## Heat Transfer - Dec 2016

### 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 questionQ.1(a,b,c,d,e)

**1(a)** Draw a neat boiling curve for water and mark the different boiling regimes.(5 marks)
**1(b)** A steel ball 50mm in diameter and at 900°C is placed in still atmosphere of 30°C. Calculate the initial rate of cooling of the ball in °C/min. Takeρ=7800kg/m^{3},C=2J/kg°C(for steel), h=30W/m^{2}°C. Neglect internal thermal resistance.(5 marks)
**1(c)** Explain non dimesional numbers used in covection heat transfer.(5 marks)
**1(d)** Explain briefly the term thermal capacity and thermal diffusivity of material.(5 marks)
**1(e)** Define intensity of radiation. What is a soild angle? What is its unit?(5 marks)
**2(a)** A wall of a furnace is made up of inside layer of silica brick 120 mm thick covered with a layer of magnestic brick 240 mm thick. The temperature at inside surface of silica brick wall and outside surface of magnesite brick wall are 725°C and 110°C respectively. The contact thermal resistance between the two walls at the interface is 0.0035°C/W per unit wall area. If thermal conductivities of silica and magnesite bricks are 1.7W/m°C and 5.8W/m°C, calculate

i) The rate of heat loss per unit area of walls.

ii) The temperature drop at interface.(10 marks)
**2(b)** Derive the formula for rate of heat transfer for an insulated tip fin from the differential equation $$\frac{d^2\theta }{dx^2}-m^2\theta =0$$(10 marks)
**3(a)** Air at 30°C flows with a velocity of 2.8m/s over a plate 1000 mm (length)×600mm (width)×25mm (thickness). The top surface of the plate is maintained at 90°C. If the thermal conductivity of the palte material is 25W/m°C, calculate: i) heat loast by the plate; ii) bottom temperature of the plate for the steady state condition. The thermo - physical properties of air at mean file temperature at 60°C areρ1.06kg/m^{3}, k=0.02894W/m°C, C_{ρ}=1.005kJ/kg°C, Pr=0.696; v =18.97×10^{-6} m^{2}/s. Choose the appropriate relation from the following: Nu
=0.664(Re_{L)1/2(Pr)1/3-For Laminar flow; Nu=0.036(ReL)0.8(Pr)1/3 - For Turbulent flow}(10 marks)
**3(b)** With the help of dimensional analysis method prove that for free convection Nu= constant x(Gr)^{m}x(Pr.)^{n}(10 marks)
**4(a)** State and expalin the reciprocity theorem. Derive the equation A_{1}F_{1-2}=A_{2}F_{2-1}.(10 marks)
**4(b)** An electric wire of 0.25mm diameter,ε=0.4 is placed within a tube of 2.5mm diameter, &epsioln;=0.6 having negligible thickness. This tube in turn is placed concentrically within a tube of 5mm diameter, ε=0.7. Annular spaces can be assumed to be evacuated compeletly. If the surface temperature of the outer tube is maintained at 5°C, what must be the temperature of wire so as to maintained the temperature of inner tube at 120°C?(10 marks)
**5(a)** Derive the expression for log mean temperature difference in a counter flow heat exchanger. State your assumption.(8 marks)
**5(b)** In a certain double pipe heat exchanger hot water flows at the rate of 50000 kg/hr and gets cooled from 95°C to 65°C. At the same time 50000kg/hr of cooling water at 30°C enters the heat exchanger. The flow conditions are such that overall heat transfer coefficient remains constant at 2270W/m^{2}K. Determine the heat transfer area required and the effecitveness, assuming two streams are in parallel flow. Assuming for the both streams C_{p=4.2kJ/kgK.}(8 marks)
**5(c)** Explain Heat Exchanges effectiveness.(4 marks)

### Write a short note any two Q6(a).(i, ii, iii)

**6(a)(i)** Hesier Chart.(4 marks)
**6(a)(ii)** Explain efficiency and effectiveness(4 marks)
**6(a)(iii)** Time constant of thermocouple.(4 marks)
**6(b)** Explain Hydrodynamic and thermal boundary layer.(4 marks)
**6(c)** A steel rod ( K=32 W/m°C), 12 mm in diameter and 60 mm long, with an insulated ends to be used as spine. It is exposed to surroundings with a temperature of 60°C and a heat transfer coefficient of 55 W/m^{2}°C. The temperature at the base the fin is 95°C. Determine-

i) The fin efficiency

ii) The temperature at the edge of the spine:

iii) The heat dissipation.(8 marks)