PES INSTITUTE OF TECHNOLOGY BANGALORE – SOUTH CAMPUSHosur Road, (1K.M. Before Electronic City), Bangalore – 560 100

DEPARTMENT OF MECHANICAL ENGINEERING

SCHEME AND SOLUTION - IST INTERNAL TEST

Subject : Heat and mass transfer

Semester: 6

Sub. Code: 10ME63 Section:Name of the faculty : Dr. Subrahmanya Katte, Thippeswamy G R

Q.No Marks

1a) Starting from the fundamental principles, derive the general heat conduction equation

in Cartesian co-ordinate system 7

B)

2

Explain briefly the various modes of heat transfer and enumerate the basic laws which governthe heat transfer

10

3 A square plate heater (15cm X 15 cm) is inserted between two slabs. The slab A is 2 cm thick(k=50 W/moC) and the slab B is 1 cm thick (0.2 W/moC). The outside heat transfer co-efficienton side A and B are 200 W/m2oC and 50 W/m2oC respectively. The temperature of thesurroundings is 250C. If the rating of the heater is 1kW, find i) maximum temperature in thesystem, ii) outer surface temperatures of two slabs. Draw an equivalent electrical circuit

10

4 a) Derive expression for heat conduction and temperature distribution for a hollow cylinder havinginner and outer radii r1 and r2 respectively with thermal conductivity k

7

b) Obtain expression for heat conduction for composite spheres having convection at both thesides 3marks

5 An insulated steam pipe having outside diameter 30 mm is to be covered with two layers ofinsulation, each having thickness of 20 mm. The thermal conductivity of one material is 5 timesthe other. Assuming inner and outer surface temperature of composite insulation are fixed, howmuch will heat transfer be increased when better insulation material is next to the pipe than it isouter layer.

10

6.Derive an expression for the heat loss per m2 of the surface area of the furnace wall, when thethermal conductivity varies with temperature according to the relation k = (a+bT2) W/moC.Where T is in oC. Also find rate of heat transfer through the wall, if L=0.2 m, T1 = 300oC, T2 =30oC, a= 0.3 and b= 5x10-6.

10

7. State the significance of critical thickness of insulation. Derive expression for critical thickness ofinsulation for cylinder

10

8. A wire of 6.5 mm diameter at a temperature of 60oC is to be insulated by a material having k =0.174W/moC. Convection heat transfer co-efficient is 8.722W/m2 oC. The ambient temperature is20 oC. For maximum heat loss what is the minimum thickness of insulation and heat loss permeter length? Also find percentage increase in the heat dissipation too 10