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Exam2_S08

Exam2_S08 - Name ME 315 Heat and Mass Transfer Spring 2008...

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Name: 1 ME 315: Heat and Mass Transfer Spring 2008 EXAM 2 Tuesday, 18 March 2008 7:00 to 8:00 PM Instructions: This is an open-book exam . You may refer to your course textbook, your class notes and your graded homework assignments. Show all work clearly for maximum credit. CIRCLE ALL ANSWERS . Problem Score 1 / 16 2 / 22 3 / 22 Total / 60

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Name: 2 1. (16 points) A very thick insulating wall of a large chemical reaction chamber is initially at 300 K and has a surface area of 1 m 2 . Once the chemical reaction begins, the interior surface of the wall is suddenly exposed to a temperature of 2000 K for the duration of the reaction. Properties of the wall material are given in the figure. a. What is the temperature of the insulating wall at a depth of x = 5 cm from the surface at the instant of time that is 5 minutes from the start of the reaction? b. What is the rate of energy (W) transferred to the wall at the time instant, t = 5 min? c. Sketch how the temperature profile in the wall will look at various times and label all important features. Chamber Wall Chamber Interior T s = 2000 K A = 1 m 2 x T i = 300 K c p = 800 J/(kg . K) ρ = 1500 kg/m 3 k = 1 W/(m . K)
q s 6.066 10 4 × W = q s k A T s T i - ( 29 π α t = Using equation 5.58 for the heat flux at t = 5 min: (b) T x 343.09 K = T x T s T i T s - ( 29 erf x 2 α t + = Solving for Tx: erf η 0.975 = erf η erf x 2 α t = η 1.581 = η x 2 α t = α 8.333 10 7 - × m 2 s = α k ρ c p = Evaluating some of the terms: T x T s - T i T s - erf x 2 α t = Recognizing the wall as a semi-infinite medium, we can use equation 5.57 for the temperature: (a) k 1 W m K = ρ 1500 kg m 3 = c p 800 J kg K = x 5cm = T s 2000 ( )K = A 1m 2 = t 5min = T i 300 ( )K = Given: Problem 1

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(c) t 1 1min = The plot should look something like this with the surface temperature at x=0 at 2000 K and exponentially decay to 300 K. As time increases, the exponential decrease occurs over a longer distance.
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Exam2_S08 - Name ME 315 Heat and Mass Transfer Spring 2008...

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