Seat No.: ________ Enrolment No.

___________
GUJARAT TECHNOLOGICAL UNIVERSITY
BE - SEMESTER–VI • EXAMINATION – SUMMER 2013
Subject Code: 161906 Date: 31-05-2013
Subject Name: Heat and Mass Transfer
Time: 10.30 am - 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. Illustrate your answer with neat sketches wherever required.
5. Notations carry usual meanings.

Q.1 (a) Write general heat conduction equation for non-homogeneous material, self 07
heat generating and unsteady three-dimensional heat flow in cylindrical co-
ordinates. Name and state the unit of each variable.
Step 1. Reduces above equation to one dimensional
Step 2. Reduces step 1 equation for steady and without heat generation
Step 3. Reduces step 2 equation for homogeneous and isotropic material
Step 4. Reduces step 3 equation to r(dt/dr) = constant.

(b) Derive a general mass diffusion equation in stationary media having NAg as 07
mass generation rate of species A in Cartesian coordinates.
Q.2 (a) Consider a cylindrical furnace with radius = 1m and height = 1m as shown in 07
fig. Take σ = 5.67 X 10-8 W/m2K4

T1= 700 K
ε = 0.8, F12=0.38
Surface 1

surface 3
Black, ε = 1
T3=400 K

Surface 2
T2= 500 K
ε = 0.4

Determine the net rate of radiation heat transfer at each surface during the
steady operation and explain how these surfaces can be maintained at specified
temperatures.

(b) Derive the governing differential equation for temperature distribution of 07

OR
(b) A cold storage room has walls made of 200 mm of brick on the outside, 80 mm 07
of plastic foam, and finally 20 mm of wood on the inside. The outside and
inside air temperatures are 25 oC and -3 oC respectively. If the outside and
inside convective heat transfer coefficients are respectively 10 and 30 W/m2 oC,
1
 and the thermal conductivities of brick, foam and wood are 1.0, 0.02 and
0.17 W/ m oC respectively.
Determine:
(a) overall heat transfer coefficient
(b) the rate of heat removed by refrigeration if the total wall area is 100 m2
(c) outside and inside surface temperatures and mid-plane temperatures of
composite wall.
Q.3 (a) Water at 10 oC, flows over a flat plate ( at 90 oC ) measuring 1 m X 1 m, with a 08
velocity of 2 m/s. Properties of water at 50 oC are ρ=988 kg/m3,
ν = 0.556 X 10-6 m2/s, Cp = 4.18 kJ/kg oC and k = 0.648 W/m oC.
Determine (a) The length of plate over which the flow is laminar
(b) The rate of heat transfer upto the above length
(c) The rate of heat transfer from the entire plate.
Useful co-relation:
Nu= 0.332 (Rex)1/2 (Pr)1/3 local Nusselt number for laminar flow
⎯Nu= [0.036 (ReL)0.8 – 836](Pr)1/3 average Nusselt number for
mixed flow

(b) Differentiate: 06
1. Mean film temp and bulk mean temp
2. Velocity and thermal boundary layer

OR

Q.3 (a) By dimensional analysis show that for natural convection heat transfer the 07
Nusselt number can be expressed as a function of Grashof number and Prandtl
number.

(b) Water (Cp=4.2 kJ/kg oC) is heated at the rate of 1.4 kg/s from 40 oC to 70 oC by 07
an oil (Cp=2 kJ/kg oC) entering at 110 oC and leaving at 60 oC in a counter flow
heat exchanger. If U = 350 W/m2 oC, calculate the surface area required.
Using the same entering fluid temperatures and the same oil flow rate, calculate
the exit temperature of oil and water and the rate of heat transfer, when the
mass flow rate of water is halved.
Q.4 (a) What do you mean by critical radius of insulation? Derive critical radius of 07
insulation rc = k / ho

(b) A steel rod (k=30 W/m oC), 12 mm in diameter and 60 mm long, with an 07
insulated end is to be used as spine. It is exposed to surrounding with a
temperature of 60 oC and heat transfer coefficient of 55 W/m2 oC. The
temperature at the base is 100 oC. Determine :
(i) The fin effectiveness
(ii) The fin efficiency
(iii) The temperature at the edge of the spine
(iv) The heat dissipation

OR

Q.4 (a) Derive the relation for temperature variation with respect to time, instantaneous 07
heat transfer rate and total heat transfer using lumped parameter analysis.
(b) A refrigeration suction line having outer diameter 30 mm is required to be 07
thermally insulated. The outside air convective heat transfer coefficient is 12
W/m2 oC. The thermal conductivity of the insulating material is 0.3 W/m oC.
2
 Determine:
(i) Whether the insulation will be effective
(ii) Estimate the maximum value of thermal conductivity of insulating
material to reduce heat transfer
(iii) The thickness of cork insulation to reduce the heat transfer to 20%
(k=0.04 W/m oC)
Q.5 (a) The temperature of an air stream flowing with a velocity of 3 m/s is measured 07
by a copper-constantan thermocouple which may be approximated as sphere of
3 mm in diameter. Initially the junction and air are at a temperature of 25 oC.
The air temperature suddenly changes to and is maintained at 200 oC.
Take ρ=8685 kg/m3, Cp = 383 J/kg oC and k =29 W/m oC and h=150 W/m2 oC.
Determine:
(i) Thermal time constant and temperature indicated by the
thermocouple at that instant
(ii) Time required for the thermocouple to indicate a temp. of 199 oC
(iii) Discuss the suitability of this thermocouple to measure unsteady
state temperature of fluid then the temperature variation in the fluid
has a time period of 30 seconds.

(b) (i) Define: Emissivity, Radiosity, Monochromatic emissive power, Irradiation 04

OR

Q.5 (a) Derive an expression for LMTD for counter flow heat exchanger stating the 07
assumption made.

(b) A condenser is to be designed to condense 2500 kg/h of dry and saturated steam 07
at a pressure of 10 kPa. A square array of 400 tubes each of 6 mm in diameter,
is to be used. If the tube surface temperature is to be maintained at 24 oC,
calculate the length of each tube assuming single pass.
Properties of dry and saturated steam at 10 kPa :

tsat= 45.8 oC, ρv=0.068 kg/m3 and hfg=2393 kJ/kg

*************