ME6502-HEAT AND
MASS TRANSFER
Unit-1 Conduction
Part-A
1.
State Fourier’s law of heat conduction.
2.
Define thermal conductivity and thermal
resistance.
3.
Write three dimensional steady state
heat conduction equation for Cartesian and cylindrical coordinates.
4.
Write Laplace equation and Poisson
equation.
5.
Define thermal diffusivity.
6.
Define overall heat transfer
coefficient.
7.
What is meant by critical radius of
insulation? Give it’s expression.
8.
Define fin efficiency and fin
effectiveness.
9.
What do you understand the term extended
surfaces or fins? Give it’s applications.
10.
Differentiate steady state and unsteady
state heat conduction with examples.
11.
Define Biot number. Mention it’s
significance.
12.
What are Heisler charts?
13.
What is meant by lumped heat analysis?
When it is used?
14.
Differentiate semi-infinite solids and
Infinite solids.
Unit-1
Conduction
Part-B(First
part)
1.
`Derive
heat conduction equation in Cartesian Coordinates.
2.
Derive
an expression for the heat conduction equation in cylindrical coordinates.
3.
A
composite wall consists of three layers of thicknesses 300 mm, 200mm and 100mm
with thermal conductivities 1.5, 3.5 and is W/m K respectively. The inside
surface is exposed to gases at 1200°C with convection heat transfer coefficient
as 30W/m2K. The temperature of air on the other side of the wall is
30°C with convective heat transfer coefficient 10 W/m2K. If the
temperature at the outside surface of the wall is 180°C, calculate the
temperature at other surface of the wall, the rate of heat transfer and the
overall heat transfer coefficient.
4.
A
furnace wall consists of three layers. The inner layer of 10 cm thickness is
made of firebrick
(k =1.04 W/mK). The intermediate
layer of 25 cm thickness is made of masonry brick (k = 0.69 W/mK) followed by a
5 cm thick concrete wall (k = 1.37 W/mK). When the furnace is in continuous
operation the inner surface of the furnace is at 800°C while the outer concrete
surface is at 50°C. Calculate the rate of heat loss per unit area of the wall,
the temperature at the interface of the firebrick and masonry brick and the
temperature at the interface of the masonry brick and concrete.
5.
A
steel pipe. Inside diameter 100 mm, outside diameter 120 mm (k 50 W/m K) IS
Insulated with a40mm thick high temperature insulation(k = 0.09 W/m K) and
another Insulation 60 mm thick (k = 0.07 W/m K). The ambient temperature IS
25°C. The heat transfer coefficient for the inside and outside surfaces is 550
and 15 W/m2K respectively. The pipe carries steam at 300oC.
Calculate (a) the rate of heat loss by steam per unit length of the pipe (b)
the temperature of the outside surface.
6.
A
steel tube k=43.26 W/mK of 5.08 cm 10 and 7.62 cm 00 is covered with 2.54 cm of
asbestos insulation k=0.208 W/Mk. The inside surface of the tube receives heat
by convection from a hot gas at a -temperature of 316°C with heat transfer
coefficient h=284 W/m2K while the outer surface of Insulation is
exposed to atmosphere air at 38°C with heat transfer coefficient of 17 W/m2
K Calculate heat loss to atmosphere for 3 m length of the tube and temperature
drop across each layer.
7.
(i)
An electric current is passed through a plane wall of thickness 150 mm which
generates heat at the rate of 50,000 W/m3. The convective heat
transfer coefficient is 65 W/m2K. The ambient air is at 28°C and the
thermal conductivity of the wall material is 22 W/mK. Calculate surface
temperature and maximum temperature in the wall.
(ii) A copper wire of 40 mm
diameter carries 250 A and has a resistance of 0.25x10-4 ohm
cm/length surface temperature of wire is 250°C and the ambient temperature is
10°C. if the thermal conductivity of wire is 175 W/mK. Calculate heat transfer
coefficient and maximum temperature of the wire.
Unit-1
Conduction
Part-B (Second
part)
8.
(i)
A Circumferential rectangular profile fin on a pipe of 50 mm outer diameter is 3
mm thick and 20 mm long. Thermal conductivity is 45 W/mK. Convection
coefficient is 100 W/m2 K. base and surrounding temperatures are 120°C and 35°C respectively. Determine heat
flow rate per fin, Fin efficiency and Fin effectiveness.
(ii) An aluminium rod (k =204
W/mK) 2 cm in diameter and 20 cm long protrudes from a wall which is maintained
at 300°C. The end of the rod is insulated and the surface of the rod is exposed
to air at 30°C. The heat transfer coefficient between the rod's surface and air
is 10 W/m2 K. Calculate the heat lost by the rod and the temperature
of the rod at a distance of 10 cm from the wall.
9. (i) Aluminums
fins 1.5 cm wide and 10 mm thick are placed on a 2.5 cm diameter tube to
dissipate the heat. The ambient temperatures are 20°C
and the tube surface temperature is 170°C calculate the
heat loss per fin. Take h = 130 W/m2°C and K = 200
W/m2°C for aluminums.
(ii) Write short
notes on fins.
10. A heating unit
made in the form of a cylinder is 5 cm diameter and 1 m long. It is provided with 10 longitudinal fins of material having
k=120 W/mK of 0.76 mm thick which protrudes 1.27 cm from the surface of the
cylinder. The surface temperature of the cylinder is 150°C
and the ambient temperature is 45°C. The heat
transfer coefficient is 17 W/m2K. Calculate the rate of heat
transfer and the temperature at the end of the fins.
11. (i) A large
steel plate 5 cm thick is initially at a uniform temperature of 400°C.
It is suddenly exposed on both sides to a surrounding at 60°C
with convective heat transfer coefficient of 285W/m2K. Calculate the
centre line temperature and the temperature inside the plate 1.25 cm from the
mid plane after 3 minutes.
Take k for steel is 42.5 W/mK, α for
steel is 0.043 m2/hr
(ii) A long
steel cylinder 12 cm diameter and initially at 20°C is placed into
furnace at 820°C with h=140 W/m2K.
Calculate the time required for the axis temperature to reach 800°C.
Also calculate the corresponding temperature at a radius of 5.4 cm at that
time.
Take k for steel is 21 W/mK, α for steel
is 6.11x10-6 m2/s.
12. A large slab
initially at a temperature of 600°C and its
surface temperature is suddenly lowered to 50°C. Calculate a)
temperature at a depth of 3 cm after 6 minutes b) How much time required, the
temperature at a depth of 3 cm will reach to 350 °C c)The quantity
of cumulative heat passed through the plate at a depth of 3 cm within first one
hour.
Take k=1.2 W/mK, α= 0.004 m2/hr.
13. Alloy steel ball
of 12 mm diameter heated to 800°C is quenched in
a bath at 100 °C. The material
properties of the ball are k=2015 kJ/m hr K, density is 7860 kg/m3,
Cp=0.45 kJ/kg K, h=150 KJ/hr m2 K. Determine (a)
Temperature of a ball after 10 sec (b) Time for ball to cool to 400°C.
Unit-2
Convection
Part-A
1.
Define convection. Give its types.
2.
What is meant by free convection? Give
examples.
3.
What is meant by forced convection? Give
examples.
4.
State Newton’s law of convection.
5.
What are the dimensionless parameters
used in forced and free convection?
6.
Indicate the significance of boundary
layer.
7.
Define boundary layer thickness.
8.
Define hydrodynamic and thermal boundary
layers.
9.
Define Nusselt number and Reynolds
number. Mention its significance.
10. Define
Prandtl number and Grashof number. Give its significance.
11. What
is meant by laminar flow and turbulent flow?
12.
In which mode of heat transfer is the
convection heat transfer coefficient usually higher, natural or forced
convection? Why?
Unit-2
Convection
Part-B
(First part)
1.
Air
at 40° C is flows over
a flat plate of 0.9 m at a velocity of 3 m/s. Calculate the following: (a)Overall drag coefficient (b) Average
shear stress, (c) Compare the average shear stress with local shear stress
(shear stress at the trailing edge)
2.
Air
at 20° C at
atmospheric pressure flows over a flat plate at a velocity of 3 m/s. if the
plate is 1 m wide and 80° C calculate the
following at x = 300. a. Hydrodynamic boundary layer thickness, b. Thermal
boundary layer thickness, c. Local friction coefficient, d. Average friction
coefficient, e. Local heat transfer coefficient
f. Average heat transfer coefficient, g. Heat transfer.
3.
Air
at 20 °C with a free
stream velocity of 6 m/s.°C flows over a
flat plate at 60°C Determine the
value of the average convective heat transfer coefficient up to a length of 1 m
in the flow direction.
4.
Engine
oil flows through a 50 mm diameter tube at an average temperature of 147°C .The flow velocity is 80 cm/s.
Calculate the average heat transfer coefficient if the tube wall is maintained
at a temperature of 200°C and it is 2 m
long.
5.
For
a particular engine, the underside of the crank case can be idealized as a flat
plat 20 cm. The engine runs at 80 km/hr and the crank case is cooled by air
flowing past it at the same speed. Calculate the loss of heat from the crank
case surface of 75°C and the
ambient air temperature 25°C. Assume the boundary
layer becomes turbulent from the loading edge itself.
6.
Air at 25°C flows over 1 m x 3 m (3 m long) horizontal
plate maintained at 200°C at 10m/s. Calculate the average heat transfer
coefficients for both laminar and turbulent regions.
Take Re (critical) = 3.5 x 105
Unit-2
Convection
Part-B
(Second part)
7. A steam pipe 10 cm OD runs horizontally in a room at 23° C. Take outside
temperature of pipe as 165 ° C. Determine the heat loss per unit length of the
pipe.Pipe surface temperature reduces to 80° C with 1.5 cm insulation. What is
the reduction in heat loss?
8. Cylindrical cans of 150 mm length and 65 mm diameter are to be cooled
from an initial
temperature of 20°C by placing them in a cooler
containing air at a temperature of 1°C and
a pressure of 1 bar. Determine the cooling rates when
the cans are kept in horizontal and
vertical
positions.
9. The water is heated in a tank by dipping a plate of 20 cm X 40 cm in
size. The temperature of
the plate surface is maintained at 100°C. Assuming the
temperature of the surrounding water is
at 30° C,
Find the heat loss from the plate 20 cm side is in vertical plane.
10. A steam pipe 10 cm outside diameter runs horizontally in a room at 23°C.
Take the outside
surface temperature of pipe as 165°C. Determine the
heat loss per unit length of the pipe.
11. A large vertical plate 5 m high is maintained at 100°C and exposed to
air at 30°C. Calculate the
convection heat transfer coefficient.
12.Sketch the boundary layer development of a flow
over a flat plate and explain the significance
of the boundary layer.
Unit-3Phase
Change Heat Transfer and Heat Exchangers
Part-A
1.Define boiling and condensation.
2.Give the applications of boiling and condensation.
3.What is meant by nucleate and film boiling?
4.Define film wise and drop wise condensation.
5.Draw different regions of boiling.
6.List out the types of heat exchangers.
7.What
is meant by compact heat exchanger?
8.Define NTU approach
and state it's use.
9.What is meant by
LMTD with it's expression.
10.What is meant by
effectiveness?
11.What is meant by
fouling factor?
12.Sketch the
temperature variations in parallel and counter flow heat exchangers.
13. What is meant by
pool boiling?
14. What is meant by
flow boiling?
Unit-3 Phase
Change Heat Transfer and Heat Exchangers
Part-B (First
Part)
1.
Water is to be boiled at atmospheric pressure in a
mechanically polished stainless steel pan
placed on
top of a heating unit. The inner surface of the bottom of the pan is maintained
at
l08°C. The
diameter of the bottom of the pan is 30 cm. Assuming Csf = 0.0130. Calculate
(i)the
rate of heat transfer to the water and ii) the rate of evaporation of water.
2. (i) It is desired to boil water at atmospheric pressure on a copper
surface which electrically heated.Estimate the heat flux from the surface to
the water, if the surface is maintained at 10°C andalso the peak heat flux.
(ii) With a neat sketch explain about regimes of
boiling.
3. A tube of 2 m length and 25 mm outer diameter is to be used to condense
saturated steam at 100°C while the tube
surface is maintained at 92°C. Estimate the average heat transfercoefficient
and the rate of condensation of steam if the tube is kept horizontal. The
steamcondenses on the outside of the tube.
4. Dry saturated steam at a pressure of 2.45 bar condenses on the surface
of a vertical tube ofheight 1 m. The tube surface temperature is kept at 117°C.
Estimate the thickness of thecondensate film and the local heat transfer
coefficient at a distance of 0.2m from the upper endof the tube.
5. A heating element cladded with metal is 8 mm diameter and emissivity of
0.92. The element is horizontally immersed in a water bath. The surface
temperature of the metal is 260°C under steady state boiling conditions.
Calculate the power dissipation per unit length of the heater.
6. A steam condenser consisting of a square array of 900 horizontal tubes
each 6 mm in diameter. The tubes are exposed to saturated steam at a pressure
of 0.18 bar and the tube surface temperature is maintained at 23°C. Calculate
heat transfer coefficient and the rate of steam is condensed.
7.
Steam condenses at atmospheric pressure on the
external surface of the tubes of a steam condenser. The tubes are 12 in number
and each is 30 mm in diameter and 10 m long. The inlet and outlet temperatures
of cooling water flowing inside the tubes are 25°C and 60°C respectively. If
the flow rate is 1.1 kg/s, calculate (i) The rate of condensation of steam (ii)
The number of transfer units (iii) The effectiveness of the condenser.
Unit-3 Phase
Change Heat Transfer and Heat Exchangers
Part-B (Second
Part)
8.
(i)Give the classification of heat exchangers.
(ii)It is
desired to use a double pipe counter flow heat exchanger to cool 3 kg/s of oil
(Cp = 2.1 kJ/kgK) from 120°C. Cooling water at 20°C enters the heat exchanger
at a rate of 10 kg/so The overall heat transfer coefficient of the heat
exchanger is 600 W/m2Kand the heat transfer area is 6 m2
.Calculate the exit temperatures of oil and water.
9.
(i)
Compare LMTD and NTU method of heat exchanger analysis.
(ii) Hot exhaust
gases which enters a finned tube cross flow heat exchanger at 300°C and leave
at 100°C, are used to heat pressurized water at a flow rate of 1 kg/s from 35
to 125°C. The exhaust gas specific heat is approximately 1000 J/kg.K, and the
overall heat transfer co-efficient based on the gas side surface area is Uh =
100W/m2K. Determine the required gas side surface area using the NTU method. Take Cp,c at Tc = 80°C
is 4197 J/kg.K and Cp,h = 1000 J/kg.K.
10. Water enters a
cross flow Heat exchanger (both fluids unmixed) at 5°C and flows at the rate of
4600 kg/h to cool 4000 kg/h of air that is initially at 40°C. Assume the
overall heat transfer coefficient value to be 150 W/m2K For an exchanger
surface area of 25m2 Calculate the exit temperature of air and
water.
11. (i) Describe the
principle of parallel flow and counter flow heat exchangers showing the axial
temperature distribution.
(ii) A parallel
flow heat exchanger has hot and cold water stream running through it, the flow
rates are 10 and 25 kg/min respectively. Inlet temperatures are 75° C and 25° C
on hot and cold sides. The exit temperature on the hot side should not exceed
50° C. Assume hi = ho = 600W/m2K. Calculate the area of heat
exchanger using E -NTU approach.
12. Water enters a
cross flow Heat exchanger (both fluids unmixed) at 5°C and flows at the rate of
4600 kg/h to cool 4000 kg/h of air that is initially at 40°C. Assume the
overall heat transfer coefficient value to be 150 W/m2K For an
exchanger surface area of 25m2 Calculate the exit temperature of air
and water.
13. Derive an
expression of LMTD for counter flow heat exchanger and parallel flow heat
exchanger.
14. In a cross flow
heat exchanger, both fluids unmixed, hot fluid with a specific heat of 2300
J/KgK enters at 380°C and leaves at 300°C. Cold fluids enter at 25°C and leaves
at 210°C. Calculate the area required. Take overall heat transfer coefficient
is 750 W/m2K. Mass flow rate of hot fluid is 1 kg/s.
Unit-4Radiation
Part-A
1.Define emissive power.
2.What is meant by
absorptivity,reflectivity,transmissivity?
3.what is blackbody and gray body?
4.Stateplanck's distribution law.
5.State Wien's displacement law.
6.State Stefan Boltzmann law.
7.Define emissivity and intensity of radiation.
8.What is meant by shape factor and mention its
significance.
9.StateKirchoff's law of radiation.
10.Differentiateradiosity and irradiation.
11. What is the use of radiation shield and state its
assumptions to calculate radiation exchange between the surfaces?
12.Discuss the radiation characteristics of carbon
dioxide and water vapour.
Unit-4 Radiation
Part-B (First
Part)
1.
(i)Define
emissivity, absorptivity and reflectivity .
(ii)Describe the
phenomenon of radiation from real surfaces.
2.
A
black body at 3000 K emits radiation. Calculate the following a)Monochromatic
emissive power at 1 micro meter wave length b) Wavelength at which emission is
maximum c) Maximum emissive power d) Total emissive power e)Intensity f) Total
emissive power if it is assumed as a real surface having emissivity 0.85.
3.
Derive
the radiation heat exchange between two parallel planes with radiation shield.
4.
800
W/m2 of radiant energy is incident upon a surface, out of which 300
W/m2 is absorbed, 100 W/m2 is reflected and the remainder
is transmitted through the surface. Calculate absorptivity, Reflectivity and
transmissivity.
5.
Write
short notes Shape factor and radiation shield.
Unit-4 Radiation
Part-B (Second
Part)
1.
Two
parallel, infinite grey surface are maintained at temperature of 127°C and
227°C respectively. If the temperature of the hot surface is increased to
327°C, by what factor is the net radiation exchange per unit area increased?
Assume the emissivity’s of cold and hot surface to be 0.9 and 0.7 respectively.
2.
Two
large parallel planes with emissivity’s 0.35 and 0.85 exchange heat by
radiation. The planes are respectively 1073K and 773K. A radiation shield
having the emissivity of 0.04 is placed between them. Find the percentage
reduction in radiation heat exchange and temperature of the shield.
3.
Two
equal and parallel discs of diameter 25 cm are separated by a distance of 50
cm. If the discs are maintained at 600°C and 250°C. Calculate the radiation
heat exchange between them.
4.
Discuss
how the radiation from gases differs from that of solids.
5.
Two
very large parallel plates with emissivities 0.5 exchange heat. Determine the
percentage reduction in the heat transfer rate if a polished aluminium
radiation shield of emissivity= 0.04 is placed in between the plates.
6.
A
thin aluminium sheet with an emissivity of 0.1 on both sides is placed between
two very large parallel plates that are maintained at uniform temperatures Tl =
800 K and T2 = 500 K and have emissivities 0.2 and 0.7 respectively. Determine the net rate of
radiation heat transfer between the two plates per unit surface area of the
plates and compare the result to that without shield.
Unit-5Mass
Transfer
Part-A
1.What is mass transfer and give any two examples.
2.What is molecular diffusion.
3.Define convective masss transfer.
4.State Fick's law of diffusion.
5.What is free convective mass transfer.
6.What is forced convective mass transfer
7.Write any two examples of convective mass transfer.
8.What is Schmidt number.
9.What are the dimensionless parameter used in
convective mass transfer.
10.StateScherwood number.
11.Define the terms(i)Mass density (ii) Molar density
12.Define the terms(i)Mass fraction (ii) Molar
fraction
Unit-5Mass
Transfer
Part-B (First
Part)
1.
A steel sphere of radius 60 mm which is initially at a uniform temperature of
325°C is suddenly exposed to an environment at 25°C; with convection heat
transfer coefficient 500 W/m2K. Calculate the temperature at a radius 36 mm and
the heat transferred 100 seconds after the sphere is exposed to the
environment.
2.
The tire tube of a vehicle has a surface area 0.62 m2 and wall thickness 12 mm.
The tube has air filled in it at a pressure 2.4 x 105 N/m2 . The air pressure
drops to 2.3 x 105 N/m2 in 10 days. The volume of air in the tube is 0.034 m3 .
Calculate the diffusion coefficient of air in rubber at the temperature of
315K. Gas constant value = 287. Solubility of air in rubber tube = 0.075m3 of
air/m3 of rubber tube at one atmosphere
3. Define mass concentration, molar
concentration, mass fraction and mole fraction.(4) The diffusivity of CCl4 in
air is determined by observing the steady state evaporation of CCl4 in a tube
of 1 cm diameter exposed to air. The CCl4 liquid level is 10 cm below the top
level of the tube. The system is held at 25°C and 1 bar pressure. The
saturation pressure of CCl4 at 25°C is 14.76 kPa. If it is observed that the
rate of evaporation of CCl4 is 0.1 kg/hour determine the diffusivity of CC14
into air.
4.
An open pan 20 cm in diameter and 8 cm deep contains water at 25°C and is
exposed to dry atm air. If the rate of diffusion of water vapour is 8.54x10-4
kg/hr. Estimate the diffusion coefficient of water in air.
5.
Explain Fick's first and second laws of diffusion.
Unit-5Mass
Transfer
Part-B (Second
Part)
6.
Discuss the analogy between heat and mass transfer.
7.
Explain the phenomenon of equimolar counter diffusion. Derive an expression for
equimolar counter diffusion between two gases or liquids.
8. Dry air at 20°C (p = 1.2 kg/m3 , v = 15 x
l0-6 m2 /s, D = 4.2 x l0-5 m2 /s) flows over a flat plate
of length 50 cm which is covered with a thin layer of water at a velocity of 1
m/s. Estimate the local mass transfer coefficient at a distance of 10 cm from
the leading edge and the average mass transfer coefficient.
9.
A mixture of 02 and N2 with their partial pressures in
the ratio 0.21 to 0.79 is in a container at 25°C. Calculate the molar
concentration, the mass density, the mole fraction and the mass fraction of
each species for a total pressure of 1 bar. What would be the average molecular
weight of the mixture?
10.
Air at 1 atm and 25°C containing small quantities of iodine flow with a
velocity of 6.2 m/s inside a 35mm diameter tube. Calculate mass transfer
coefficient. The thermo physical properties of air are ( v = 15 x l0-6
m2 /s, D = 4.2 x l0-5 m2 /s)
