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Course Syllabus

# Course Syllabus - ECH 3264 Elementary Transport Phenomena...

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Unformatted text preview: ECH. 3264 Elementary Transport Phenomena Exam 1 (2 problems) Closed Notes, Homework Solutions, and Books 1. (a) A rectangular furnace wall consists of three layers of equal. thickness L labeled as l, 2, and 3 (see ﬁgure below). The smface area of the wall in the: plane perpendicular to the-x—axis is the same for each layer. Find the ”expressions for the ratios between the thermal Conductivities of the layers 1 and 2 as well as 2 and 3- (i.e-., k1! kg, and k2/ k3) if the temperatures at each interface of the wall (To, '3'}, T3, and "T3 for x = 0, L, 2L and 313, see ﬁgure) are given. Note that the flow of heat occurs in the positive x-direction under the _-steady-.state conditions. f} L .213 3-1... (h) The ﬁgures below shows the temperature proﬁles (T(x)j in rectangular composite walls at steady-state. There is no heat: generation inside the walls. The surface area of the wall in the plane” perpendicular to the x-directi-on is the-same for each layer of the wall. Which proﬁles are physically possible? Provide a short explanation of your answer. (1) ('2) (3) (6 points for problem 1) 2. A cylindrical vacuum tube with a- high vacuum inside is made of a heat-generatingcylindrical layer with the uniform thickness L; = R2 - R1 and a homogeneous external wall with the uniform thickness Lw = R3 — R; (see ﬁgure bolow). Heat is generated. inside the layer with a volumetric rate SOT). There is no heat generation inside the external Wall. The rate of heat generation in the layer 8(r), which can be understood as theenergy generated per unit volmne per unit time, depends on a distance from the axis of the cylindrical tube (r) as S(r) = Ar5, where A is a known constant. Find the temperature at the internal surface of the heat-generating layer (tie. for r = Rf) under the steady-state conditions if the thermal conductivities of the layer and of the external wall are equal to In and k2, respectively The temperature and heat flux at the external .surfaee' of the wall (:13. for r = R3) are known and equal to T3 and q3,_ respective-1y. Assume that there is no. heat conduction in vaeuum. Black circle indicates vacuum External wall {Ks wuss ‘ §§§~ as ms§““ ‘S‘ /“‘§§%“‘ ///“ :9 :3 n-t-J ”4': 2 9. 1g ‘1 I H 5° 3“ “as ﬂ ‘3‘? / Layer with heat generation ' \'\\\\‘\‘\'\ sws “A . . -. «a \\\\\\\\‘b 3 if see“ eta s» esteem: _ .' k the“ \$119!!!) . j I’ll]. "ll - ”gamma? (6. points fer problem 2) 0) nm‘ Mum/69 [005554416 gﬂ'auS( .._. [2) (3) r / ,‘ =L= T j I I.“ "5%: ”1 ”film! 2—3 2_3 S‘WS 61/4 (1er rend: (c 1(th (y/I‘hauﬁf wc'H/l PM Fadl'i F and (“f-ﬂ I" Assam 4m; € = éengfﬁ 0* ' . (2 JTWH (a): Ca ) H K2 :1!” b (if (2) F (2) __ __ (o if GIT - k2- r“ _ (=:)_ _ (a) h) _ _. Ca an‘ C ‘ LA; [LC I 71:) 7:? JW‘ r:iPZ hf?) {2) T: Z ._ i9, {,1 U67) f C, f?)_, “H“ . (up), _ C1 ‘ /3 "’— Kg (/1 [8?) 13,0 {225 71/;3 c}; - (of?) (‘909— . P dig '— {83 { \$3 3 ...
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Course Syllabus - ECH 3264 Elementary Transport Phenomena...

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