Heat and Mass Transfer (ME3104)
Assignment 1: Modules 1 & 2
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Faculty: Dr. Sebastian Uppapalli (sebastian.uppapalli@mahindrauniversity.edu.in)
TA: MD Irfan Ali (se23pmee006@mahindrauniversity.edu.in)
Subjective and Short Questions:
1) Write the governing equation for 2-D transient heat conduction. What are the minimum boundary
conditions required to solve the 2-D transient heat conduction equation.
2) Write different boundary conditions that are used to solve heat transfer problems.
3) The lumped capacitance approach is used when the Biot number is ____.
4) Find the characteristic length of cylinder of diameter 1mm and thermal conductivity 200 W/mK immersed
in a fluid with convective heat transfer coefficient 20 W/m2K.
5) Derive the expression for the critical radius of insulation for cylinder.
6) In order to achieve maximum heat dissipation, the fin should be designed in such a way that has a _____.
a) Maximum lateral surface towards the tip side of fin
b) Minimum lateral surface near the center line
c) Maximum lateral surface at the root side of fin
d) Maximum lateral surface near the center of fin
7) A fin will be necessary and effective only when _____.
a) k is small and h is large
b) k is large and h is also large
c) k is small and h is also small
d) k is large and h is small.
Problems:
8) A steam pipe of 170mm outer diameter and 160 mm inner diameter is covered with two layers of insulation.
The thickness of the first layer is 30 mm and that of the second layer is 50mm. The thermal conductivities of
the pipe and insulating layers are 58, 0.175, and 0.093 W/mK respectively. The temperature of steam is
350 OC and the ambient air temperature is 30 OC. The convective heat transfer coefficients at inner and outer
sides of the pipe are 230 W/m2K and 7 W/ m2K respectively. Evaluate the heat lost per unit length of the
steam pipe and layers contact temperatures.
9) In order to prevent the freezing of oranges during cold nights, it is necessary to heat the surrounding
atmosphere. For this, it is necessary to find out the temperature at the center of the orange. Assume that the
diameter of the orange is 8 cm and initially at 15 OC. It is then suddenly exposed to the cooling atmosphere
at -5 OC at night from 10 PM to 6 AM. If the heat transfer coefficient is 10 W/m 2K, state whether there will
be a formation of frost in the center of orange or not.
Properties of orange: k=0.5 W/mK; α=0.54X10-3 m2/hr.; Freezing temperature of orange= -2 OC.
10) Stainless steel square cross-sectional (1 cm X 1 cm) fin of length 8 cm with thermal conductivity 18
W/mK is attached to a base whose temperature is 300 OC. The fin is exposed to a convective environment
with fluid temperature 50 OC and heat transfer coefficient 45 W/m2K. Compute the fin efficiency and the
heat lost by the fin.
