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MEL301 Heat and Mass Transfer I.I.T - Ropar

1st

Semester 2014-15

Tutorial Sheet #4

(This is a Draft Version. Some more questions may be added but none will be removed, so you

may start solving these one-by-one)

General Instructions:

1. Deadline to submit this assignment: To be announced

2. Study and revise Chapter-4 (Transient Heat Conduction) from the textbook.3. The thermal properties of various materials can be obtained from the several tables given in the Appendix of the

textbook

4. While solving problems in this course draw the system/control volume boundary and follow rest of the procedure

mentioned in the class (identification of problem, governing equations, assumptions etc.), where applicable.

PRACTISE PROBLEMS (These problems are for practice, no need to submit them however each student must solve ALL

these problems themselves)

1) Read and analyze all the solved examples of this chapter from the textbook

2)

Consider a sphere and a cylinder of equal volume made of copper. Both the sphere and the cylinder are initially

at the same temperature and are exposed to convection in the same environment. Which do you think will cool

faster, the cylinder or sphere? Why?

3)

In what medium is the lumped system analysis more likely to be applicable: in air or in water? Why?

4)

To warm up some milk for a baby, a mother pours milk into a thin - walled glass whose diameter is 6-cm. The

height of the milk in the glass is 7-cm. She then places the glass into a large pan filled with hot water at 70oC.

The milk is stirred constantly, so that its temperature is uniform at all times. If the heat transfer between the

water and glass is 120 W/m2K, determine how long it will take for the milk to warm up from 3

oC to 38

oC. Take

the properties of the milk to be the same as those of water. Can the milk in this case be treated as a lumped

system? Why? Repeat this problem for the case of water also being stirred, so that the heat transfer coefficient

is doubled to 240 W/m2K.

5)

Can the transient temperature charts in Fig. 4-16 for a plane wall exposed to convection on both sides be usedfor a plane wall with one side exposed to convection while the other side is insulated? Explain.

PROBLEMS (These must be submitted)

1)

Consider a 800-Watt iron whose base plate is made of 0.5-cm-thick aluminium alloy 2024-T6 (=2770 kg/m3,

cp= 875 J/KgK, = 7.310-5

m2/s). The base plate has a surface area of 0.03 m

2. Initially, the iron is in thermal

equilibrium with the ambient air at 22oC. Taking the heat transfer coefficient at the surface of the base plate to

be 12 W/m2K and assuming 85% of the heat generated in the resistance wires is transferred to the plate,

determine how long it will take for the plate temperature to reach 140oC. Is it realistic to assume the plate

temperature to be uniform at all times?

2)

Consider a spherical shell satellite with outer diameter of 4 m and shell thickness of 10 mm is re-entering the

atmosphere. The shell satellite is made of stainless steel with properties of = 8238 kg/m3, cp = 468 J/kgK and k

= 13.4 W/mK. During the re-entry the effective atmosphere temperature surrounding the satellite is 1250oC

with convection heat transfer coefficient of 130 W/m2K. If the initial temperature of the shell is 10oC,determine the shell temperature after 5 minutes of re-entry. Assume heat transfer occurs only on the satellite

shell.

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3)

An electronic device dissipating 18 Watts has a mass of 20 gm, a specific heat of 850 J/kgK, and a surface area

of 4 cm2. The device is lightly used, and is on for 5 minutes and then off for several hours, during which it cools

to the ambient temperature of 25oC. Taking the heat transfer coefficient to be 12 W/m

2K, determine the

temperature of the device at the end of the 5 minutes of operating period. What would your answer be, if the

device were attached to an aluminum heat sink having a mass of 200 gm and a surface area of 80 cm2? Assume

the device and the heat sink to be nearly isothermal.

4)

A long roll of 2-m-wide and 0.5-cm-thick 1-Mn manganese steel plate coming off a furnace at 820oC is to be

quenched in an oil bath (cp= 2.0 kJ/kgK) at 45oC. The metal sheet is moving at a steady velocity of 20 m/min,

and the oil bath is 9m long. Taking the convection heat transfer coefficient on both sides of the plate to be

860W/m2K, determine the temperature of the sheet metal when it leaves the oil bath. Also, determine the

required rate of heat removal from the oil to keep the temperature constant at 45oC.

5) A watermelon initially at 35oC is to be cooled by dropping it into a lake at 15

oC. After 4h and 40 min of cooling,

the centre temperature of watermelon is measured to be 20oC. Treating the watermelon as a 20-cm diameter

sphere and using the properties k = 0.618 W/mK, = 0.1510-6

m2/s, = 995kg/m

3 and cp= 4.18 kJ/kgK,

Determine the average heat transfer coefficient and the surface temperature of watermelon at the end of the

cooling period.

6)

An exothermic process occurs uniformly throughout a 10-cm-diameter sphere (k = 300 W/mk, cp= 400 J/kgK,

= 7500kg/m3), and generates heat at a constant rate of 1.2 MW/m

3. The sphere initially is at a uniform

temperature of 20oC, and the exothermic process is commenced at time t= 0. To keep the sphere temperature

under control, it is submerged in a liquid bath maintained at 20oC. The heat transfer coefficient at the sphere

surface is 250 W/m2

K.Due to high thermal conductivity of sphere, the conductive resistance within the sphere can be neglected

in comparison to the convective resistance at its surface. Accordingly, this unsteady heat transfer situation

could be analyzed as a lumped system.

(a) Show that the variation of sphere temperature Twith time t can be expressed as dT/dt= 0.5 0.005T

(b)

Predict the steady state temperature of the sphere.

(c)

Calculate the time needed for the sphere temperature to reach the average of its initial and final

(steady) temperatures.