Sample Exam

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School

University of Houston *

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Course

4364

Subject

Mechanical Engineering

Date

Oct 30, 2023

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1 MECE 4364 Heat Transfer Midterm Examination Sample Name: _______________________ People Soft ID: _____________________ Please sign the Honor Pledge below: I have not discussed the exam with anyone. I have not used resources other than my course textbook and class/personal notes, including the homework solutions and Internet. I will not disclose the content of the exam to anyone who may take this course later. Signature: ____________________________________ Instructions: 1. The exam problems are intentionally broken into a set of sub-questions. This does not mean the problems are super-hard. The purpose is to ensure that everyone can solve part or all of the problem. Hence, please answer each of them explicitly and clearly. 2. Please provide sufficient intermediate steps to show how you obtain your final result. Otherwise, you may lose the points associated with these details if your final answer is wrong. 3. As future engineers and scientists, ME students should understand that mathematical details play an equally important role as the physical concepts and the numbers. So show your equations and solve them symbolically before you plug in numerical values.

2 Total: 80 points 1. ( 25 points ) A composite wall has three layers of materials, A, B and C. We know the thermal conductivities of two materials, 𝑘 ? = 20 𝑊/𝑚? and 𝑘 ? = 50 𝑊/𝑚? . The thicknesses are ? ? = 0.3 𝑚 , ? ? = ? ? = 0.15 𝑚 . The left surface of the wall is exposed to a hot air flow ( T ∞ = 800°C and h = 25 W/m 2 K). Under steady-state conditions, we find the left surface temperature of 𝑇 ?,𝑖 = 600℃ and the right surface temperature 𝑇 ?,𝑂 = 20℃ . a. ( 10 points ) Draw the thermal network of the system and mark all the thermal resistances (including the expressions). b. ( 5 points ) What is the heat flux through the composite wall? c. ( 10 points ) What is the thermal conductivity of material B, 𝑘 ? ?

3 2. ( 55 points ) As shown in the following figure, we have a plane wall of thickness L = 1 m and thermal conductivity 𝑘 = 2 𝑊/𝑚? . Due to internal heating, the wall experiences uniform heat generation at a rate of 𝑞̇ = 20 𝑊/𝑚 3 . The left surface of the wall is exposed to the ambient air ( T ∞ = 20°C and h = 10 W/m 2 K), and it also receives solar irradiation in the amount of G s = 200 W/m 2 . The right surface of the wall is perfectly insulated. Meanwhile, the surface is irradiating to the universe of 𝑇 ?𝑢?? = 3 ? . The solar absorptivity and emissivity of the surface are α = ε = 0.9 8. a. ( 5 points ) What is the boundary condition at the right surface ( 𝑥 = ? )? Write down the mathematical expression. b. ( 10 points ) Assuming the temperature of the left surface is T s , write down the surface energy balance equation for the left boundary ( 𝑥 = 0). Note: Do not calculate anything, just the symbolic expression is fine. c. ( 15 points ) Calculate the steady state surface temperature T s for the given conditions. Note: 1) This is a problem unrelated to Part b, so do not try to get the result directly from your answer to Part b; 2) The Stefan-Boltzmann constant is 𝜎 = 5.67 × 10 −8 𝑊/𝑚 2 ? 4 ; and 3) You may need to do trial-and-error when calculating T s . d. ( 10 points ) Assuming steady state, what is the conduction equation that governs heat transfer in the wall? e. ( 10 points ) Now you have the conduction equation and the two boundary conditions, solve the equation and find the surface temperature 𝑇(𝑥 = ?) . f. ( 5 points ) What is the conduction heat flux at the left surface 𝑥 = 0 at steady state?

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