1. (a) Give three examples for each of natural (free) convection and forced convection which occur in industrial processes.

(b) The Grashof number and the Reynolds number appear in most correlations of experimental data for convective heat transfer. Explain, in a maximum of 150 words, the mechanisms of natural and forced convection with particular reference to the above non- dimensional groups.

(c) An appropriate correlation for heat transfer by natural convection from a horizontal pipe to the atmosphere is

Nu = 0.53Gr^0.25 Pr^0.25

where Gr = (αρ²d³ (T_s - T_f)g)/μ²

and Pr = c_pμ/k

Show that the above correlation can be simplified to

h ≈ 1.34 (T_s - T_f /d)^0.25 Wm^-2 K^-1

when air has the values listed below

α = 3.077 x 10^-3 K^-1, ρ = 1.086 kg m^-3, c_p = 1.0063 kJ kg^-1 K^-1

k = 2.816 x 10^-5 kW m^-1 K^-1, μ = 1.962 x 10^-5 kg m^-1 s^-1

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

2. (a) Explain how heat is lost from a hot surface to the surrounding 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, on the outside of most insulation?

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

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

Data:

ρ = 950 kg m^-3

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

μ = 2.9 x 10^-3 kg m^-1 s^-1 at 28^oC

μ = 1.2 x 10^-3 kg m^-1 s^-1 at 90^oC

k = 2.4 x 10^-4 kW m^-1 K^-1

4. Liquid ammonia is heated as it flows at a mean velocity of 2 m s^-1 through a circular pipe. The pipe, which has an internal diameter of 75 mm, 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 l = 1.2 m. Note, the properties of ammonia liquid have been taken at -23°C, except where 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 = 2.05 x 10^-4 kg m^-1 s^-1
Thermal conductivity = 5.11 x 10^-4 kW m^-1 s^-1

Heat transfer correlations:

Nu = 1.86Re^1/3Pr^1/3(d/l)^1/3(μ/μ_w)^0.14 for laminar flow

Nu = 0.023Re^0.8 Pr^0.33  for turbulent flow.

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

(b) Explain what is meant by fouling 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 process liquid within the tubes using saturated steam at 100ºC. The tubes have an inside diameter of 20 mm and outside diameter of 22 mm. It is estimated that the inner surface heat transfer coefficient will be 4.2 kW m^-2 K^-1 and the outer surface heat transfer coefficient will be 15.4 kW m^-2 K^-1 when the exchanger is clean. In order to allow for possible fouling during 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 50ºC and the heat exchanger has 100 tubes each of 5 m in length.