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/m³,C=2J/kg°C(for steel), h=30W/m²°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/m³, k=0.02894W/m°C, C_ρ=1.005kJ/kg°C, Pr=0.696; v =18.97×10^-6 m²/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)^mx(Pr.)ⁿ(10 marks) 4(a) State and expalin the reciprocity theorem. Derive the equation A₁F_1-2=A₂F_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/m²K. 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/m²°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)