Name of the Candidate: Reg. No.
:
18ME520
B.E DEGREE– NOVEMBER 2022 –EXAMINATIONS
BRANCH : MECHANICAL ENGINEERING
HEAT AND MASS TRANSFER
Duration : 3Hours Maximum: 100 Marks
SPECIAL INSTRUCTIONS: Use of approved HMT data book and Steam table is
permitted
Answer All Questions
PART – A (5 x 2 = 10) CO Marks
A1. Distinguish between thermal conductivity and thermal differentivity. CO1 (2)
A2. What is the physical interpretation of the Biot number? CO2 (2)
A3. Draw the thermal and hydrodynamic boundary layer for laminar forced CO3 (2)
convection over a flat plate for Pr =1 and Pr >1.
A4. The emissive power of a blackbody is P. Find the emissive power of the same CO4 (2)
when its absolute temperature is doubled.
A5. What is the limitation of LMTD method in a heat exchanger? CO5 (2)
PART – B (5 x 6 = 30) CO Marks
B1. Obtain an expression for temprture distribution for a short and end insulated fin. CO1 (6)
What are the influences of fin length over fin efficiency and effectiveness?
B2. Describe the significance of non-dimensional numbers and draw the velocity CO3 (6)
boundary layer and thermal boundary layer.
B3. Prove that the net radiation heat transfer between any two black surface is given CO4 (6)
by Q1 2 A1 F1 2 E b ,1 E b , 2 .
B4. Derive the expression for calculating the LMTD of parallel flow heat exchangers. CO5 (6)
B5. In the context of mass transfer analysis, explain the significance of non- CO6 (6)
dimensional numbers.
PART – C (60 Marks) CO Marks
C1. (a) A steel tank of wall thickness 10 mm contains water at 85 °C. the k of the CO1 (10)
steel is 50 W/m K and the h for inside and outside of the tank are 2850
W/m2 °C and 10 W/m2 °C. Assume surrounding temperature be 15 °C.
Calculate (i) the rate of heat loss per unit area of the tank surface (ii) the
temperature of the outside of the tank.
(b) The temperature of a gas stream is to be measured by a thermocouple CO2 (10)
whose junction can be considered as a 1.5 mm diameter sphere. The
properties of the junction are k = 40 W/(mK), ρ = 8000 kg/m3, C = 300
J/(kg.K) and the heat transfer coefficient between the junction and the gas
is h = 75 W/(m2°C). (a) Determine the time constant of the thermocouple
junction and (b) the time it takes to read a temperature which corresponds
to a temperature difference (the difference in temperature between the
gas steam and the thermocouple junction) of 99 per cent of its initial
value.
(OR) CONTD…,
C2. (a) An electric current of 34000 A flows along a steel wire of 12.5 mm radius CO1 (10)
and 1 mm length. The temperature of surface of the wire is 95 °C. Find the
value and position of the maximum temperature. Also, calculate the total
amount of heat generated per Unit volume of the wire. Given for steel
resistivity ρ=12 x 10-6 Ω cm and k = 52.4 W/m K.
(b) A glass of diameter 50 mm contains some hot milk. The height of the milk CO2 (10)
in the glass is 100 mm. To cool the milk, a glass is placed in a large pan
filled with cold water at 25 °C. The initial temperature of the milk is 80 °C.
The milk is stirred slowly and continuously so that its temperature remains
uniform at all times. The heat transfer coefficient between the water and
glass is 2.1 W/(m2 °C). Can the milk in this case be treated as a lumped
parameter system? If so, determine (a) The time taken for the milk to cool
from 80 °C to 30 °C and (b) The total amount of energy transferred from
the milk to water during the cooling process. Assume, ����� =0.6
W/(mK), �� = 900 kg/m3, Cp,���� = 4.2 KJ/(kg K). Neglect the effect of
stirring work.
C3. (a) Air at 20 oC is heated to 400 C as it flows through a tube with a diameter CO3 (5)
of 1 in (2.54 cm) at a velocity of 10 m/s. Calculate the heat transfer per
unit length of tube. The wall temperature is 80 oC.
(b) An aeroplane flies with a speed of 450 km/h at a height where the CO3 (5)
surrounding air has a temperature of 1 °C. The aeroplane wing idealized
as a flat plate 6 m long and 1.2 m wide is maintained at 19 °C. If the
flow is made parallel to the 1.2 m width, calculate (a) the heat loss from
the wing, (b) the drag force on the wing. The properties of air at 10 °C
are: k = 0.02511 W/mK, U = 14.16 x 10-6 m2/s, Pr = 0.705.
(OR)
C4. (a) Liquid sodium of 3700C flows over a long cylinder of 7.5 cm diameter in CO3 (5)
the flow direction. The plate temperature is uniform at 2300C. Calculate
the average heat transfer coefficient.
(b) A vertical cylinder 1.5 m high and 180 mm in diameter is maintained at CO3 (5)
1000C in an atmosphere environment of 200C. Calculate the heat loss by
free convection from the surface of the cylinder.
C5. (a) Two very large parallel planes with emissivities 0.3 and 0.8 and CO4 (5)
temperatures of 300K and 800K respectively exchange radiative energy.
Determine the percentage reduction in radiative energy transfer when
both planes are maintained with ϵ = 0.04.
(b) Determine the rate of heat loss by radiation from a steel tube of outside CO4 (5)
diameter 0.07 m and 3 m long at a temperature of 2270C if tube is placed
within a square brick conduit 0.3 m side and at 270C. Take
ϵ (steel) = 0.79 and ϵ (brick) = 0.93.
(OR) CONTD…,
C6. (a) A hot water tank 0.65 m in diameter and 1.15 m in height is located in a CO4 (5)
large room. The water tank surface temperature is 87 C. The surrounding
0
room temperature is 240C. Emissivity of the tank surface is 0.75.
Determine the heat transfer by radiation.
(b) A cryogenic fluid is to be flown through a pipe having 12 cm outside CO4 (5)
diameter at a temperature of -178 C. 0
The cryogenic fluid flow pipe is
surrounded by another pipe of 15 cm outside diameter. The space
between the two pipes is evacuated. The outer pipe is maintained at 70C.
Both the pipe surfaces have emissivity 0.2. If the length of pipe is 4.5 m,
calculate the radiant heat flow.
C7. (a) A thin plastic membrane separates hydrogen from air. The molar CO6 (10)
concentrations of hydrogen in the membrane at the inner and outer
surfaces are determined to be 0.070 and 0.003 kmol/m3 respectively. The
binary diffusion coefficient of hydrogen in plastic at the working
temperature is 5 10 -10
m /s. Determine the mass flow rate of hydrogen
2
by diffusion through the membrane under steady conditions if the
thickness of the membrane is 4 mm.
(b) A counter-flow double-pipe heat exchanger is to heat water from 20 °C to CO5 (10)
80 °C at a rate of 1.2 kg/s. The heating is to be accomplished by
geothermal water available at 160 °C at a mass flow rate of 2 kg/s. The
inner tube is thin-walled and has a diameter of 1.5 cm. If the overall heat
transfer coefficient of the heat exchanger is 640 W/m2°C, determine the
length of the heat exchanger required to achieve the desired heating
(OR)
C8. (a) Steam with 5 kg/s in the condenser of a power plant is to be condensed at CO5 (10)
a temperature of 30 °C with cooling water from a nearby lake, which
enters the tubes of the condenser at 14 °C and leaves at 22 °C. The
surface area of the tubes is 45 m2, and the overall heat transfer coefficient
is 2100 W/m2·°C. Determine the rate of condensation of the steam in the
condenser.Take Cp of Water = 4187 J/kg OC.
(b) Spilled out water layer thickness on a floor is 1.25 mm and at 250C. The CO6 (10)
pressure and temperature of the surrounding air are 1.032 bar and 250C.
Find out the time required to evaporate the complete water layer if
evaporation takes place through an air film of 6 cm thick. Take the
following: The Diffusion coefficient, D = 0.26 10 -4
m /s, absolute
2
humidity of air = 0.002 kg/kg of dry air and saturation pressure at 250C as
3.166 kPa.
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