tute

[Prince maurya]

Mech. Engg. Dept.
ME 402 Heat & Mass Transfer (ME-402 ) & Heat Transfer Operations
(CL-402 )
Conduction-Fundamentals, Electrical Analogy and Composite
Layers TS1/2009/VKN
Q1. A guest house has a multilayer composite layer wall constructed
as shown in the figure given below. The temperature of air inside the
room is 200C and surface coefficient of heat transfer between the room
air and wall is 6.25 W/m2 K. The outside temperature is -120C with an
outside surface co-efficient of heat transfer 17.25 W/m2-K. The wall
measures 2 m high and 4 m deep. The different wall thicknesses are as
indicated in the figure and thermal conductivities of wall materials
are:
ka = 0.16 W/m K, kb = 0.21 W/m K, kc = 0.04 W/m K, kd = 0.17 W/m K.
Calculate the heat transfer rate across the wall in steady
state.
(Ans: 183.9 W)








Q2. A cylindrical liquid oxygen tank has a diameter of 1.2 m, a length
of 6 m and has hemispherical ends. The boiling point of liquid oxygen
is -1820C and its heat of vaporisation is 214 kJ/kg. The tank needs to
be insulated so as to reduce the boil off rate of oxygen in steady
state to be no more than 13.85 kg/hr. Work out the thermal
conductivity of the insulating material if its maximum thickness is
limited to 7.5 cm and the room temperature outside the insulation is
200C. (Ans: 0.0105 W/mK)
Q3. Establish a relation for the time taken to form a layer of ice on
the surface of pond. How much time it will take for a layer of ice of
thickness 20 cm to increase by 1 mm on the surface of a pond when the
temperature of surrounding is -200C? Take k of ice = 2.1 W/m K, Latent
heat of ice =335 kJ /kg, Density of ice at 00C =1000 kg/
m3.
(Ans: 1599 sec)
Q4. A layer of 5 cm thick insulating brick having conductivity of 1.5
W/mK is placed between two 0.5 cm thick steel plates. The conductivity
of mild steel is 50 W/mK. The faces of brick adjacent to the plates
are rough having solid-to-solid contact of 30% of the total area. The
average height of asperities is 0.1 cm. if the outer plate surface
temperatures are 1000C and 5000C respectively. Calculate the rate of
heat transfer per unit area. The conductivity of air is 0.02 W/
mK. (Ans:10.44 kW)
Q5. A 10 mm OD cable is to be laid in the atmosphere of 200C with
outside heat transfer co-efficient 8.5 W/m2K. The surface temperature
of cable is likely to be 650C due to heat generation within. Will the
rubber insulation, k = 0.155 W/mK, be effective? If yes, how
much? (Ans. 159%
effective)
Q6. Thermal Conductivity, k, of a certain material is given by k = a +
bT + cT2 , where a,b,c are constants and T is the absolute
temperature. Derive an expression for heat flow per unit length of a
hollow cylinder made of this material. Assume that inner and outer
radii of the cylinder are r1 and r2 respectively and cylinder ends are
perfectly insulated.
Q7. For a hollow cylinder, internal diameter is 5 cm, outer diameter
is 10 cm, temperature at inner surface is 2000C and temperature at
outer surface is 1000C. Find T half way between inner and outer
surface if thermal conductivity of the material of the cylinder is 70
W/mK. Find heat transfer per meter length of
cylinder.
(Ans: 142.280C, 63.43 kW/
mK)
Q8. A steam pipe 170mm O.D. &160mm ID is covered with two layers of
insulation. Thickness of the first layer is 30mm and that of the
second layer is 50mm. Thermal conductivities of the pipe and
insulating layers are 58, 0.175 and 0.093 W/mK, respectively.
Temperatures of steam and the inner surface of the steam pipe are
3500C and that of the outer surface of the insulation layer is 1000C.
Ambient air temperature is 300C. Surface coefficients for the inside
and outside surfaces are 230 and 7W/m2K respectively. Calculate the
heat lost per metre length of the pipe and layer contact temperatures.
Also calculate the overall heat transfer coefficient base on inner
surface.
(Ans. 307.988 W/m, 3500C, 265.330C, 0.928 W/m2K)


Mech. Engg. Dept.
ME 402 Heat & Mass Transfer (ME-402 ) & Heat Transfer Operations
(CL-402 )

Conduction with thermal energy
generation
TS2/2009/VKN


Q.2.1. A square plate heater measuring 16cm*16cm and of rating 1kW is
inserted between two slabs. Slab A is 2cm thick (k=60W/m-K) and Slab B
is 1cm thick (k=0.25W/m-K). The outside heat transfer coefficients on
side A and B are 200W/m2 -K and 50W/m2 -K, respectively. If the
surrounding air is at 200C, make calculations for the maximum
temperature in the system and outer surface temperature of the two
slabs. Also calculate the heat transfer through the two
slabs. (Ans 211.220C,
199.250C, 83.740C, 917.76 W, 81.6
W)

Q.2.2. A plane wall 10cm thick generates heat at the rate of 30kW/m3
when an electric current is passed through it. One face of the wall is
insulated, and the other face is exposed to 250C air. If the
convective heat transfer coefficient between the air and the exposed
surface of the wall is 50 W/m2 -K, determine the maximum temperature
in the wall. The thermal conductivity of the wall is 3 W/m -
K. (Ans 1350C)

Q.2.3. Nichrome , having a resistivity of 110µΩ cm is to be used as a
heating element in an electric heater . The wire used is 2mm in
diameter and the other design features include:
Current flow = 25A
Surrounding air temperature=200C
k for Nichrome wire =17.5W/mK
Surface heat transfer coefficient=46.5 W/m2 -K
Calculate the rate of heat flow for one metre long heater, and also
the temperature at the surface and central line of the nichrome
wire.
(Ans 218.5W/m , 768.50C, 769.70C)

Q.2.4 Radioactive wastes (krw=20W/mK) are stored in a spherical,
stainless steel (kss=15 W/mK) container of inner and outer radii equal
to ri= 0.5m and ro = 0.6m. Heat is generated volumetrically within the
wastes at a uniform rate of q=105 W/m3, and the outer surface of the
container is exposed to a water flow for which h=1000W/ m2 -K and T =
250C.
(a) Evaluate the steady -state outer surface temperature, Ts,o.
(b) Evaluate the steady -state inner surface temperature, Ts,i.
(c) Obtain an expression for the temperature distribution, T(r), in
the radioactive wastes. Express your results in terms of ri , Ts,i,
krw, and q. Evaluate the temperature at r=0.

Q.2.5 Unique characteristics of biologically active materials such as
fruits, vegetables, and the other products require special care in
handling. Following harvest and separation from producing plants,
glucose is catabolised to produce carbon dioxide, water vapour, and
heat, with attendant internal energy generation. Consider a carton of
apples, each of 80-mm diameters, which is ventilated with air at 50C
and a velocity of 0.5m/s. The corresponding value of the heat transfer
coefficient is 7.5 W/m2 -K. Within each apple thermal energy is
uniformly generated at a total rate of 4000 J/kg.day. The density and
thermal conductivity of the apple are 840 kg/ m3 and 0.5 W/mK,
respectively.
(a) Determine the apple center and the surface temperatures.
(b) For the stacked arrangement of the apples within the crate, the
convention coefficient depends on the velocity as h=C1V.425, where
C1=10.1W/m2 -K.(m/s).425.

Q. 2.6. A plane wall is a composite of the two materials A and B. The
wall of the material A has a uniform heat generation q =1.5*106 W/m3,
ka=75W/m.K and thickness La = 50mm. The wall material B has no
generation with kb =150 W/m-K and the thickness of Lb=20mm. The inner
surface of the material A is well insulated while the outer surface of
the material B is cooled by the water stream with T=300C and h=1000W/
m2 -K.
1. Sketch the temperature distribution that exists in the composite
under steady state conditions.
2. Determine the temperature T0 of the insulated surface and the
temperature T2 of the cooled surface.

(Ans T0=1400C, T11050C)



Mechanical Engineering Department
ME 402- Heat & Mass Transfer, CL-402 Heat Transfer Operations

Theory of fins
TS3/2009/VKN
Q.3.1 Pin fins are widely used in electronic systems to provide
cooling as well as to support devices. Consider the pin fin of uniform
diameter D length L and thermal conductivity k connecting two
identical devices of length Lg and the surface area Ag. The devices
are characterized by a uniform volumetric generation of the thermal
energy q and a thermal conductivity Kg. Assume that the exposed
surfaces of the devices are at uniform temperature corresponding to
that of the pin base, Tb, and that heat is transferred by convection
from the exposed surfaces to an adjoining fluid. The back and the
sides of the devices are perfectly insulated.
Derive an expression for the base temperature Tb in terms of the
device parameters (Kg, q, Lg, Ag), the convection parameters (T, h),
and the fin parameters, i.e. k,D, and L.

Q.3.2 Turbine blades, mounted to a rotating disc in a gas turbine
engine, are exposed to a gas stream that is at T=1200 0C and maintains
a convection coefficient of h=250W/ m2 -K over the blade.The blades,
which are fabricated from Inconel, k=20W/mK, have a length of L =50mm.
The blade profile has a uniform cross sectional area of Ac= 6*10-4m2
and a perimeter of P=110mm. a proposed blade -cooling scheme, which
involves routing air through the supporting disc, is able to
maintain the base of each blade at a temperature of Tb=3000C.

(a) If the maximum allowable blade temperature is 10500C and the blade
tip may be assumed to be adiabatic, is the proposed cooling scheme
satisfactory?
(b) For the proposed cooling scheme, what is the rate at which heat is
transferred from each blade to the coolant?

Q.3.3 What is the significance of fin effectiveness and fin efficiency
of the fin?
Why is the assumption of 1-D heat flow made in the analysis of fin?
Prove that with an adiabatic tip condition, length of the fin should
be 2.3/m for achieving 98% of the maximum fin heat transfer
rate

Q.3.4. Three rods, one made of silver (k=420 W/m K), second made of
aluminium (k=210 W/m K) and the third made of wrought iron (k=70 W/m
K) are coated with a uniform layer of wax all around. The rods are
placed vertically in a boiling water bath with 250mm length of each
rod projecting outside. If all the rods are 15mm diameter, 300mm
length and have identical surface coefficient 12.5 W/m2K, work out the
ratio of the lengths up to which wax will melt on each
rod. . (Ans 2.45:1.732:1)

Q.3.5.A steel tube carries steam at a temperature of 3200C. A
thermometer pocket (k=52.3W/mK) of the diameter 1.5cm and 1mm thick is
used to measure the temperature. The error to be tolerated is 1.5%
maximum. Estimate the length of the pocket necessary to measure the
temperature within the error. The diameter of the steel tube is 9.5cm.
Suggest a suitable method of locating the thermometer pocket. Assume
h=93 W/m2K. Tube wall temperature
=1200C. (Ans 10.5cm)

Q3.6 The Al alloy absorber plate of a flat plate solar collector is
6mm thick and well insulated on its bottom. The top surface of the
plate is separated from a transparent cover plate by an evacuated
space. The tubes are spaced a distance L of 0.2 m from each other, and
water is circulated thru the tubes to remove the collected energy.
Water is assumed to be at 600C. Find the max. temp. on the plate if
the net effect of radiation is q’’=800W/m2. Assume that the absorber
plate temp directly above a tube is equal to water temperature.



Mechanical Engineering Dept.
ME 402 - Heat & Mass Transfer, CL-402 - Heat Transfer Operations
Transient heat
conduction TS4/2009/VKN


Q4.1 The temperature of an air stream flowing with a velocity of 3m/s
is measured with a copper-constantan
thermocouple which may be approximated as a sphere of 3mm
diameter. Initially the junction and
air are at a temperature of 250C. The air temperature
suddenly changes to and is maintained at 2000C.
(a). Determine the time required for the thermocouple to
indicate the temperature of 1500C. Also
determine the thermal time constant and temperature indicated
by the thermocouple at that instant.
(b)Discuss the suitability of this thermocouple to measure
unsteady state temperature of a fluid when the
temperature variation in the fluid has a time period of 3
seconds. The thermocouple bead properties
are: r=8960 kg/m3, c= 366 J/kg K, k=27.78W/mK ; h =144.4W/m2
K (Ans. 11.35s, 14.22s)

Q4.2. A 15mm diameter mild steel sphere (k=42W/m K) is exposed to
cooling air flow at 200C resulting in
the convective coefficient h=120W/m2 K.
Determine the following:
(a). time required to cool the sphere from 5500C to 900C.
(b). instantaneous heat transfer rate 2 minutes after the start of
cooling.
(c). total energy transferred from the sphere during the first 2
minutes.
For mild steel take: r=7850kg/m3, c=475J/kg K ( Ans
t=141.7seconds, Q=-81W, Q’=-2862.3J)

Q4.3. A 3.6cm diameter egg, approximately spherical in shape, is
initially at 250C temperature. To boil it to
the consumer’s taste, it needs to be placed for 225 seconds
in a saucepan of the boiling water at
1000C. For how long should a similar egg for the same
consumer be boiled when taken from a refrigerator
at a temperature of 50C.?
Thermo-physical properties of egg are: k=2.5W/m-K: r=1250kg/
m3 : c=2200J/kg-K
The heat transfer coefficient for the shell-water interface
may be taken as 280 W/m2-K
Compare the center temperature attained with that computed by
treating the egg as a lumped-heat-
capacity
system.
( Ans t=253seconds, t=98.30C)

Q4.4. A thermocouple junction, which may be approximated as a sphere,
is to be used for temperature
measurement in a gas stream. The convection coefficient
between the junction surface and the gas is
known to be h=400W/m2-K, and the junction thermo-physical
properties are k=20W/m-K, c=400J/kg-
K, and r=8500kg/m3. Determine the junction diameter needed
for the thermocouple to have a time
constant of 1 s. If the junction is at 250C and is placed in
a gas stream that is at 2000C, how long will it
take for the junction to reach
1990C? (Ans
D=7.06*10-4m), t=5.2s)

Q4.5. A mild steel slab 5cm thick, very long and very wide, is
initially at a uniform temperature of 500C.
One of the surfaces is exposed to a fluid which suddenly
causes the surface temperature to increase to
and remain at 1000C. Estimate the temperature at the mid
plane and at 1cm from the mid plane 1 min
after the surface temperature change. Take α=1.26*10-5m2/s,
k=42.5 W/m2K and h=285 w/
m2K.

( Ans 760C)

Q4.6. At what depth should a water pipe be buried in wet soil
(α=0.001m2/h) initially at 50C for the surrounding
soil temperature to remain above 00C (to avoid freezing of
water), if the soil surface temperature drops to
-50C and remains at this value for 12
hours?
(Ans 10.5cm)







Mechanical Engg. Dept.
ME 402 Heat & Mass Transfer (ME-402 ) & Heat Transfer Operations
(CL-402 )

Num. Relaxation Method for 2-D Steady State
Conduction TS5/2009/VKN

5.1 Calculate the heat flow rate per unit depth and the steady state
temperature distribution in a Two-
dimensional square plate having each side of 4 cm with
boundary conditions as shown in Fig: 1.

5.2 Find the temperature at the point (1/2, 1/2) for the
configuration shown in the following figure: 2.
(Ans. 102.750C)
5.3 Calculate the steady state temperatures T1, T2, T3, T4 at the
four nodes in the following figure: 3 .Each block is a square of side
1 m.

5.4. Calculate the steady state temperatures T1, T2……………T6 at six
nodes in the following figure: 4. The left face is insulated. Take k=
20 W/mK and h= 10 W/m2 K for the convective boundary condition. Each
block is a square of side 1 m.
y

00C 1400C

2



1000C 00C 1000C
1000C



x

2
00C 1000C
Figure: 1 Figure: 2
Assume for fig.1: T1=25, T2=15, T3=50, T4=40, T5=75, T6=65 as initial
guess

T= 1000C T= 1000C





Convection Into
T1
T3
T1 T3 a medium at T∞=
300C

T5
Insulated T=
2000C
Insulated


T2
T4
T2 T4
T6



T= 4000C T= 5000C

Figure: 3 Figure:
4


Assume for fig.3: T1=300, T2=350, T3=250, T4=300, and
Assume for fig.4: T1=300, T2=400,T3=200,T4=300,T5=200,T6=200 as
initial guess


Mechanical Engg. Dept.
ME 402 Heat & Mass Transfer (ME-402 ) & Heat Transfer Operations
(CL-402 )
Fundamentals of Convection and forced
convection TS6/2009/VKN

6.1. (a) When a fluid flows over a flat plate, the velocity profile
within the boundary layer at a section located at a distance x from
the leading edge may be assumed to be
U/U∞ = [3/2(y/δ)-1/2(y/δ)3 ] for y< δ and Ux = U∞ for y>
δ
Where U∞ is a constant.
Derive an expression for local boundary layer and local wall
shear stress, average skin friction over length L.
(b) Repeat the problem when the velocity varies as u/u∞=sin(π/
2*y/δ)

6.2. For the forced convection heat transfer, when frictional heating
in the fluid cannot be neglected show the dimensional analysis
Nu=f(Re,Pr,C2/CpT)
Discuss the physical significance of each of
them. (8c/1997)

6.3.Air flows over a heated flat plate at a velocity of 50 m/s. the
local skin friction coefficient at a point an the plate is 0.004.
Estimate the local heat transfer coefficient at that point. The
following property data for air are given.
Density=0.88kg/m3; viscosity=2.286*10-5kg/m-s.
Specific heat cp=1.001 kJ/ kg-K, thermal conductivity=0.035W/mK
Use the Colburn analogy between momentum and heat transfer
St*Pr2/3 =Cr/
2

(6a/1993) [ans: hx=116.93 W/m2K]

6.4. Air at a pressure of 800kN/m2 and a temperature of 2500C flows
over a flat plate 0.3m wide and 1 m long at a velocity of 8 m/s. If
the plate is to be maintained at a temperature of 780C, estimate the
rate of heat to be removed continuously from the plate.
Also estimate the drag force exerted on the plate using the
analogy between fluid friction and heat
transfer.
[ans: h=3.04W/m2K, Q=313.7W]

6.5. Experimental results for heat transfer over a flat plate with an
extremely rough surface were found to be correlated by an expression
of the form
Nux = 0.04Rex0.9Pr0.33
Where Nux is the local value of the Nusselt number at a
position x measured from the leading edge of the plate. Obtain an
expression for the ratio of the average heat transfer coefficient hx
to the local coefficient hx.

6.6. Air at an atmospheric pressure and 200C flows past a flat plate
with a velocity of 4m/s. the plate is 390cm wide is heated uniformly
throughout its entire length and is maintained at a surface
temperature of 600C. Make calculations for the following parameters at
40cm distance from the leading edge:
(a) Thickness of hydrodynamic and thermal boundary layers.
(b) Local and average friction coefficient.
(c) Local and average heat transfer coefficient and (d). Total
drag force on the plate.
Take the following thermo-physical properties of air at the mean film
temperature of 400C:
r= 1.18 kg/m3: v=17*10-6 m2/s: c=1007 J/kg-deg and k=0.0272W/m-deg
(Ans a=6.517,
b=0.00216, 0.00432, c=12.548W/m2K, d=0.00476N)


Mechanical Engg. Dept.
ME 402 Heat & Mass Transfer (ME-402 ) & Heat Transfer Operations
(CL-402 )
CONVECTION
(CONTINUED)
TS7/2009/VKN

Q.7.1. Using the linear velocity profile u/u∞=y/δ, and A cubic profile
for temperature distribution (T-T∞)/ (Ts-T∞) = 3/2(y/δt)-1/2(y/δt)3,
determine the expression for the heat transfer coefficient.

Q.7.2. During a test run in a wind tunnel, air at 200m/s velocity and
200C is made to flow over a thin airfoil maintained at 54 0C. If the
chord length is 15cm, calculate the following for unit width assuming
the aerofoil to behave as a flat plate and both surfaces effective
(i) Drag force, (ii) Heat transferred
You may use average drag coefficient for combined laminar and
turbulent flow which are available for critical Reynolds no. of 5*105.
Cf=0.072/ And Nu=0.036Pr.33[ ]
Air properties at 310 are ρ = 1.128 kg/cm3, μ = 180 x 10-7 Ns/m2, k =
27x 10-3 W/mk.

Q.7.3. The velocity profile for water flowing in a pipe 20cm diameter
is given by u=180r-200r2 and the temperature profile is given by
T=100-200r, where r is the distance in metres measured from the
surface of the tube towards the axis. Calculate the bulk temperature
of the water. ( Ans 85
0C)
Q.7.4. Show that the axial distribution of mean temperature, Tb, and
the heat transfer rate, Q, for a fluid flowing through a pipe whose
surface is maintained at constant temperature Ts, are given by
(Ts-Tb)/ (Ts-Tb,i)=exp[(-Px/mcp) ]
Q= Pl (∆To-∆Ti)/ ln(∆To-∆Ti) = mcp(Tbo-Tbi)
Where suffixes i and o denote the inlet and outlet of the pipe of
length L and perimeter P, and m is the mass flow rate.

Q.7.5. Water at 500C enters a 1.5cm diameter and 3m long pipe with a
velocity of 1m/s.The tube wall is maintained at a constant temperature
of 900C. Calculate the heat transfer coefficient, if the exit water
temperature is 640C, using
(i) Dittus Boelter equation NuD=0.023 ReD.8Pr.4, and
(ii) Exponential decay of the bulk temperature of the fluid (obeying
eq. given in Q.7.4).

Q.7.6. Consider a thin walled tube of 10mm diameter and 2m length.
Water enters the tube from a large reservoir at m= 0.2kg/s and Tb,i
=470C.
(a) If the tube surface is at a uniform temperature of 270C, what is
the outlet temperature of the water, Tb,o? To obtain the properties of
water assume an average mean temperature of Tb,m=300K.
(b) What is the exit temperature of the water if it is heated by
passing air at T∞=1000C and V=10m/s in the cross flow over the tube?
The properties of air may be evaluated at an assumed film temperature
of Tf=350K.
(c) In the foregoing calculations, were the assumed values of Tb,m and
Tf appropriate? If not, use properly evaluated properties and
recompute Tm,o for the conditions of part (a) and (b).
For cross flow over a cylinder you may use where constants are given
in the following table. Take properties at film temperature.
Re
C n
.4-4 0.989 0.330
4-40 0.911 0.385
40-4000 0.683 0.466
4000-40000 0.193 0.618
40000-400000 0.027 0.805








P.T.O



Q.7.7. Air flow through a long rectangular heating duct, 0.75m wide
and 0.3m high, maintains the outer duct surface at 450C. If the duct
is uninsulated and exposed to air at 150C, what is the heat loss from
the duct per meter. Take air properties at film temperature.
For vertical plate: NuL =0.59 , 104< <109 And NuL =0.10 , 109<
<1012
For horizontal surface:Upper surface heated or lower surface cooled
NuL =0.54 , 2.6*104< <107 And NuL =0.15 , 107< <3*1010
Lower surface heated or upper surface cooled:
NuL =0.27 , 3*105< <3*1010
For vertical surface: NuL =0.59 , 104< <109 & NuL =0.10 , 109<
<3*1012
(Ans: 246 W/
m)
Q.7.8. A vertical pipe of 20cm outer diameter at a surface temperature
of 1000C is in a room where the air is at 200C. The pipe is 3m long.
What is the heat loss from the pipe?
Hint: check (for eqn. for vertical plate to apply
here) (Ans 241.27W/m)

Q.7.9. A horizontal, high pressure steam pipe of 12cm outer diameter
passes through a large room whose wall and air temperatures 230C. The
pipe has an outside wall temperature of 1600C, and an emissivity of
ε=0.8. Estimate the heat loss from the pipe per unit length.
For horizontal isothermal cylinder [Morgan (1975)] NuD=c Ra,dn.
Hint Properties at film temperature.
Ra,d
c n
10-10-10-2 0.675 0.058
10-2-102 1.02 0.148
102-104 0.850 0.188
104-107 0.480 0.250
107-1012 0.125 0.333








Q.7.10. Water at atmospheric pressure is boiled in a kettle made of
copper. The bottom of the kettle is flat, 30cm in diameter and is
maintained at a temperature of 1180C. Calculate the rate of heat
required to boil water. Also estimate the rate of evaporation of water
from the kettle. Liquid properties at film temperature & hfg at Tsat.

(17.2kW, 27.41kg/h)
Q.7.11. Calculate the heat transfer and mass of the steam condensed
per hour on a vertical square plate 0.3m by 0.3m maintained at 980C
and exposed to steam at atmospheric pressure.
(Ans 2.36kW, 96.84kg/h)

Q.7.12. A vertical tube 12.5mm diameter and 1.7m long is used for
condensing steam at 0.4bar. The tube surface temperature is maintained
at 540C. Determine the average heat transfer coefficient in
condensation. What would be the value of the heat transfer coefficient
if the plate were held in a horizontal
position? (Ans 11.06kW/
m2K, 3.88 kW/m2K)

Q.7.13. (a). Water flows normal to a polished 15mm diameter copper
tube at the rate of 3.5m/s. the tube is maintained at 116 0C and
stable film boiling occurs. Workout the boiling heat transfer
coefficient. Vapour properties at film temperature and liquid
properties at Tsat and ε=0.22.
For V∞> 2(gD)1/2, hc =2.7[V∞kgpg(hfg+0.8cp,f∆t)/D∆t]0.5 , For V∞
< 2(gD)1/2
hc = C[Kg3 ρg(σf - ρg)g (hfg+0.8cp,f∆t)/(D∆tμg)]0.25 , C = 0.62 for
hori. Cylinder & 0.67 for sphere.
hrad= σbε(Ts4- Tsat4)/( (Ts- Tsat), htot=hc
+(3/4)hr . (Ans 1868.447 W/m2K)

(b). Evaluate the above if the ambient air is
stationary.




Mechanical Engg. Dept.
ME 402 Heat & Mass Transfer (ME-402 ) & Heat Transfer Operations
(CL-402 )
RADIATION
TS8/2009/VKN

8.1. Calculate the hourly loss of water from a well of 6m depth and
cross sectional area of 5m2. Temperature is 300C and pressure is
1.013bar. Given D=0.256cm2/s. Also saturated pressure of water at
300C=0.042bar.

(Ans 0.00235kg/h)

8.2. a. How does the thermal radiation differ from other types of
electromagnetic radiation? Differentiate electromagnetic with quantum
approach.
b. What are Planck’s law, Stefan boltzmann law and Wein’s displacement
law, and radiation intensity.
c. Define between specular and diffuse reflecting surfaces, and
diffuse emitter.
d. Define irradiation, radiosity, space resistance and surface
resistance.
e. What is Kirchoff’s law? When does it apply?
f. What is the concept of black, white, and gray bodies.

8.3. A small body at 270C is placed in a large furnace whose walls are
maintained at 1000K. The total absorptivity of the body at 270C varies
with the temperature of the incident radiation as follows:
Temperature 300K 500K 1000K
α= 0.75 0.6 0.5
Determine the rate of absorption and emission of radiation by the
small body. (Ans 0.2835*105W/m2, 345W/
m2)

8.4.The transmissivity of silica glass is opaque at longer and shorter
wave lengths. Determine the percentage of solar radiation transmitted
by the glass. Assume that sun radiates at 5600K as a black
body. (Ans 83.6 %)

8.5. Calculate the heat transfer per hour between the two surfaces
maintained at 7270C and 2270C, respectively for following situation.
a. Two black discs of diameter 50cm placed parallel to each other
concentrically at a distance of 1m.
b. Two black square plates of sides 50cm placed perpendicular with a
common edge. (2260kJ/h, 9568.12kJ/
h)

8.6. Two concentric spheres, 20cm and 30cm in diameter are used to
store liquid O2(-1530C) in a room at 300K. The space between the
spheres is evacuated. The surfaces of the spheres are highly polished
as ε=0.04. Find the rate of evaporation of liquid O2 per hour. Take
latent heat of O2=290kJ/kg. (Ans 0.00938kg/h)

8.7. A hole of area dA=2 cm2 is opened on the surface of a large
spherical cavity whose inside is maintained at 1000K. Calculate
a. The radiation energy streaming through the hole in all direction
into space
b. The radiating energy streaming per unit solid angle in a direction
making an angle of 600 angle with the normal to the surface of the
opening.

8.8. The temperature of the body of area 0.1m2 is 900K. Calculate the
total rate of energy emission, intensity of normal radiation in W/m2,
maximum monochromatic emissive power, and wavelength at which it
occurs.

8.9. Spectral emissivity of a particular surface at 800K is
approximated by a step function as follows
ε1 = 0.1(for l=0 to 2 mm), ε2 = 0.5(for l=2 to 15 mm), ε3= 0.8(for
l=15 to ∞ mm)
Calculate (i) The total (hemispherical) emissive power and (ii) Total
hemispherical emissivity, ε overall wavelength.

8.10. Two parallel plates of size 1m*1m, spaced 0.5m apart, are
located in a very large room, the walls of which are maintained at a
temperature of 270C. One plate is maintained at a temperature of 9000C
and the other at 4000C. There emissivities are 0.2 and 0.5,
respectively. If the plates exchange heat between themselves and
surroundings, find the net heat transfer to each plate and to the
room. Consider only the plate surfaces facing to each
other.
(Ans 20.8kW)