2014+SQ+EME165+Midterm+Solutions

8/11/2019 2014+SQ+EME165+Midterm+Solutions

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UC Davis EME-165 Heat Transfer Midterm 2014 SPRING, CRN: 22057 (Prof. Aldred

YOU HAVE 1 HOUR AND 50 MINUTES TO COMPLETE THIS EXAM. PLEASE SHOW ALL OF YOUR WO

ON THE PAGE PROVIDED.

YOU MAY NOT REFER TO ANY PRINTED OR DIGITAL MATERIALS OR USE ANY ELECTRONDEVICE, EXCEPT A CALCULATOR FOR BASIC COMPUTATION AND ANY NOTES PROVIDED BY T

INSTRUCTOR FOR USE DURING THE EXAM.

I HAVE READ AND UNDERSTAND THESE EXAMINATION RULES.

Name: ______________________________ Signature: ________________________________


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Name: Student ID: Score: ___

1.

Carefully draw on the diagram below the profile of temperature along the centerline axis of a solid

from its point of attachment to a hot surface at x = 0, where T = T , to its tip at x = L, where T =

Assume that the cross-sectional area of the fin is constant along the axis and that steady-state heat trans

away from the fin and into the surrounding fluid at T occurs. Explain the shape of the temperat

profile using heat-transfer principles and mathematical relations (i.e., why it is linear, concave up

concave down). Also, label and explain the values of Tand T (i.e., why each is greater than, less than

equal to T). Note that there is no internal heat generation within the fin. (15 points)

T

X (fin centerlinex = L

(fin tip)

T

x = 0

(fin base)


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2.

A perfectly round hot steel ball with uniform temperature Tand conductivity k is immersed into a c

bath of water at T T. You must fully justify your answers to the following questions to receive cre

(15 points)

a.

Explain whether the temperature gradient dT/dr at the center of the ball is positive, negative or z

and how its absolute value varies from the beginning through the end of the cooling process (

the radial coordinate measured from the center of the ball).

b.

Now consider the temperature gradient dT/dr in the water bath on the outside surface of the band explain whether this gradient is positive, negative or zero and how its absolute value va

from the beginning through the end of the cooling process.


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3.

An experimental arrangement for measuring the thermal conductivity of solid materials involves the

of two long rods that are equivalent in every respect, except that one is fabricated from a standard mate

of known thermal conductivity kA while the other is fabricated from the material whose therm

conductivity kBis desired. Both rods are attached at one end to a heat source of fixed temperature Tb,

exposed to a fluid of temperature T

, and are instrumented with thermocouples to measure

temperature at a fixed distance x1from the heat source. If the standard material is aluminum, with k

200 W/m!

K, and measurements reveal values of TA= 75C and TB= 60

C at x1for Tb= 100

C and T

25C, what is the thermal conductivity kBof the test material? (25 points)


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4.

A spherical vessel used to contain a hot liquid has a 5-cm-thick stainless steel wall (k = 17 W/m!K) and

inner diameter Di= 1.0 m. The hot liquid inside of the vessel has a density != 1100 kg/m3and spec

heat c = 2400 J/kg!K and is initially at a temperature of 100C. The exterior surface of the vesse

exposed to ambient air at T

= 25C, with h = 6 W/m2!K. Assuming validity of the lumped-capacita

model, determine (a) the amount of time required for the liquid to cool to 50 C and (b) the temperature

the vessels outer wall at this time. (c) How large does the thermal conductivity of the liquid need to be

justify your assumption of validity of the lumped-capacitance model? Note that no heat generation occin either the liquid or the vessel wall. (30 points)

2014+SQ+EME165+Midterm+Solutions

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