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## Heat Transfer - Jun 2015

### Mechanical Engineering (Semester 5)

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.

### Answer any one question from Q1 and Q2

**1 (a)** Derive three dimensional general heat conduction equation in Cartesian coordinates for anisotropic material for unsteady state condition with uniform internal heat generation.(7 marks)
**1 (b)** What is unsteady state? Define internal temperature gradient. When can it be neglected?(3 marks)
**10 (b)** A parallel flow heat exchanger is to be designed to cool oil (C_{p}=2.1 kJ/kgK, 20kg/min) from 70°C to 40°C by using cold water (C_{p}=4.2 kJ/kg K, 50 kg/min), available at 30°C. The overall transfer coefficient is 133 W/m^{2}K. Find the area of heat exchanger, outlet temperature of water and effectiveness.(8 marks)
**10 (a)** Explain dropwise condensation and filmwise condensation. compare these two.(6 marks)
**10 (c)** Explain effectiveness and NTU for a heat exchanger.(4 marks)
**2 (a)** Write a note on temperature boundary condition and heat flux boundary condition.(4 marks)
**2 (b)** A long hollow cylinder has inner and outer radii as 10cm and 20cm respectively. The rate of heat generation is 1 kW/m 3 , the thermal conductivity of cylinder material is 0.2 W/mk. If the maximum temperature occurs at radius of 15cm and temperature of Outer surface is 607deg;C, find temperature at the inner surface of the cylinder.(6 marks)

### Answer any one question from Q3 and Q4

**3 (a)** Explain critical radius of insulation.(4 marks)
**3 (b)** A 5cm diameter steel ball, initially at a uniform temp of 450°C is suddenly placed in an environment at 100°C with h=10 W/m^{2} K. Steel properties: Cp=460 J/kgK, density=7800 kg/m^{3} , K=35 W/mK. Calculate the time required for the ball to attain a temperature of 150°C.(6 marks)
**4 (a)** Write a note on Overall heat transfer coefficient.(4 marks)
**4 (b)** A cylindrical metal rod of 5 cm diameter and 20 cm long with thermal conductivity 225 W/mK protrudes in atmosphere at 30°C. It projects from furnace wall at 300°C. A convective heat transfer coefficient of air is 10 W/m^{2}K. Determine temperature at the free end of the rod assuming it as a fin insulated at end.(6 marks)

### Answer any one question from Q5 and Q6

**5 (a)** Explain physical significance of any four dimensionless numbers used in convection.(8 marks)
**5 (b)** Water flows at the rate of 360kg/hr through a metallic tube of 10mm diameter and 3m length. It enters the tube at 25°C. Outer surface of the tube is maintained at a constant temperature of 100°C. Calculate the exit temperature of the water. Properties of water:

μ=5.62×10^{-4} kg/ms; C_{p}=4174J/kgK; K=0.664 W/mK.

Use the following correlation:

N_{u}=0.023 Re^{0.8} Pr^{0.4} for turbulent flow

N_{u}=3.66 for laminar flow.(8 marks)
**6 (a)** Write a note on velocity boundary layer and thermal boundary layer.(6 marks)
**6 (b)** Explain mechanism of natural convection. Distinguish it from forced convection.(4 marks)
**6 (c)** A rectangular plate of length 7cm and width 4cm maintained is at 115°C. It is exposed to still air at 25°C on both sides. Calculate convective heat transfer rate if smaller side of the plate is held vertical.

Use Correlation N_{u}=0.59 (Gr.Pr)^{0.25}

For air at 70°C, K=0.03 W/mK; Pr=0.679; kinematic viscosity v=2.076 × 10^{-6} m^{2}/s.(6 marks)

### Answer any one question from Q7 and Q8

**7 (a)** State and explain following laws of radiation:

i) Planck's Law

ii) Wein's Law

iii) Lambert's cosine rule

iv) Kirchoff's Law

v) Stefan Boltzmann Law(10 marks)
**7 (b)** Two large parallel steel plates of emissivities 0.8 and 0.4 are held at temperatures 1100 K & 500 K respectively. If a thin radiation shield of emissivity 0.09 is introduced between two plates, determine radiation heat exchange in W/m 2 with and without radiation shield.

Use σ=5.67×10^{-8} W/m^{2} K^{4}.(6 marks)
**8 (a)** What is shape factor? What is shape factor for a plane surface and convex surface with respect to itself?

Find the shape factor of following with respect to itself:

i) Cylindrical cavity of diameter D and depth H,

ii) Hemispherical cavity of diameter D,

iii) Conical hole of diameter D and depth H(10 marks)
**8 (b)** Consider two concentric spheres 'A' and 'B' with diameter of 200mm and 300mm respectively. Space in between these two spheres is evacuated. Liquid air at -153°C is stored inside sphere 'A'. The surfaces of spheres 'A' and 'B' facing each other are coated with aluminium foil ( ε=0.03). Latent heat of vaporization of liquid air is 209.35 kJ/kg. If the system is kept in a room where ambient temperature is 30°C,

Calculate the rate of evaporation of liquid air.(6 marks)

### Answer any one question from Q9 and Q10

**9 (a)** What is the significance of critical heat flux in design of evaporators? Explain different regimes in pool boiling curve with neat sketch.(10 marks)
**9 (b)** What is LMTD for a heat exchanger? Derive an expression for LMTD of parallel flow heat exchanger.(8 marks)