Homework02 - MECE E3311 Heat Transfer Homework 2 Arvind...

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MECE E3311 Heat Transfer: Homework 2 Arvind Narayanaswamy, Department of Mechanical Engineering, Columbia University. Please submit problems 1 – 3 in one document (to be corrected by Jonathan) and 4 in another (Sybille). Problem 1 Derive the temperature distribution for the case of uniform heat generation in a metallic wire of radius R . The thermal conductivity of the material is k . The boundary condition ar r = R is T = T o . The wire is assumed to be very long in the axial direction – you can assume the heat flow only along the radial direction. What is the temperature difference between center of the wire and r = R . Derive the results for this problem without using any standard heat transfer text book as a reference – you will learn a lot that will be useful for exams. Problem 2 Example 2.8 with the following numbers: heat dissipation rate is 0.2 W, 4.0 mm OD, length is 12 mm. Air in cabinet is at 32 o C. Natural convection is 12 Wm - 2 K - 1 , and you can neglect thermal radiation for now. This is a good problem. Please do not read
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