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Unformatted text preview: 3.13 A house. has a compositewall of wood, ﬁberglasainsula
.tion,_ and pleater board, as indicated in the sketch. On a
cold winter day the convection heat. transfer coefﬁcients.
are ha = 60 W/m2  K and hi = 30 W/m2  K. The total
wall surface area is 350 m2. Glass fiber blanket
(28 kenl3). a, Plaster board, kp Plywood siding, k3 I
[I1
IIIIIIIII 10 mm —> h—lOO’ mm—,.>'l k—ZO mm LP Lb L3 (a) Determine a symbolic expression for the total ther—
mal resistance of'the wall, including inside and out
side convection effects'for the prescribed conditions. (b) Determine the. total heat loss through the wall. (c) If the wind were blowing violently, raising. ho to
300 W/m2  K, determine the percentage. increase
in the heat loss. ((1) What is the controlling resistance that detennjnes
the amount of heat ﬂow through the wall? 3.26 In a particular application, it is desirable to minimize
the effects of the thermal contact resistance between
two plane mating surfaces as shown in part (a) of the
schematic. An engineer suggests that the overall resis
tance to heat transfer can be. reduced by cutting rela
tively deep linear grooves in each surface, resulting in
the interlocking finlike structure shown in part (b)
of the schematic. If the grooves in material A are of
the same width as “the grooves. in material B, evaluate
the merit of" the proposed scheme using an appropriate analysis.
Contact
Contact _ __ _
resistance Material A. resistance Material B
(a) (b) 3.4 In a manufacturing process, .a transparent ﬁlm is being
bonded to a substrate as shown in the sketch. To cure the
bend at a temperature To, a radiant source is used to pro—
Vide a heat ﬂux q'E, ’.(W/r‘n2) all of which is absorbed at the
bonded surface. The back of the substrate IS maintained
at T1 while the free. surface of the ﬁlm is exposed to air at
Tm. and a convection heat transfer coefﬁcient k. Lf =0;25 mm
kf= 0.025 WlmK
L3 = 1.0 mm k3 = 0.05 W/mK (a) Show the thermal circuit representing the stready—state
heat transfer situation. Be sure to label all elements,
nodes, andheat rates. Leave in symbolic form. (b) Assume the following CDﬂdIthﬂS' T = 20°C h —
50 W/;n12K and T1—= 309C. Calculate the heat
flux «:13 "that 1s required to maintain the bonded sur— face. at :111 = 60°C.... Compute and plot the required heat ﬂux as a funcr
tion of the ﬁhn thickness for .0 E Lfﬁ 1 mm, (d) If the "ﬁlm is not transparent and all Of the radiant
heat'ﬂux is absorbed at its upper. surface, determine
the: heat. ﬂux required to achieve. bonding. Plot your
results as a function 'of L); for O E L; E 1 mm. 3.4.6 A composite cylindrical wall is composed of two mate—
rials of thermal conductivity kg and kB_,.._ which are sepa
rated by a very thin. electric resistance heater for which
interfacial contact resistances are negligible. Liquid pumped. through the tube is at a. temperature Twig
and provides a convection coefﬁcient hat the inner sur
face of the composite; The outer surface is exposed to
ambient air, which is at Tm and provides a convection
coefﬁeient of hi. Under steady—state; conditions, a uni~
for: heat ﬂux of q}: is dissipated. by the. heater. (a5) Sketch the equivalent thermm circuit ofthe system
and express all resistances in terms of relevant
variables. (b) Obtain an expression that may housed to determine
the heater temperature, Th. (e) Obtain an eXpression for the ratio of heat ﬂows to
the outer and inner ﬂuids, q; M}. How might the
variables of the problem be adjusted to minimize
this. ratio? 3.6.4 Theenergytrahsferred from "the antener ehamber of the
eye ”through the. cornea varies cnalderaly depending
on Whether a contact lens is Worn. Treat the eye as a spherical system and assume the system to he at steady
1s te The cenvection coefﬁc1ent h... is unchanged Wlth
I”i151 without the contact lens. in place. The cornea and .Il. ;;;;;; e lens cover onethird of the: . spheneal surfaeearea 14 Anterior
member Cornea  .f'ijlf‘i_3*alues of the parameters representing this situation
if; e as follows: ' 34:102 111m 2 = 12.7 mm
16.5mm TM 21°C  37°C  k2= 0.80 W/m * K
=— 1) 35 W/m K h; =. 6 W/rn K II. . '53? et lens and meludrng the. Contact lens. Write resis— ‘ “ tance elements in terms of appropriate parameters.
_IJ. ' Determme the heat loss from the anterior chamber
. With and Without the. eerrtaet lens 111 place. 1181:1133 theimplieation of your results. 1111; leer fuel element of thickness 2L" 1s covered with
1 claddmg of thickness '19. Heat generated within
,1 111“ clear fuel at a rate 1:] is removed by a ﬂuid at Tm,
.[1¢;11 ='_"o1ns one surface and is characterized bya 1 vii11 coefﬁc1ent h The other surface 1s well msu—
and the fuel and steel have. thermal conductivities ...... 1 111d 1113, respecuvely 1' :1 .
‘9 ' Steal Nuclear fuel '11 an equation for the temperature distribution
) 1n the nuclear fuel. Express your results in 111111; 11.1. b 11.11 and r1...  1 1:11th the temperamre distribution T01) for the
the system. ...
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 Spring '11
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