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W Two-dimensional transient- Consider a 60-mm long aluminum fin (k = 186) with thickness of 1 mm (into the paper). The width is 45 mm. The aluminum is exposed to air with an ambient temperature of T = 15°C and convective heat transfer coefficient of h = 50-The fin is utilized to remove heat from a surface whose temperature is T = 80° C (left side). We will here assume that the convection perpendicular to the paper is not included.

W Two-dimensional transient- Consider a 60-mm long aluminum fin (k = 186) with thickness of 1 mm (into the paper). The width is 45 mm. The aluminum is exposed to air with an ambient temperature of T = 15°C and convective heat transfer coefficient of h = 50-The fin is utilized to remove heat from a surface whose temperature is T = 80° C (left side). We will here assume that the convection perpendicular to the paper is not included.

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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**Two-Dimensional Transient Analysis** *Problem Statement:* Consider a 60-mm long aluminum fin with a thermal conductivity \( k = 186 \, \frac{W}{mK} \) and a thickness of 1 mm (into the paper). The width of the fin is 45 mm. The aluminum is exposed to air with an ambient temperature of \( T_f = 15^\circ C \) and a convective heat transfer coefficient \( h = 50 \, \frac{W}{m^2K} \). The fin is used to remove heat from a surface with a temperature \( T_b = 80^\circ C \) on the left side. The convection perpendicular to the paper is not considered. *Diagram Explanation:* The schematic diagram shows a grid with nodes labeled 1 to 20, representing discrete sections of the fin. The nodes at \( T = 80^\circ C \) are highlighted along the left boundary (nodes 1, 6, 11, 16), while the rest are subject to convection. The dimensions are marked: 60 mm along the length and 45 mm along the width. Convective effects are highlighted around the periphery of the fin. *Analysis Task:* Conduct a transient thermal analysis using implicit or explicit methods to determine the temperature distribution until steady state. Select an appropriate time step for explicit method stability. Assume the following properties: density \( \rho = 2500 \, \frac{kg}{m^3} \) and specific heat capacity \( C_p = 900 \, \frac{J}{kgK} \). Initially, the entire fin is at \( 25^\circ C \), except nodes 1, 6, 11, and 16 which remain at \( 80^\circ C \) from \( t = 0 \) seconds. *Tasks:* a. Show the discretization for node 17. b. Show the discretization for node 12. c. Show the discretization for node 20. d. Show the discretization for node 15. e. Provide a script (EES or Matlab) to solve the problem, explaining the logic and ensuring the use of symmetry. f. Provide a table of temperatures for several time stamps. *Educational Notes:* This exercise illustrates the transient heat conduction problem in two dimensions, commonly encountered in thermal management systems. Understanding the discretization process and
Transcribed Image Text:**Two-Dimensional Transient Analysis** *Problem Statement:* Consider a 60-mm long aluminum fin with a thermal conductivity \( k = 186 \, \frac{W}{mK} \) and a thickness of 1 mm (into the paper). The width of the fin is 45 mm. The aluminum is exposed to air with an ambient temperature of \( T_f = 15^\circ C \) and a convective heat transfer coefficient \( h = 50 \, \frac{W}{m^2K} \). The fin is used to remove heat from a surface with a temperature \( T_b = 80^\circ C \) on the left side. The convection perpendicular to the paper is not considered. *Diagram Explanation:* The schematic diagram shows a grid with nodes labeled 1 to 20, representing discrete sections of the fin. The nodes at \( T = 80^\circ C \) are highlighted along the left boundary (nodes 1, 6, 11, 16), while the rest are subject to convection. The dimensions are marked: 60 mm along the length and 45 mm along the width. Convective effects are highlighted around the periphery of the fin. *Analysis Task:* Conduct a transient thermal analysis using implicit or explicit methods to determine the temperature distribution until steady state. Select an appropriate time step for explicit method stability. Assume the following properties: density \( \rho = 2500 \, \frac{kg}{m^3} \) and specific heat capacity \( C_p = 900 \, \frac{J}{kgK} \). Initially, the entire fin is at \( 25^\circ C \), except nodes 1, 6, 11, and 16 which remain at \( 80^\circ C \) from \( t = 0 \) seconds. *Tasks:* a. Show the discretization for node 17. b. Show the discretization for node 12. c. Show the discretization for node 20. d. Show the discretization for node 15. e. Provide a script (EES or Matlab) to solve the problem, explaining the logic and ensuring the use of symmetry. f. Provide a table of temperatures for several time stamps. *Educational Notes:* This exercise illustrates the transient heat conduction problem in two dimensions, commonly encountered in thermal management systems. Understanding the discretization process and
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