Heat Transfer - May 2015

Mechanical Engineering (Semester 5)

TOTAL MARKS: 80
TOTAL TIME: 3 HOURS (1) Question 1 is compulsory.
(2) Attempt any three from the remaining questions.
(3) Assume data if required.
(4) Figures to the right indicate full marks.

Solve any four:

1 (a) What is meant by film condensation and dropwise condensation? (5 marks)

1 (b) What is Fin? What are the various types of fins? (5 marks)

1 (c) Explain the number of transfer units (NTU). (5 marks)

1 (d) Define Thermal Diffusivity and state its significance. (5 marks)

1 (e) Define: Radiosity and Irradiation. (5 marks)

2 (a) Derive the relation for heat transfer through fin with insulated tip. State the assumptions clearly. (10 marks)

2 (b) Explain the term 'Time Constant' of thermocouple. (3 marks)

2 (c) A copper wire of radius 0.5mm is insulated uniformly with plastic (k=0.5 W/m K) sheathing 1mm thick. The wire is exposed to atmosphere at 30°C and the outside surface coefficient is 8 W/m² K. Find the maximum safe current carried by the wire so that no part of the insulated plastic is above 75°C. Also calculate critical thickness of insulation. For copper, thermal conductivity = 400 W/m K, specific electrical resistance=2 X10^-8 ohm-m. (7 marks)

3 (a) Using dimensional analysis, derive an expression for forced convection:- Nu=Constant X(Re)^mX (Pr)ⁿ. (8 marks)

3 (b) Air at atmospheric pressure and 207deg;C flows with 6 m/s velocity through main trunk duct of air condisioning system. The duct is rectangular in cross-section and measures 40cm × 80cm. Determine heat loss per meter length of duct corresponding to unit temperature difference.
The relevant thermo-physical properties of air are: v=15×10^-6, α=7.7×10^-2 m²/hr, k=0.026 W/m-deg-k.
Use Nu=0.023 (Re)^0.8 × (Pr)^0.4. (8 marks)

3 (c) What is meant by Fouling in Heat Exchangers. (4 marks)

4 (a) Distinguish between specular and diffuse radiation. (4 marks)

4 (b) Prove that the total emissive power of black surface is π time the intensity of radiation. (6 marks)

4 (c) 16.5 kg/s of the product at 650°C (c_p=3.55 kJ/kg K), in a chemical plant, are to be used to heat 20.5 kg/s of the incoming fluid from 100°C (c_p=4.2 kJ/kg K). If the overall heat transfer coefficient is 0.95 kW/m² K and the installed heat transfer surface is 44 m², calculate the fluid outlet temperature for the counter flow and parallel flow arrangements. (10 marks)

5 (a) Derive the relationship between the effectiveness and the number of transfer units for a parallel flow heat exchanger. (10 marks)

5 (b) A thermocouple indicates a temperature of 800°C when placed in a pipeline where a hot gas is flowing at 870°C. If the convective heat transfer cofficient between the thermocouple and gas is 60 W/m² K, find the duct wall temperature, ε (thermocouple)=0.5. (5 marks)

5 (c) A thin copper sphere with its internal surface highly oxydises, has a diameter of 20 cm. How small a hole must be made in the sphere to make an operating that will have an absorptivity of 0.9? (5 marks)

Write a short note (Any Two):

6 (a) (i) Heisler chart. (4 marks)

6 (a) (ii) Importance of numerical methods. (4 marks)

6 (a) (iii Heat Pipe. (4 marks)

6 (b) Draw the boiling curve and identify the different boiling regimes. (5 marks)

6 (c) A 15 mm diameter mild steel sphere (k=42 W/m °C) is exposed to coding airflow at 20°C resulting in the convective coefficient h=120 W/m² °C.
Determine the following:
i) Time required to cool the sphere from 550°C to 90°C
ii) Instantaneous heat transfer rate 2 minutes after the start of cooling.
For mild steel take: ρ=7850 kg/m³, c=475 J/kg °C, α=0.045 m²/h. (7 marks)