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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 thex—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 xdirection under the _steady.state conditions. f} L .213 31... (h) The ﬁgures below shows the temperature proﬁles (T(x)j in rectangular composite walls at
steadystate. There is no heat: generation inside the walls. The surface area of the wall in the plane”
perpendicular to the xdirection is thesame 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 heatgeneratingcylindrical
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 heatgenerating
layer (tie. for r = Rf) under the steadystate 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,_ respective1y. Assume that
there is no. heat conduction in vaeuum. Black circle indicates vacuum External wall {Ks
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 Spring '09
 ASTHAGIRI

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