1
Seat No.: Enrolment
GUJARAT TECHNOLOGICAL UNIVERSITY
BE SEMESTER-VII EXAMINATION WINTER 2017
Subject Code: 2171911 Date:02/11/2017
Subject Name: Advance Heat Transfer(Department Elective
Time: 10:30 AM TO 01:00 PM Total Marks: 70
Instructions:
1. Attempt all questions.
2. Make suitable assumptions wherever necessary.
3. Figures to the right indicate full marks.
4. Use of Heisler chart and Correction factor chart for temperature history are
permitted.
Q.1 Define fin. List at least six practical and specific examples of use of fin in
heat transfer.
03
Prove that the temperature of a body at any time during newtonian
heating or cooling is given by the relation i o
i a
a exp B
t t
t t



where
Bi and Fo are the Biot and Fourier modulus respectively; ta is the ambient
temperature and ti is the initial temperature of the body.
04
A two dimensional square isotropic plate is provided with constant edge
temperature given in Fig.-1. Determine the temperature at point 3
and 4 for two-dimensional steady heat conduction without heat
generation using finite difference method.
07
Q.2 Define non-dimensional Bi (Biot) number. State its importance in
transient heat conduction analysis.
03
Interpret Grashof number and Rayleigh number with mathematical
formula. Explain their significance in natural convection heat transfer
analysis in 100 words.
04
Develop the numerical formulation and solution of two-dimensional
steady heat conduction with heat generation in rectangular coordinates
using the finite difference method. Prove that finite difference
formulation of an interior node is obtained by adding the temperatures of
the four nearest neighbors of the node, subtracting four times the
temperature of the node itself, and adding the heat generation term.
07
OR
Steam in a heating system flows through tubes whose outer diameter is
D1 3 cm and whose walls are maintained at a temperature of 120°C.
Circular aluminum fins 180 of outer diameter D2 6 cm
and constant thickness t 2 mm are attached to the tube, as shown in Fig.
2. The space between the fins is 3 mm, and thus there are 200 fins per
meter length of the tube. Heat is transferred to the surrounding air at T∞
25°C, with a combined heat transfer coefficient of h 60 W/m2-deg.
Determine the increase in heat transfer from the tube per meter of its
length as a result of adding fins under steady operating conditions and
neglecting heat transfer by radiation. Assume: 1. The heat transfer
coefficient is uniform over the entire fin surfaces. 2. Thermal
conductivity is constant.
07
2
Q.3 Define following terms.
Boiling
ii) Optically thick medium
iii) Monochromatic transmissivity of gas (spectral transmissivity of a
medium)
03
Prove that fully developed flow in a tube subjected to constant surface
heat flux, the temperature gradient is independent of x and thus the shape
of the temperature profile does not change along the tube.
04
Derive the governing differential equation for steady state condition for
temperature distribution of constant area heat extended surface in the
following forms:
c kA
hP
m where m
dx
d t
0 2
2
2

where θ is excess temperature above the ambient air of the fin
temperature at distance x from the root; P is the perimeter; Ac the cross
sectional area of the fin; h is the heat transfer coefficient and k is the
thermal conductivity of the material. State clearly assumption consider in
derivation of formula.
07
OR
Q.3 Mention at least four cases where heat is generated internally at uniform
rate in the conducting medium itself.
03
State eight assumptions of Nusselt theory of condensation. (Laminar film
condensation on a vertical plate)
04
A large steel plate 50 mm thick is initially at a uniform temperature of
4250C. It is suddenly exposed on both sides to an environment with
convective coefficient 285 W/m2-K and temperature 650C. Determine the
centre line temperature and the temperature inside the plate 12.5 mm
from the mid plane after 3 minutes.
For steel:
Thermal conductivity, k 42.5
Thermal diffusivity, α 0.043 m2/hr
Heisler chart for temperature history at the centre of a plane and
Correction factor chart for temperature history in a plate are given in Fig.
3 and Fig.4 respectively.
to temperature t the mid plane
ta ambient temperature.
07
Q.4 Define following:
Efficiency of fin
ii) Effectiveness of fin.
Write mathematical formula for both performance parameters. Express
mathematical formula which correlate them.
03
Explain heat transfer from the human body in 200 words. 04
A 25-cm-diameter stainless steel ball 8055 kg/m3, Cp 480 J/kgdeg)
is removed from the oven at a uniform temperature of 300°C (Fig.
5). The ball is then subjected to the flow of air at 1 atm pressure and 25°C
with a velocity of 3 m/s. The surface temperature of the ball eventually
drops to 200°C. Determine the average convection heat transfer
coefficient during this cooling process and estimate how long the process
will take.
The dynamic viscosity of air at the average surface temperature is
@250 °C 2.76 × 10-5 kg/m-s. The properties of air at the free-stream
temperature of 25°C and 1 atm are
k 0.02551 W/m-deg 1.562 × 10-5 m2
1.849 × 10-5 kg/m-s Pr 0.7296
07
3
.
Use the following correlation.

1 4
1 2 2 3 0 4 2 0 4 0 06

s
. Pr Re . Re . Nu








Following assumption to be considered during cooling of ball for
simplicity.
Steady operating conditions exist. Radiation effects are negligible.
Air is an ideal gas. The outer surface temperature of the ball is
uniform at all times. The surface temperature of the ball during
cooling is changing. Therefore, the convection heat transfer coefficient
between the ball and the air will also change. To avoid this complexity,
take the surface temperature of the ball to be constant at the average
temperature of (300 200)/2 250°C in the evaluation of the heat
transfer coefficient.
OR
Q.4 State six practical example of transient heat conduction occurs. 03
Define shape factor or view factor. Explain minimum six salient features
of shape factor.
04
Consider a 0.6 m × 0.6 m thin square plate in a room at 30˚C. One side of
the plate is maintained at a temperature of while the other side is
insulated. Consider steady operating conditions exist, air is an ideal gas
and local atmospheric pressure is 1 atm.
Determine the rate of heat transfer from the plate by natural convection if
the plate is horizontal with hot surface facing up, and horizontal
with hot surface facing down.
In which case natural convection heat transfer is the lower? Explain it.
The properties of air at the film temperature of Tf (Ts T∞) 2 (90
and 1 atm are
k 0.02808 W/m-deg 1.896 × 10-5 m2
β 1/333 K Pr 0.7202
Use the following correlation for horizontal with hot surface facing up
1 4 0 54
L Nu . Ra
Use the following correlation for horizontal with hot surface facing
down.
1 4 0 27
L Nu . Ra
where Ra Rayleigh number
07
Q.5 State Beer's law. Derive a mathematical expression for radiation beam
while passing through an absorbing medium of thickness L in following
forms
L

L e
I
I



0
where
Iλ,0 A spectral radiation beam of intensity when it is incident on the
medium, L participating medium of thickness, κλ spectral absorption
coefficient of the medium whose unit is Iλ,L A spectral radiation
beam of intensity at medium thickness L
03
A thermocouple used to measure the temperature of hot air flowing in a
duct whose walls are maintained at Tw 400 K shows a temperature
reading of Tth 650 K (Fig. 6). Assuming the emissivity of the
thermocouple junction to be ε 0.6 and the convection heat transfer
04
4
coefficient to be h 80 W/m2-deg, determine the actual temperature of the air. The surfaces are opaque, diffuse, and gray.

Explain Nusselt theory of condensation for Laminar film condensation on a vertical plate and obtain an expression for local value of condensing heat transfer coefficient over a vertical flat plate length Also show that average value of heat transfer coefficient is equal to 4/3 times the local value of condensing heat transfer coefficient at x l.
07
OR
Q.5

State three special features of radiation from gases.
03

An electric wire of 1.25 mm diameter and 250 mm long is laid horizontally and submerged in water at 7 bar. The wire has an applied voltage of 2.2 V and carries a current of 130 amperes. If the surface of the wire is maintained at 2000C, make calculation for the heat flux and boiling heat transfer coefficient. Saturation temperature corresponding to 7 bar is 1650C.
04

Discuss in detail the various regimes in boiling with sketch in 500 words.
07
Fig. 1
Fig. 2
5
Fig. 3
Fig. 4
6
Fig. 5
Fig. 6