aer205_exam_2007_questions

aer205_exam_2007_questions - University of Toronto Faculty...

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Page 1 of 14 University of Toronto Faculty of Applied Science and Engineering FINAL EXAMINATION – December, 2007 SECOND YEAR -- ENGINEERING SCIENCE Program 5 AER205F FLUID MECHANICS and TRANSPORT PHENOMENA Examiners: Y-L Cheng and J. W. Davis _________________________________________________________ Instructions: (1) Closed book examination; except for a non-programable calculator, no aids are permitted (2) Write your name and student number in the space provided below. (3) Answer as many questions as you can. Parts of questions may be answered. (4) The questions are NOT assigned equal marks. (5) Boldface quantities represent vectors. (6) Use the overleaf side of pages for additional or preliminary work. (7) Do not separate or remove any pages from this exam booklet. (8) Use g = 10 m/s 2 , D water = 1000 kg/m 3 where appropriate. (9) Species Continuity Equation and Fick’s Law are included on page 2 (10) When differential equations of change can be applied to solve a problem, you have the choice of either using those equations or using the shell control volume approach. ____________________________________________________________________ Family Name:________________________________________________________ Given Name:________________________________________________________ Student #:________________________________________________________

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AER205F (2007) Final Examination 2 Species Continuity Equation and Fick’s Law of Diffusion D C A D t = D 2 C A + R A Cartesian Coordinates ∂C A ∂t + v x A ∂x + v y A ∂y + v z A ∂z = D ± 2 C A 2 + 2 C A 2 + 2 C A 2 ² + R A J Ax = - D A J Ay = - D A J Az = - D A Cylindrical Coordinates A + v r A ∂r + v θ r A ∂θ + v z A = D ± 1 r ³ r A ´ + 1 r 2 2 C A 2 + 2 C A 2 ² + R A J Ar = - D A J = - D r A J Az = - D A Spherical Coordinates A + v r A + v θ r A + v φ r sin θ A ∂φ = D ± 1 r 2 ³ r 2 A ´ + 1 r 2 sin θ ³ sin θ A ´ + 1 r 2 sin 2 θ 2 C A 2 ² + R A J Ar = - D A J = - D r A J = - D r sin θ A
AER205F (2007) Final Examination 3 Problem 1 [35 Marks] The three parts in this problem can be done independently of each other, but they all relate to the ﬁlm theory for convective mass transfer as described below. A chemical species ”A” is being released from a rectangular solid into a ﬂowing ﬂuid. With the concentration of ”A” in the ﬂuid being denoted by C A , the processes are such that C A = C A 0 at the solid/ﬂuid interface x = 0 , and C A 0 in the bulk ﬂuid. As you know, convective mass transfer coefﬁcients, k c , are used to describe the rate of mass transfer from a surface to a ﬂowing ﬂuid. Film theory is an alternative way of modelling convective mass transfer in which one imagines that a hypothetical stagnant (no ﬂow) ﬂuid ﬁlm of thickness L exists next to the surface. L

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aer205_exam_2007_questions - University of Toronto Faculty...

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