Question 1. (a) A small reheating furnace wall consists of 200 mm of firebrick. The inner surface of the wall is at a temperature of 320 °C and the outside temperature is 35 °C. Calculate the rate at which heat is transferred, by conduction, through unit area of the wall. The thermal conductivity of the firebrick used can be taken as 1.8 W m^-1 K^-1.

If the outside surface area of the furnace is 50 m² estimate the heat losses through the furnace wall per hour.

(b) A furnace wall consists of three layers of material as shown below.

The thermal conductivities are:

firebrick = 1.15 W m^-1 K^-1

insulating brick = 0.17 W m^-1 K^-1

ordinary brick = 0.62 W m^-1 K^-1

Calculate:
(i) the thermal resistance of each layer
(ii) the heat loss per unit area
(iii) the temperature at the two interfaces.

Question 2. A surface condenser consists of a bank of horizontal tubes contained within a steel shell. Saturated steam is condensed on the outside of the water-cooled tubes and the condensate drains to the bottom of the shell where it collects and is pumped out. Tubes towards the bottom of the tube bank are drenched by the water draining from above, and the average thickness y (metres) of the laminar water film flowing over a tube is given by the equation

y = 1.39 (μΓ/ρ²g)^1/3

where Γ is the mass flowrate of water falling onto unit length of tube, and the other symbols have their usual meanings. Since the water falling onto the top of the tube divides and flows down both sides, the average Reynolds number is given by

Re = 2Γ/μ

Assuming that local condensation does not significantly increase the film thickness on the drenched tubes, use the following data to find the heat flux and condensation rate per unit area for one particular tube.

Saturation temperature of condensing steam 40 °C
Temperature of outer surface of tube 38.5°C
Dynamic viscosity of water 6.51 x 10^-4 kg m^-1 s^-1
Density of water 992 kg nr^-3
Thermal conductivity of water 6.32 x 1a^-1 kW ni-1 K 1
Latent heat orsteani 2406 kJ kg^-1
Mass flowrate of draining condensate 0.57 kg m^-1 s^-1

Question 3. A pipe of outside diameter 200 mm is lagged with an insulating material of thermal conductivity 0.06 W m^-1 K^-1 and thickness 75 mm. The pipe carries a process fluid at a temperature of 300 °C and the average temperature of the outer surface of the lagging is 45 'C.
(a) Estimate the rate of heat loss per metre length of pipe.
(b) Explain why the thermal resistance of the pipe wall can be ignored.

Question 4. A pipe carrying superheated steam at 300 °C has an outside diameter of 120 mm and is lagged with two layers of insulating material. The first layer (adjacent to the outer pipe wall) is 25 mm thick and has a thermal conductivity of 0.072 W m^-1 K^-1. The second layer (covering the first layer) is 20 mm thick, has a thermal conductivity of 0.051 W m^-1 K^-1 and an outside temperature of 28 °C.
Estimate the rate of heat loss per metre length of pipe (assume the thermal resistance of the pipe wall is negligible).

Question 5 (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
N_u = 0.53Gr^0.25Pr^0.25
where G_r = 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^-2K^-1

when air has the values listed below

a = 3.077 x 10^-3 K^-1, p =1.086 kg m^-3, cp =1.0063 kJ kg^-1K^-1  k = 2.816 x 10^-5 kW m^-1K^-1,  μ = 1.962 x 10^-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 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.

Question 6. (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?

Question 7. Butanol at a temperature of 28°C 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 kg^-1 K^-1
μ = 2.9 x 10^-3 kg m^-1 s^-1 at 28°C p = 1.2 x 10^-3 kg m^-1 s^-1 at 90°C k = 2.4 x 10-4 kW m^-1 K^-1

Question 8. 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 I = 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 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:

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

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

Question 9. (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 100°C. 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 50°C and the heat exchanger has 100 tubes each of 5 m in length.

Question 10 (a) Process water with a specific heat capacity of 4.182 kJ kg^-1 K^-1 flows at a rate of 0.050 kg 5^-1 through a heat exchanger where its temperature is increased from 16°C to 85°C. Heat is supplied by exhaust gases (mean specific heat capacity 1.075 kJ kg^-1 K^-1) which enter the heat exchanger at a temperature of 420°C. If the mass flowrate of the exhaust gases is 0.044 kg s-1, determine their outlet temperature.

(b) The heat exchanger in Question 1 (a) above is of the double-pipe type, and the fluids are in counter flow. If the overall heat transfer coefficient is 35 W m^-2 K^-1, calculate the size of the heat transfer surface.

(c) What would be the new heat transfer area if the fluids were in parallel flow?

(d) Describe what is wrong with the sketch of the temperature profiles for the parallel-flow heat exchanger shown in FIGURE 1 and draw the correct version.

FIG. 1

Question 11. (a) The data in TABLE I below relates to a specific heat exchanger. A reliable colleague has looked up an effectiveness chart and says that the effectiveness in the given operating conditions is 0.82.

TABLE 1

Area of heat transfer surface 14 m².
Overall heat transfer coefficient 360 W m^-2 K^-1. Determine:
(i) the two outlet temperatures
(ii) the heat transfer rate.

(b) Another colleague, who is not altogether reliable, has analysed the heat exchanger, referred to in Question 2 (a), using the correction-factor method and he claims that the correction factor is 0.595. Confirm whether he is correct or not.

Question 12. (a) Dry saturated steam at a temperature of 180°C is to be produced in a fire tube boiler from the cooling of 50 000 kg h^-1 of flue gases from a pressurised combustion process. The gases enter the tubes of the boiler at 1600°C and leave at 200°C. The feed water is externally preheated to 180°C before entering the boiler.

The mean specific heat capacity of the flue gases is 1.15 kJ kg^-1K^-1. The latent heat of vaporisation of the water at 180°C is 2015 kJ kg^-1. Feed water temperature = 180°C.

Determine the amount of steam produced per hour, if the total heat loss is 10% of the heat available for steam raising.

(b) The overall heat transfer coefficient based on the outside area of the tubes is given as 54 W m^-2 K^-1. Determine the area of heat transfer required to perform this duty.

(c) The tubes within the boiler are to be 25 mm inside diameter with a wall thickness of 3 mm. The average flue gas velocity through the tubes to maintain the overall heat transfer coefficient value and to minimise pressure losses is to be more than 22 m s^-1 and less than 28m s^-1.
Assuming that the average density of the flue gases is 1.108 kg m^-3, calculate:
(i) the minimum and maximum number of tubes in each pass
(ii) the overall length of tubes at each of these numbers of tubes
(iii) the minimum number of tube passes in each case, if the length of a boiler tube is to be less than 5 metres.

Question 13. A fuel gas consists of 75% butane (C₄H₁₀), 10% propane (C₃H₈) and 15% butene (C₄H₈) by volume.

It is to be fed to the combustion chamber in 10% excess air at 25°C, where it is completely burnt to carbon dioxide and water. The flue gases produced are to be used to generate 5 bar steam from water at 90°C.

With the aid of the data at the end of the question, steam tables and the enthalpy table given in the Appendix of lesson HTC - 4 - 2:
(a) Write balanced equations for the combustion of each component of the fuel gas.
(b) Explain the need for excess air.
(c) Determine the actual fuel:air ratio
(i) by volume
(ii) by mass.
(d) Calculate:
(i) the net calorific value (CV) per m3 of the fuel/air mix at 25°C
(ii) the net calorific value (CV) per kmol of the fuel/air mix at 25°C.

(e) Determine the composition of the flue gases by volume (assuming the inlet air is dry):
(1) on a wet basis
(ii) on a dry basis.

(f) Determine the maximum flame temperature.

(g) State how varying the amount of excess air may affect the flame temperature.

(h) Determine the 'furnace efficiency' if the flue gases leave the boiler at 300°C.

(i) If 5% of the heat available for steam production is lost to the atmosphere, determine the amount of steam raised per hour when the total flow of flue gases is 1400 kmol h-I.

(j) Determine the dew point temperature assuming that the flue gas pressure is 1.00 bar and the inlet air:
(i) is dry

(ii) contains 0.8 kg water per kmol of air at the temperature of the inlet air.

(k) If the flue gases exiting the boiler are used to preheat the water fed to the boiler from a temperature of 28°C to 90°C and assuming:

• a mean specific heat capacity for water over this temperature range to be 4.2 kJ kg^-1K^-1

• a mean molar heat capacity for the flue gases up to 300°C to be 31 kJ kmol^-1 K^-1

• 10% of the heat required to heat the water is lost in the heat exchanger

• all water entering the system is converted to steam

determine the final outlet temperature of the flue gas and state if the dew point will be reached in both of the cases given in part (j).

(l) Give two advantages of preheating the water in this way and one disadvantage.

(m) Give two reasons why the presence of any sulphur in the fuel mix would be undesirable.

Data:
Net calorific value (MJ m^-3) at 25°C of:
Butane (C₄H₁₀) = 111.7 MJ m^-3 Butene (C₄H₈) = 105.2 MJ m^-3 Propane (C₃H₈) = 85.8 MJ m^-3

Air is 21% oxygen, 79% nitrogen by volume and 23.3% oxygen and 76.7% nitrogen by mass.

Atomic mass of C = 12, 0 = 16, N=14 and H = 1.