## Heat & Mass Transfer - May 2016

### Mechanical Engg. (Semester 6)

TOTAL MARKS: 100

TOTAL TIME: 3 HOURS
(1) Question 1 is compulsory.

(2) Attempt any **four** from the remaining questions.

(3) Assume data wherever required.

(4) Figures to the right indicate full marks.
**1(a)** What do you mean by boundary condition of 1st,

2nd

3rd kind?(6 marks)
**1(b)** Derive the general three dimensional heat condition heat conduction equation in cartesian co-ordinates and state the assumptions made.(8 marks)
**1(c)** A pipe with outside diameter 20 mm is covered with two insulating materials. The thickness of each insulting layer is 10 mm. The conductivity of 1st insulating layer is 6 times that of the 2nd insulating layer. Initially insulating layer is placed in the order 1st and 2nd layer. Then it is placed in the order of 2nd layer and 1st layer. Calculate percentage change in heat transfer and increase or decrease. Assume a length of 1 m. In both the arrangement, there is no change in temperature.(6 marks)
**2(a)** What is physical significance of critical thickness of insulation? Derive an expression for critical thickness of insulation fo a cylinder.(6 marks)
**2(b)** Derive an expression for the temperature distribution for a pinfin, when the tip of the fin is insulated.

(8 marks)
**2(c)** Find the amount of heat transferred through an iron fin of thickness of 5 mm, height 50 mm and width 100 cm. Also determine the temperature difference at the tip of the fin assuming atmospheric temperature of 28°C and base temperature of fin = 108°C. Assume the following K = 50W/mK,

h=10W/m^{2}K.(6 marks)
**3(a)** Write a note on Biot number and Fourier number.(4 marks)
**3(b)** Obtain an expression for instantaneous heat transfer and total heat transfer for lumoed heat analysis treatment of heat conduction problem.(8 marks)
**3(c)** A lot mild steel sphere (K = 43W/mK) having 10 mm diameter is planned to be cooled by an air flow at 25°. The convection heat transfer coefficient is 115W/m^{2}K. Calculate the following

i) time required to cool the sphere from 600°C to 100°C

ii) Instantaneous heat transfer rate 1.5 min after the start of cooling

iii) total energy transferred from the sphere during the first 1.5 min.(8 marks)
**4(a)** Explain the following :

i) Velocity boundary layer

ii) Thermal boundary layer.(6 marks)
**4(b)** Using dimensional analysis derive an expression relating Nusselt number, Prandtl and Grashoff numbers for natural convection.(8 marks)
**4(c)** Air at 20°C flows over thin place with a velocity of 3m/sec. The plate is 2 m long and 1 m wide. Estimate the boundary layer thickness at the trailing edge of the plate and the total drag force experienced by the plate.(6 marks)
**5(a)** Explain the physical significance of the following of dimensionless numbers:

i) Reynolds number

ii) Prandtl number

iii) Nusselt number

iv) Stanton number.(8 marks)
**5(b)** Air at 20°C flows past a 800 mm long plate at velocity of 45m/sec. If the surface of the plate is maintained at 300°C. Determine

i) The heat transferred from the entire plate length to air taking into consideration both laminar and tubulent portion of the boundary layer.

ii) The percentage error if the boundary layer is assumed to be of turbulent nature from the very leading edge of the plate. Assume unit width of the plate and critical Reynolds number to be 5×10^{5}.(12 marks)
**6(a)** Derive an expression for LMTD for counter flow heat exchanger and state the assumptions made.(10 marks)
**6(b)** A counter flow, cocentric tube heat exchanger used to cool the lubricating oil for a large industrial gas turbine engine. The flow rate of cooling water through the inner tube. (d_{1}=20mm) is 0.18kg/sec. While the flow rate of engine oil through the outer annulus (d_{0}=40mm) is 0.12kg/sec. The inlet and outlet temperature of oil are 95°C and 65°C respectively.The water enter at 30°Cto the exchanger. Neglecting tube wall thermal resistance, fouling factors abd heat loss to the surroundings, calculate the length of the tube.(10 marks)
**7(a)** Clearly explain the regions of pool boiling with neat sketch.(6 marks)
**7(b)** State and explain Ficks law of diffusion.(6 marks)
**7(c)** Air free saturated steam at 85°C and pressure of 57.8KPa condenses on the outer surface of 225 horizontal tubes of 1.27 cm outside diameter arranged in 15×15 array. Tube surfaces are maintained at a uniform temperature of 75°C. Calculate the total condensation rate/m length of the tube bundle.(8 marks)
**8(a)** Explain :

I) Stefan Boltzmann law.

ii) Kirchoff 's law

iii) Plank ' s law

iv)Wein ' s displacement law.

v) Radiation shield.(10 marks)
**8(b)** Calculate the net radient heat exchange per m^{2} area for two large parallel plates at temperatures of 42°C and 27°C respectively. Take emissivity of the hot plate and cold plates are 0.9 and 0.16 respectively. If the polished aluminium shield is placed between them, Find the percentage reduction in the heat transfer. Take emissivity of shield as 0.4.(10 marks)