Unit 4013 Fundamentals of Thermodynamics and Heat Transfer (D/651/0727) Assignment Brief 2026

Vocational Scenario

You are working as a mechanical engineering consultant. Your task is to analyse various devices that operate based on heat transfer or fuel-based energy conversion, and to evaluate and comment on their performance and efficiency.

Assignment Activity and Guidance

Task 1

An industrial furnace wall is constructed from a 120 mm thick refractory brick and a 130 mm thick insulating firebrick, separated by an air gap. The external surface of the wall is coated with 15 mm of plaster.

The inner surface temperature of the wall is 1080 oc, while the surrounding room air temperature is 30 oc. The convective heat transfer coefficient between the outer wall surface and the ambient air is 20 W/m2•K. The thermal resistance of the air gap is 0.16

The thermal conductivities of the materials are as follows:

• Refractory brick: 1.4 W/m•K
• Insulating firebrick: 0.38 W/m•K
• Plaster: 0.17 W/m•K

Calculate the rate of heat loss per unit area of the furnace wall.

Task 2

A counter-flow double-pipe heat exchanger is used to heat water from 20 oc to 75 oc at a mass flow rate of 1.3 kg/s. The heating process is achieved using hot thermal fluid entering the exchanger at 155 oc with a mass flow rate of 1.7 kg/s.

The inner tube of the heat exchanger is thin-walled and has a diameter of 18 mm. The overall heat transfer coefficient for the heat exchanger is 700 W/m²•⁰C. The specific heat capacity of water is 4.18 kJ/kg•⁰C, while the specific heat capacity of the thermal fluid is 2.30 kJ/kg•⁰C.

1. Determine heat transfer rate of this heat exchanger, using formula:
   Q̇ = m C_p ΔT
2. Find the exit temperature of thermal fluid, using formula:
   T_out = T_in mC_p
3. Calculate mean temperature difference, using formula:
   ΔT mean =     
   
   ΔT1 – LT2
   
   ln(ΔT1 / ΔT2)
   
4. Determine the heat transfer area required using the formulae for area of exchanger:  A = UTmean
5. Calculate the tube length for counter-flow using:
   L =
6. Repeat the length calculation for a parallel-flow heat exchanger.
7. Using the above results and supporting literature, compare parallel-flow and counter-flow heat exchangers in terms of:
   • Temperature profiles
   • Typical industrial applications
   • Thermal efficiency
      

     Include clearly labelled diagrams and appropriate references.

Steam at Tool — 330 ^oc flows through a steel pipe with a thermal conductivity of k = 65 W/m•0C. The pipe has an inner diameter (DI) of 55 mm and an outer diameter (D2) of 65 mm. The pipe is insulated with 180 mm thick mineral wool insulation having a thermal conductivity of k = 0.045 W/m•0C. Heat is lost from the outer surface of the insulation to the surroundings at an ambient temperature of Tc02 = 18 ^oc by natural convection and radiation, with a combined heat transfer coefficient of m = 22 W/m2•0C. The convective heat transfer coefficient between the steam and the inner pipe wall is hl = 45 Wim².^OC.

Determine the rate of heat loss from the steam per unit length of the pipe.

Task 4

A 12 m long, 250 mm diameter hot-water pipe forming part of a district heating network is buried 0.6 m below the ground surface. The outer surface temperature of the pipe is 65 ^oc. The temperature at the ground surface is 8 ^oc, and the thermal conductivity of the surrounding soil is 0.9 W/m•⁰C.

The shape factor for heat transfer from the buried pipe is given by:

2TtL   S = ————In(%

where:

• L is the pipe length,
• z is the distance from the pipe centre to the ground surface,
• D is the pipe diameter.

Determine the rate of heat loss from the buried pipe.

Task 5

Describe the four thermodynamic processes that constitute the ideal Diesel cycle, based on the air-standard assumptions. Your answer should include the following:

1. Clearly labelled pressure-volume (P-V) and temperature-entropy (T-S) diagrams, showing all four processes of the cycle.
2. Identification and explanation of the maximum temperature reached during the cycle, including the process at which it occurs.
3. Description of the heat addition and heat rejection processes, stating:

During which processes heat is added to the working fluid

During which processes heat is rejected

The thermodynamic nature of each process (constant pressure, constant volume, isentropic)

Your explanation should demonstrate a clear understanding of the Diesel cycle operation under ideal conditions.

Task 6

Describe the operating principle of a heat pump system used for space heating or industrial applications.

Your answer should include the following:

1. Identification of the thermodynamic cycle on which the heat pump is based, with a brief explanation of its relationship to a heat engine or refrigeration cycle.
2. Clearly labelled pressure-volume (P-V) and temperature-entropy (T-S) diagrams, illustrating the main processes of the heat pump cycle.
3. Explanation of the maximum theoretical efficiency of a heat pump, including reference to the ideal (Carnot) heat pump and the factors that influence its coefficient of performance (COP).
4. Description of the heat transfer processes, clearly indicating:

• Where heat is absorbed from the low-temperature reservoir

Where heat is rejected to the high-temperature reservoir

Your answer should demonstrate an understanding of both the thermodynamic principles and the practical operation of heat pumps.

Task 7

A heat engine operates between a high-temperature reservoir at 950 oc and a lowtemperature reservoir at 180 oc. It is claimed that this engine achieves a thermal efficiency of 72%.

1. Determine the maximum theoretical efficiency of a heat engine operating between these two temperatures using the Carnot efficiency formula:
Tcold
nmax (Temperature in K)
Thot

2. Compare the claimed efficiency with the maximum possible efficiency to assess whether the claim is physically possible.

3. Provide a brief analysis of the operating conditions, including:

• • Whether the claimed efficiency is realistic
  • Possible reasons why real engines always operate below the Carnot limit
  • Practical considerations affecting efficiency (e.g., friction, heat losses)

Task 8

An Otto cycle operates as follows: Air at 120 kPa and 25 oc is compressed reversibly and adiabatically. The air is then heated at constant volume to 1400 oc. Subsequently, the air expands reversibly and adiabatically back to the original volume and is cooled at constant volume to the initial pressure and temperature.

The volume compression ratio is 9. Calculate:

1. The thermal efficiency
2. The heat input per kg of air
3. The net work output per kg of air
4. The maximum cycle pressure

Take the properties of air as:

% = 720 ² K; y = 1.4 and R = 287 ² K

kg                                                      kg

Relevant equations: n= 1 -1/ r(y-l)

Thermal efficiency (n):

• Heat input (Qin): Qin = mcv (T3 -TD
• Net work output (Wnet):        ^wnet = Qin – Qout

Learning Outcomes and Assessment Criteria