## 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/m^{2} 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)^{m}X (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} m^{2}/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/m^{2} K and the installed heat transfer surface is 44 m^{2}, 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/m^{2} 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/m^{2} °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/m^{3}, c=475 J/kg °C, α=0.045 m^{2}/h. (7 marks)