UNIVERSITY OF SOUTH AFRICA
College of Science, Engineering and Technology
⋄ ⋄ ⋄ ⋄ ⋄ ⋄ ⋄ ⋄ ⋄⋄
HMT4801: Heat and Mass Transfer
Assignment 01 — Semester 1, 2026
⋄ ⋄ ⋄ ⋄ ⋄ ⋄ ⋄ ⋄ ⋄⋄
HMT4801
Module Code:
Heat and Mass Transfer
Module Name:
Assignment 01
Assignment:
[Student Full Name]
Student Name:
[Student Number]
Student Number:
[Unique Number]
Unique Number:
2026
Due Date:
Semester 1, 2026
Semester:
Submitted in partial fulfilment of the requirements for HMT4801 — UNISA 2026
,UNISA | HMT4801 Assignment 01 – 2026
Question 1: Analytical vs Experimental Approach to Heat Transfer
Heat transfer is the study of how thermal energy moves between systems. Two distinct
methodologies guide how engineers investigate it: the analytical approach and the experi-
mental approach. Each has a different starting point, a different relationship with reality, and
its own trade-offs (Cengel, Ghajar and Cimbala, 2020).
1.1 The Analytical Approach
The analytical approach uses mathematics as its primary language. Governing equations,
derived from the laws of thermodynamics and the fundamental mechanisms of heat transfer
(conduction via Fourier’s law, convection via Newton’s law of cooling, and radiation via the
Stefan-Boltzmann law), are set up and solved either exactly or through numerical approxima-
tion. The engineer builds a mathematical model of the physical world, then asks the model to
predict behaviour under defined conditions.
The real strength of this approach is flexibility. Once a governing equation is in place, an
engineer can rapidly test the effect of changing a parameter such as wall thickness or fluid
velocity without running a single physical test. Simple geometries yield clean closed-form
solutions. For more complex systems, numerical methods such as Finite Element Analysis
and Computational Fluid Dynamics extend the reach of analytical work considerably (Kreith
and Manglik, 2017).
However, every analytical model rests on assumptions. Real materials are rarely perfectly
homogeneous; boundary conditions in practice are messier than on paper; and phenomena
such as turbulent convection and phase-change heat transfer resist neat mathematical de-
scription.
1.2 The Experimental Approach
Experimental heat transfer places physical hardware at the centre. Thermocouples, infrared
cameras, heat flux sensors, and calorimeters measure real temperatures and heat flows in
laboratory or field settings. The data collected is actual rather than predicted, capturing all the
complexity of the real system including effects that an analytical model might have idealised
away.
Experimental work is especially valuable for validating analytical predictions. Before a new
Page 2 of 18
,UNISA | HMT4801 Assignment 01 – 2026
heat exchanger design goes into production, engineers will often build a prototype and com-
pare measured performance against what the model forecast. Where the two diverge, the
model is refined. The practical limitations are time and cost: specialised equipment must be
procured and calibrated, tests must be repeated for statistical confidence, and isolating a
single variable while holding everything else constant is rarely straightforward in a physical
system (Cengel et al., 2020).
1.3 Comparison
Table 1: Analytical vs Experimental Approaches to Heat Transfer
Aspect Analytical Approach Experimental Approach
Basis Mathematical models and gov- Physical measurements using
erning equations instruments
Cost Generally lower; no hardware Higher; equipment and setup
needed required
Speed Fast once model is built Slower; testing takes time
Accuracy Limited by model assumptions Limited by measurement uncer-
tainty
Applicability Best for simple to moderate Best for complex, real-world
geometries systems
Primary use Design prediction and optimisa- Validation and empirical correla-
tion tion
Key Distinction
The analytical approach predicts behaviour through mathematics; the experimental
approach observes it through physical testing. In engineering practice neither method
is complete on its own. Analytical models direct experimental design, and experimental
data calibrates and validates analytical models (Cengel et al., 2020).
Page 3 of 18
,UNISA | HMT4801 Assignment 01 – 2026
Question 2: Heat Absorbed by Air in a House and Cost of Electricity
2.1 Given Information
• Floor area: Af loor = 200 m2 ; ceiling height: h = 3 m
• Atmospheric pressure: P = 101.3 kPa (sea level)
• Initial temperature: T1 = 10◦ C = 283 K
• Final temperature: T2 = 22◦ C = 295 K
• Process: constant pressure (air escapes through cracks as it expands)
• Air constants: Rair = 0.287 kJ/(kg · K); cp = 1.005 kJ/(kg · K)
• Electricity cost: Ce = R0.075 per kWh
2.2 Volume of House
V = Af loor × h = 200 × 3 = 600 m3
2.3 Initial and Final Mass of Air
Using the ideal gas relation m = P V /Rair T :
101.3 × 600 60 780
m1 = = = 748.3 kg
0.287 × 283 81.221
101.3 × 600 60 780
m2 = = = 718.0 kg
0.287 × 295 84.665
Mass that escaped through cracks:
mout = m1 − m2 = 748.3 − 718.0 = 30.3 kg
2.4 Heat Absorbed at Constant Pressure
Because the house is not perfectly sealed, pressure remains atmospheric throughout the
heating process. This is an isobaric open system. Applying the first law energy balance to the
house as a control volume, the net heat input reduces to:
Page 4 of 18
, UNISA | HMT4801 Assignment 01 – 2026
Q = m1 · cp · (T2 − T1 )
Q = 748.3 × 1.005 × (295 − 283) = 748.3 × 1.005 × 12
Q ≈ 9 025 kJ ≈ 9.0 MJ
2.5 Cost of Electricity
Converting to kilowatt-hours:
9 025
Q= = 2.507 kWh
3 600
Cost = 2.507 × R0.075 = R0.19
Implementation Insight
The R0.19 figure represents only the energy absorbed by the air volume inside the
house. In practice the actual electricity consumed would be considerably higher be-
cause the heater must also compensate for continuous heat loss through the building
envelope. This distinction is central to energy efficiency assessments under SANS
10400-XA.
Page 5 of 18
College of Science, Engineering and Technology
⋄ ⋄ ⋄ ⋄ ⋄ ⋄ ⋄ ⋄ ⋄⋄
HMT4801: Heat and Mass Transfer
Assignment 01 — Semester 1, 2026
⋄ ⋄ ⋄ ⋄ ⋄ ⋄ ⋄ ⋄ ⋄⋄
HMT4801
Module Code:
Heat and Mass Transfer
Module Name:
Assignment 01
Assignment:
[Student Full Name]
Student Name:
[Student Number]
Student Number:
[Unique Number]
Unique Number:
2026
Due Date:
Semester 1, 2026
Semester:
Submitted in partial fulfilment of the requirements for HMT4801 — UNISA 2026
,UNISA | HMT4801 Assignment 01 – 2026
Question 1: Analytical vs Experimental Approach to Heat Transfer
Heat transfer is the study of how thermal energy moves between systems. Two distinct
methodologies guide how engineers investigate it: the analytical approach and the experi-
mental approach. Each has a different starting point, a different relationship with reality, and
its own trade-offs (Cengel, Ghajar and Cimbala, 2020).
1.1 The Analytical Approach
The analytical approach uses mathematics as its primary language. Governing equations,
derived from the laws of thermodynamics and the fundamental mechanisms of heat transfer
(conduction via Fourier’s law, convection via Newton’s law of cooling, and radiation via the
Stefan-Boltzmann law), are set up and solved either exactly or through numerical approxima-
tion. The engineer builds a mathematical model of the physical world, then asks the model to
predict behaviour under defined conditions.
The real strength of this approach is flexibility. Once a governing equation is in place, an
engineer can rapidly test the effect of changing a parameter such as wall thickness or fluid
velocity without running a single physical test. Simple geometries yield clean closed-form
solutions. For more complex systems, numerical methods such as Finite Element Analysis
and Computational Fluid Dynamics extend the reach of analytical work considerably (Kreith
and Manglik, 2017).
However, every analytical model rests on assumptions. Real materials are rarely perfectly
homogeneous; boundary conditions in practice are messier than on paper; and phenomena
such as turbulent convection and phase-change heat transfer resist neat mathematical de-
scription.
1.2 The Experimental Approach
Experimental heat transfer places physical hardware at the centre. Thermocouples, infrared
cameras, heat flux sensors, and calorimeters measure real temperatures and heat flows in
laboratory or field settings. The data collected is actual rather than predicted, capturing all the
complexity of the real system including effects that an analytical model might have idealised
away.
Experimental work is especially valuable for validating analytical predictions. Before a new
Page 2 of 18
,UNISA | HMT4801 Assignment 01 – 2026
heat exchanger design goes into production, engineers will often build a prototype and com-
pare measured performance against what the model forecast. Where the two diverge, the
model is refined. The practical limitations are time and cost: specialised equipment must be
procured and calibrated, tests must be repeated for statistical confidence, and isolating a
single variable while holding everything else constant is rarely straightforward in a physical
system (Cengel et al., 2020).
1.3 Comparison
Table 1: Analytical vs Experimental Approaches to Heat Transfer
Aspect Analytical Approach Experimental Approach
Basis Mathematical models and gov- Physical measurements using
erning equations instruments
Cost Generally lower; no hardware Higher; equipment and setup
needed required
Speed Fast once model is built Slower; testing takes time
Accuracy Limited by model assumptions Limited by measurement uncer-
tainty
Applicability Best for simple to moderate Best for complex, real-world
geometries systems
Primary use Design prediction and optimisa- Validation and empirical correla-
tion tion
Key Distinction
The analytical approach predicts behaviour through mathematics; the experimental
approach observes it through physical testing. In engineering practice neither method
is complete on its own. Analytical models direct experimental design, and experimental
data calibrates and validates analytical models (Cengel et al., 2020).
Page 3 of 18
,UNISA | HMT4801 Assignment 01 – 2026
Question 2: Heat Absorbed by Air in a House and Cost of Electricity
2.1 Given Information
• Floor area: Af loor = 200 m2 ; ceiling height: h = 3 m
• Atmospheric pressure: P = 101.3 kPa (sea level)
• Initial temperature: T1 = 10◦ C = 283 K
• Final temperature: T2 = 22◦ C = 295 K
• Process: constant pressure (air escapes through cracks as it expands)
• Air constants: Rair = 0.287 kJ/(kg · K); cp = 1.005 kJ/(kg · K)
• Electricity cost: Ce = R0.075 per kWh
2.2 Volume of House
V = Af loor × h = 200 × 3 = 600 m3
2.3 Initial and Final Mass of Air
Using the ideal gas relation m = P V /Rair T :
101.3 × 600 60 780
m1 = = = 748.3 kg
0.287 × 283 81.221
101.3 × 600 60 780
m2 = = = 718.0 kg
0.287 × 295 84.665
Mass that escaped through cracks:
mout = m1 − m2 = 748.3 − 718.0 = 30.3 kg
2.4 Heat Absorbed at Constant Pressure
Because the house is not perfectly sealed, pressure remains atmospheric throughout the
heating process. This is an isobaric open system. Applying the first law energy balance to the
house as a control volume, the net heat input reduces to:
Page 4 of 18
, UNISA | HMT4801 Assignment 01 – 2026
Q = m1 · cp · (T2 − T1 )
Q = 748.3 × 1.005 × (295 − 283) = 748.3 × 1.005 × 12
Q ≈ 9 025 kJ ≈ 9.0 MJ
2.5 Cost of Electricity
Converting to kilowatt-hours:
9 025
Q= = 2.507 kWh
3 600
Cost = 2.507 × R0.075 = R0.19
Implementation Insight
The R0.19 figure represents only the energy absorbed by the air volume inside the
house. In practice the actual electricity consumed would be considerably higher be-
cause the heater must also compensate for continuous heat loss through the building
envelope. This distinction is central to energy efficiency assessments under SANS
10400-XA.
Page 5 of 18
