). The figure labels the significant quantities and dimensions, providing a clear visual representation of the problem setup.
Transcribed Image Text:### Problem: A straight rectangular fin of uniform cross-section is connected to a base with a constant temperature of 100°C (\(T_b\)). The fin is made of copper (\(k = 400 \, W/mK\)) with a thickness (\(t\)) of 1 mm, width (\(w\)) of 3 cm, and length (\(L\)) of 5 cm. The system is exposed to ambient air with a temperature of 30°C and a heat transfer coefficient of 30 [\(W/m^2K\)]. If the temperature at the tip is known to be 40°C (\(T(x = L)\)), determine the following: 1. Temperature at the middle of the fin (i.e., at \(x = 2.5 \, cm\)). 2. The fin efficiency ### Diagram Explanation: A schematic diagram of the fin is provided, illustrating the setup. The diagram shows a rectangular fin connected to a base: - The base has a constant temperature \(T_b\). - The fin has a length \(L\), thickness \(t\), and width \(w\). - The fin extends from the base into the ambient air. - The diagram also indicates parameters \(T_{\infty}\) (ambient temperature) and \(h\) (heat transfer coefficient). The figure labels the significant quantities and dimensions, providing a clear visual representation of the problem setup.
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