**T.E. (Mechanical Engineering)****HEAT TRANSFER(2015 Pattern)**

**Time : 2.30 HoursMax. Marks : 70 Instructions to the candidates:1) Answer Q.1 Or Q.2, Q.3 or Q.4, Q.5 or Q.6, Q.7 or Q.8 and Q.9 or Q.10.2) Neat diagrams must be drawn wherever necessary.3) Figures to the right indicate full marks.4) Use of logarithmic tables slide rule, mollier charts, electronic pocketcalculator and steam tables in allowed.5) Assume suitable data, if necessary.**

Q1) a) Explain variation of thermal conductivity of metals and non-metals with temperature. **[4M]**

b) An Industrial freezer is designed to operate with an internal air temperature of –20°C when the external air temperature is 25 °C and the internal and external heat transfer coefficients are 12 W/m^{2} °C and 8 W/m^{2} °C respectively. The walls of the freezer are composite construction, comprising of an inner layer of plastic (K = 1 W/m ºC and thickness of 3 mm), and an outer layer of stainless steel (K = 16 W/m °C and thickness of 1mm). Sandwiched between these two layers is a layer of insulating material with K = 0.07 W/m °C. Find the thickness of insulation that is required to reduce the heat loss to 15 W/m2.** [6M]**

**OR**

Q2) a) Explain Thermal Contact Resistance. **[4M]**

b) An electrical cable of 6.5 mm diameter at a temperature of 60 °C is to be insulated by a material having k = 0.174 W/m°C. The cable runs through air at 20 °C and having heat transfer coefficient is 8.72 W/m2 °C. Find the thickness of insulation, so that heat dissipated is maximum and heat dissipated at this thickness of insulation per meter length of the cable.**[6M]**

Q3) a) Explain the significance of dimensionless parameters used in transient heat conduction. **[4M]**

b) The electric wire of thermal conductivity k = 20 W/m °C, 3 mm in diameter and 1m long has current flow = 200 amperes, ρ(resistivity) = 70 μΩ-cm. The wire is submerged in a liquid at 100 °C and the surface heat transfer coefficient is 2000 W/m^{2} °C. Calculate the center temperature of the wire.**[6M]**

**OR**

Q4) a) Fins are provided to increase the heat transfer rate from a hot surface. Which of the following arrangements will have the maximum heat transfer rate

i) 8 fins with 16 cm length or

ii) 16 fins with 8 cm in length

Take conductivity of fin material as 300W/m °C, heat transfer coefficient, h = 20 W/m2 °C cross sectional area of the fin = 2cm^{2}, perimeter of fin cross section = 4cm, temperature of the hot surface = 230 °C, ambient temperature = 30 ºC. Assume fins of insulated ends. **[6M]**

b) What is the purpose of insulation? List any two insulating materials with their thermal conductivity values. **[4M]**

Q5) a) Calculate appropriate Reynolds numbers and state if the flow is laminar or turbulent for the followings :** [4M]**

i) The roof of coach 6m long, travelling at 100 km/hr in air (ρ = 1.2 kg/m3, μ = 1.8 × 10–5 kg/ms)

ii) 0.05 kg/s of carbon dioxide gas at 400 K flowing in a 20mm diameter pipe (μ = 1.97 × 10–5 kg/ms)

b) List various dimensionless numbers in Natural and forced convection. Also state their expressions. **[4M]**

c) Estimate the heat loss from a vertical wall exposed to Nitrogen at 1 atm & 4 °C. The wall is 2m high and 2.5m wide and is maintained at 56 ºC. The average Nusselt number over height of the wall for Natural convection is given by **[8M]**

Nu_{μ}=0.13 (G_{r}P_{r})^{1/3}

The properties for Nitrogen at a mean film temperature are given as

ρ = 1.142 kg/m^{3}, K = 0.026 W/m, ν = 15.63 × 10–6 m^{2}/s, Pr = 0.713.

**OR**

Q6) a) Explain with neat sketch mechanism of formation of thermal boundary layer when cold air blown over a hot flat plate. **[6M]**

b) A metallic bar 2.5cm in diameter carrying current and should be maintained at 85 °C which is achieved by allowing the air at 30 °C to flow at 2.5m/s perpendicular to its axis. Find the heat transfer coefficient on the surface of the bar and permissible current flow. Take resistivity of the metallic bar = 0.015 × 10–6 Ωm. Use the following properties of air at mean film temperature. **[10M]**

ν = 18.65 × 10^{-6} m^{2}/s, K = 0.029 W/mK, Pr = 0.7

Use the following correlation

Nu_{d}=0.683(Re_{d})^{0.47}(P_{r})^{0.33}

Q7) a) State and explain any four rules regarding radiation shape factor. **[8M]**

b) Liquid oxygen (Boiling Temperature = –182°C) is to be stored in spherical container of 30cm diameter. The system is insulated by an evacuated space between inner space and surrounding 45cm inner diameter concentric sphere. For both spheres ε = 0.03 and temperature of the outer sphere is 30°C. Estimate the rate of heat flow by radiation to the oxygen in the container and rate of evaporation of liquid oxygen if its latent heat is 220 kJ/kg. **[8M]**

**OR**

Q8) a) Explain “Surface resistance” and “Space resistance”. Construct radiation network for two gray surfaces exchanging radiant energy. Give the formula for the radiant heat exchange between them. **[6M]**

b) Write the statements and mathematical expressions of the following laws in radiation heat transfer : **[4M]**

i) Planck’s Law

ii) Lambert’s cosine law.

c) Determine the radiant heat exchange between two large parallel steel plates of emissivity 0.8 and 0.5 held at temperature of 1000 K and 500 K respectively, if a thin copper plate of emissivity 0.1 is introduced as a radiation shield between two plates. **[6M]**

Q9) a) Explain the six regimes of pool boiling with the help of neat curve. **[8M]**

b) What is fouling? What are the factors causing fouling?** [4M]**

c) Air cooled condenser of 1 TR split air-conditioner rejects heat 4.2 kW. The ambient temperature is 30 °C whereas condensing temperature of the refrigerant is 45 °C. Calculate the temperature rise of the air as it flows over the condenser tubes. Take for condenser UA = 350 W/K**.[6M]**

**OR**

Q10)a) Differentiate between Film wise condensation and Drop wise condensation. **[4M]**

b) Draw labelled temperature profiles of the following types of heat exchangers : **[4M]**

i) Direct transfer type parallel flow.

ii) Direct transfer type counter flow.

iii) Condenser.

iv) Evaporator.

c) A steam condenser consists of 3000 brass tubes of 20mm diameter. Cooling water enters the tube at 20 °C with a mean flow rate of 3000kg/s. The heat transfer coefficient on the inner surface is 11270 W/m2 °C and that for condensation on the outer surface is 15500 W/m2 °C. The steam condenses at 50 °C and the condenser load is 230 MW. The latent heat of steam is 2380 KJ/kg. Assuming counter flow arrangement, Calculate the tube length per pass if two tube passes are used. If flow arrangement is parallel what is the effect on LMTD of steam condenser. **[10M]**

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