An appropriate correlation for heat transfer by natural commotion from a honzontal pipe to the atmosphere is

Nu = 033Gr^0.25PPr^0.25

Show that the above correlation can be simplified to

when air has the values listed bclow

3.077x10^-3K^-1, ρ = 1.086 kg m^-3, c_p at 1.083 kg m^-3 k=2.816x10^-5 kWm^-1K^-1, μ = 1962 x10^-5 kg m^-1s^-1

(d) The outer surface of the insulation on a horizontal steam pipe has a radius of 50 mm and is at a termxratim of 90°C. The atmospheric air surrounding the pipe is at a temperature of 14°C. and has the property s alms listed in part (c) above. Estimate the rate of heat loss by natural convection to the atmosphere by cach metit length of pipe.

2. (a) Explain how hcat is lost from a hot surface to the swrounding air.

(b) (i) Explain the effect of insulating a hot surface.

(ii) What is meant by the economic thickness of lagging?

(c)  What is the purpose of a silvered coating. usually of a good conductor. m the outside of most insulation?

3. Butanol at a tcmperaturc of 28°C is pumped at a velocity of 14 ms^-1 through a 100 mm diameter tube kept at a wall temperature of 90°C. The properties of butrol are given below.

Determine the connective heat transfer coefficient (you will find the appropriate correlation in the lessons).

Data:

p = 950 kg m^-3

c_p = 2.142 kJ kg^-1 K^-2

μ = 29 x 10^-3 kg m^-2 s^-1 at 28°C

μ = 12 x 10^-3 kg m^-1s^-1 at 90^oC

k = 2.4 x10^-4 kW m^-1 K^-1

4. Liquid ammonia is heated as it flows at a mean velocity of 2 ins-¹ through a circular pipe. The pipe, which has an internal diameter of 75 nun. is at a uniform temperature of 27°C. and the ammonia at a section 1.2 m from the inlet to the pipe has a temperature of -23°C. Use the following information to estimate the local heat transfer flux at I = 12 m. Note, the properties of ammonia liquid base been taken a -23°C, except whew stated.

Liquid ammonia properties:

Density = 600 kg m^-3

Specific heat capacity = 4.86 kJ kg^-1 K^-1

Dynamic viscosity (at 27°C) = 1.19 x 10^-4 kg m-¹ s-¹ Dynamic viscosity = 2D5 x 10⁴ kg m^-1 s^-1

Thermal conductivity = 5.11 x 10-⁴ kW nr¹ s-¹

Heat transfer conelations:

5. (a) Explain what is meant by an overall heat transfer coefficient.

(b) Explain what is mean by failing and what its effect will be on the value of the overall heat transfer coefficient.

(c) A heat exchanger is to be used to heat a ;micas liquid within the tubes using saturated steam at 100°C. The tubes have an inside diameter of 20 min and outside diameter of 22 trim. it is estimated that the imer surface heat transfer coefficient will be 42 kW m^-2 K^-1 and the mot surface heat transfer coefficient will be 15A kW m^-2 K^-1 when the exchanger is clean. In order to allow for possible fouling dining use you should assume a fouling factor of 1.12 x 10-4 m² K W^-1 will be applicable.

Estimate:

(i) the overall heat transfer coefficient in use

(ii) the heat transfer rate when the relevant average temperature difference between steam and fluid is 50°C and the heat exchanger has 100 tubes each of 5 m in length.