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A TYPICAL QUESTION PAPER OF HEAT TRANSFER SPECIALLY FOR UNIVERSITY OF PUNE
SUBJECT-HEAT TRANSFER DUTATION-1.5 hrs
Qu.1a) Derive the general heat conduction equation in Cartesian co-ordinates. under
what condition does this get reduced to Poisson equation; Laplace equation
and Fourier equation. 10 marks
b) Two slabs each 120mm thick, have thermal conductivities of 14.5 W/moC and
210 W/moC. These are placed in contact but due to roughness only 30 % of the area is in contact and the gap in the remaining area is 0.025mm thick and is filled with air. If the temperature of the face of the hot surface is at 220oC and the outside surface of the other slab is at 30oc. Determine
1) Heat flow through composite system
2)The contact resistance and temperature drop in contact
Assume that the conductivity of air is 0.032 W/moC and that half of the contact(of the contact area) is due to either metal. 7 marks
b) Discuss ‘Electrical Analogy’ of heat conduction and Thermal contact resistance.
Qu 2 a) Define thermal diffusivity and explain its significance. 4 marks
b) Explain the concept of Log mean area. 4 marks
c) Derive the equation for total heat transfer rate through a hollow cylinder having
inner and outer radii r1 and r2 resp. its inner and outer surface temp are T1 and
T2 resp.. There is no heat generation and its conductivity is constt. 9 marks
Qu3 a) Explain critical radius and economic thickness of insulation 4 marks
b) Write a short note on ‘ Thermal conductivity of gases’ 4 marks
c) A small electric heating application uses wire of 2mm dia with 0.8mm thick
insulation (K= 0.12 W/moC ). The heat transfer coeff (ho) on the insulated
surface is 35 W/m 2oC. Determine the critical thickness of insulation in this
case and percentage change in heat transfer rate if the critical thickness is used,
assuming the temp difference between the surface of the wire and surrounding
air remains unchanged. 10 marks
Qu 4a) The temp on the two surfaces of a 25mm thick steel plate (K= 48 W/moC) having
uniform volumetric heat generation of 30x 106 W/m3. are 1800C and 120oC.
Neglecting the end effects, determine the following-
1) Temp distribution across the plate
2) The value and position of the max temp.
3) Flow of heat from each surface of the plate 9 marks
b) A chemical reaction takes place in a packed bed (K= 0.6 W/moC) between two
co-axial cylinder with radii 15 mm and 45 mm . The inner surface is at 580oC
and it is insulated. Assuming the reaction rate of 0.55 MW/m3 in the reactor
volume find the temp at the outer surface of the reactor. 9 marks
Qu5a) State assumption made in lumped capacitance method, using this method derive
the following relation.
t - ta
--------- = e-Bi Fo with usual notations 6 marks
ti - ta
b) Explain Biot and Fourier numbers. 4 marks
c) An egg with mean dia of 40 mm and initially at 20oC is placed in boiling water
pan for 4 min and found to be boiled to the consumer taste for how long should
a similar egg for same consumer be boiled when taken from refrigerator at 5oC
Take following properties for egg.
K = 10 W/moC , Density= 1200 Kg/m3, C = 2 KJ/kgoC, h = 100 W/m2oC
Use lump theory. 7 marks.
Qu6a) Explain time constt of thermocouple
A thermocouple junction of spherical form is to be used to measure the temp of a gas stream. h = 400 W/m2oC , K(thermocouple junction)= 20 W/moC
C = 400 J/kgoC , Density= 8500 Kg/m3
Calculate the following
1) junction dia needed for the thermocouple to have thermal time constt of 1 sec.
2) Time required for the thermocouple to reach 198oC if the junction is initially at 25oC and is placed in a gas stream which is at 200oC. 12 marks
b) Draw the temperature profile for
1) When the plate temp is more than the approaching fluid temp.
2) When the approaching fluid is at higher temp than that of the plate.
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