Homework Help is Here – Start Your Trial Now!
Engineering
Electrical Engineering
Your task The initial design for the pin fin has been suggested. This states that the pin fin should be made of carbon steel (k = 55 W/mK), with a length of five centimetres and a diameter of one millimetre. The fin is to be located in stagnant air at 22°C, with a convective heat transfer coefficient of 20 W/m2K. You are required to produce a report on your findings as to how effective the proposed design is at dissipating heat away from the electrical component, and suggestions you have for improvements. To undertake this study, you must develop a numerical model by applying both a third order Runge Kutta method, and an Euler method of your choice, to the differential equation in equation 1. This model must be written using MatLab. Any design improvements you make must be justified by use of your model. The appendix must include a copy of your code, which should be adequately annotated. Things to consider • How will you verify your model? • Look at which variables you can change in equation 1 to improve the design. The report The report should be written according to the School of Engineering report template. The introduction and literature review should be brief, and provide enough information to help set up your model. The methodology should include a brief mathematical description of your models, and a flowchart of your code. The results should include the necessary information to evaluate the fin design, and graphs of temperature against length for any design presented. The report should be typed. Further information If you are intending to enhance the fin by changing the shape such that the cross-sectional area increases with the length of the fin, then equation 1 is no longer valid. You will need to modify equation 4 according to the shape you choose. 1 hdA. Ack dx 1 dA. dT (T – Ta) = 0 dx? Ac dx dx

Your task The initial design for the pin fin has been suggested. This states that the pin fin should be made of carbon steel (k = 55 W/mK), with a length of five centimetres and a diameter of one millimetre. The fin is to be located in stagnant air at 22°C, with a convective heat transfer coefficient of 20 W/m2K. You are required to produce a report on your findings as to how effective the proposed design is at dissipating heat away from the electrical component, and suggestions you have for improvements. To undertake this study, you must develop a numerical model by applying both a third order Runge Kutta method, and an Euler method of your choice, to the differential equation in equation 1. This model must be written using MatLab. Any design improvements you make must be justified by use of your model. The appendix must include a copy of your code, which should be adequately annotated. Things to consider • How will you verify your model? • Look at which variables you can change in equation 1 to improve the design. The report The report should be written according to the School of Engineering report template. The introduction and literature review should be brief, and provide enough information to help set up your model. The methodology should include a brief mathematical description of your models, and a flowchart of your code. The results should include the necessary information to evaluate the fin design, and graphs of temperature against length for any design presented. The report should be typed. Further information If you are intending to enhance the fin by changing the shape such that the cross-sectional area increases with the length of the fin, then equation 1 is no longer valid. You will need to modify equation 4 according to the shape you choose. 1 hdA. Ack dx 1 dA. dT (T – Ta) = 0 dx? Ac dx dx

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
Section: Chapter Questions
Problem 1P: Visit your local library (at school or home) and describe the extent to which it provides literature...
See similar textbooks
icon
Related questions
Question

Please need a full  solution to the attached assignment ASAP

 

Thanks

Your task The initial design for the pin fin has been suggested. This states that the pin fin should be made of carbon steel (k = 55 W/mK), with a length of five centimetres and a diameter of one millimetre. The fin is to be located in stagnant air at 22°C, with a convective heat transfer coefficient of 20 W/m2K. You are required to produce a report on your findings as to how effective the proposed design is at dissipating heat away from the electrical component, and suggestions you have for improvements. To undertake this study, you must develop a numerical model by applying both a third order Runge Kutta method, and an Euler method of your choice, to the differential equation in equation 1. This model must be written using MatLab. Any design improvements you make must be justified by use of your model. The appendix must include a copy of your code, which should be adequately annotated. Things to consider • How will you verify your model? • Look at which variables you can change in equation 1 to improve the design. The report The report should be written according to the School of Engineering report template. The introduction and literature review should be brief, and provide enough information to help set up your model. The methodology should include a brief mathematical description of your models, and a flowchart of your code. The results should include the necessary information to evaluate the fin design, and graphs of temperature against length for any design presented. The report should be typed. Further information If you are intending to enhance the fin by changing the shape such that the cross-sectional area increases with the length of the fin, then equation 1 is no longer valid. You will need to modify equation 4 according to the shape you choose. dT 1 dA.\ dT Ac dx 1 h dA. (Т — Т.) — 0 dx? dx Ack dx
Transcribed Image Text:Your task The initial design for the pin fin has been suggested. This states that the pin fin should be made of carbon steel (k = 55 W/mK), with a length of five centimetres and a diameter of one millimetre. The fin is to be located in stagnant air at 22°C, with a convective heat transfer coefficient of 20 W/m2K. You are required to produce a report on your findings as to how effective the proposed design is at dissipating heat away from the electrical component, and suggestions you have for improvements. To undertake this study, you must develop a numerical model by applying both a third order Runge Kutta method, and an Euler method of your choice, to the differential equation in equation 1. This model must be written using MatLab. Any design improvements you make must be justified by use of your model. The appendix must include a copy of your code, which should be adequately annotated. Things to consider • How will you verify your model? • Look at which variables you can change in equation 1 to improve the design. The report The report should be written according to the School of Engineering report template. The introduction and literature review should be brief, and provide enough information to help set up your model. The methodology should include a brief mathematical description of your models, and a flowchart of your code. The results should include the necessary information to evaluate the fin design, and graphs of temperature against length for any design presented. The report should be typed. Further information If you are intending to enhance the fin by changing the shape such that the cross-sectional area increases with the length of the fin, then equation 1 is no longer valid. You will need to modify equation 4 according to the shape you choose. dT 1 dA.\ dT Ac dx 1 h dA. (Т — Т.) — 0 dx? dx Ack dx
The Brief Background An electrical component should not exceed a temperature of 55 C. In order to maintain the temperature, a pin fin style heat sink (see figure 1) has been attached to the component to enhance the heat transfer to the surrounding air. There will be heat transfer through conduction along the length of the pin, and heat transfer through convection from the surface of the pin. Ta qconv Tw qcond L Figure 1: Heat transfer through a Pin Fin This system can be described by the second order differential equation in 1, where h is the convective heat transfer coefficient, p is the perimeter (circumference) of the pin, k is the conductive heat transfer coefficient and Acis the cross-sectional area. dT hp (Т — Та) %—D 0 kAc dx2 Fourier's law (2) is an equation relating the heat dissipated by the fin (q), to the rate of change of temperature along the length of the fin. No heat transfer is assumed to take place at the tip of the fin. dT q = -kAc- dx
Transcribed Image Text:The Brief Background An electrical component should not exceed a temperature of 55 C. In order to maintain the temperature, a pin fin style heat sink (see figure 1) has been attached to the component to enhance the heat transfer to the surrounding air. There will be heat transfer through conduction along the length of the pin, and heat transfer through convection from the surface of the pin. Ta qconv Tw qcond L Figure 1: Heat transfer through a Pin Fin This system can be described by the second order differential equation in 1, where h is the convective heat transfer coefficient, p is the perimeter (circumference) of the pin, k is the conductive heat transfer coefficient and Acis the cross-sectional area. dT hp (Т — Та) %—D 0 kAc dx2 Fourier's law (2) is an equation relating the heat dissipated by the fin (q), to the rate of change of temperature along the length of the fin. No heat transfer is assumed to take place at the tip of the fin. dT q = -kAc- dx
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 2 steps with 2 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Similar questions
  • SEE MORE QUESTIONS
Recommended textbooks for you
Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
Electrical Engineering
ISBN:
9780133923605
Author:
Robert L. Boylestad
Publisher:
PEARSON
Delmar's Standard Textbook Of Electricity
Delmar's Standard Textbook Of Electricity
Electrical Engineering
ISBN:
9781337900348
Author:
Stephen L. Herman
Publisher:
Cengage Learning
Programmable Logic Controllers
Programmable Logic Controllers
Electrical Engineering
ISBN:
9780073373843
Author:
Frank D. Petruzella
Publisher:
McGraw-Hill Education
Fundamentals of Electric Circuits
Fundamentals of Electric Circuits
Electrical Engineering
ISBN:
9780078028229
Author:
Charles K Alexander, Matthew Sadiku
Publisher:
McGraw-Hill Education
Electric Circuits. (11th Edition)
Electric Circuits. (11th Edition)
Electrical Engineering
ISBN:
9780134746968
Author:
James W. Nilsson, Susan Riedel
Publisher:
PEARSON
Engineering Electromagnetics
Engineering Electromagnetics
Electrical Engineering
ISBN:
9780078028151
Author:
Hayt, William H. (william Hart), Jr, BUCK, John A.
Publisher:
Mcgraw-hill Education,
SEE MORE TEXTBOOKS