JNTU III B.Tech II Semester Supplimentary Examinations, Aug/Sep 2008

HEAT TRANSFER

( Common to Mechanical Engineering and Automobile Engineering)

SET-IV

1. (a) Derive steady state general heat conduction equation without heat generation

in spherical systems.

(b) State and explain the mode of conduction heat transfer.

2. (a) What is critical thickness of insulator on a small diameter wire or pipe, explain

its physical significance and derive an expression for the same.

(b) A plane wall 10 cm thick generated heat at the rate of 4×104W/m3. When an electric current is passed through it. The convective heat transfer co-efficient between each face of the wall and the ambient air is 50 W/m2k.

Determine

i. The surface temperature

ii. The maximum temperature in the wall.

Assume the ambient air temperature to be 200C and the thermal conductivity of the wall material to be 15 W/mK.

3. (a) What are Biot and Fourier numbers? Explain their physical significance.

(b) A slab of Aluminum 10cm thick is originally at a temperature of 5000C. It is suddenly immersed in a liquid at 1000C resulting it a heat transfer coefficient of 1200 W/m2k. Determine the temperature at the centerline and the surface 1 min after the immersion. Also the total thermal energy removal per unit area slab during this period. The properties of aluminum for the given condition

are: ? = 8.4 × 10?5m2 /s, K=215 W/mk, ? = 2700 kg/m3, Cp= 0.9 kJ/kg.

4. Nitrogen at 300C flows over a plate maintained at 700C with a free stream velocity

of 10 m/s.

(a) Determine the local and average values of convective heat transfer co-efficient.

(b) Also calculate the values of the boundary layer thickness (velocity, thermal) and momentum and displacement thickness at these locations.

(c) Determine also the location at which the flow turns turbulent, considering

critical Reynolds number = 5 x 105.

5. (a) What is the recommended correlation for natural convection over a vertical plate or cylinder in the turbulent region?

(b) How is the velocity field developed in front of a vertical plate which is maintained at a temperature?

i. Higher

ii. Lower, than the surrounding fluid.

6. (a) Distinguish between nucleate and film boiling.

(b) A heated 30 × 30 cm square copper plate, serves as the bottom for a pan of water at 1 atm. Pressure. The temperature of the plate is maintained at 119oC. Estimate the heat transferred per hour by the plate.

7. In a cross flow heat exchanger hot exhaust gases (Cp = 1000 J/kgK) entering at 300oC and leaving at 100oC are used to heat water, flowing at 1 kg/s from 35oC to 125oC. The overall heat transfer coefficient based on the gas side surface area has been found to be 100 W/m2K. Using the NTU method, estimate the required gas side surface area.

8. A long cylinder having a diameter of 2 cm is maintained at 600oC and has an emissivity of 0.4. Surrounding the cylinder is another long, thin walled concentric cylinder having a diameter of 6 cm and an emissivity of 0.2 on both the inside and outside surfaces. The assembly is located in a large room having a temperature of 27oC. Calculate the net radiant energy lost by the 2 cm diameter cylinder per meter length. Also calculate the temperature of the 6 cm diameter cylinder.