UNIVERSITY OF SOUTH AFRICA (UNISA)
College of Science, Engineering and Technology
⋄
HMT4801 — ASSIGNMENT 01
Semester 1, 2026
⋄
Module Code: HMT4801
Module Name: Heat and Mass Transfer
Student Name: [Student Name]
Student Number: [Student Number]
Assignment No.: 01
Due Date: [Due Date]
Semester: Semester 1, 2026
Unique Number: [Unique Number]
,UNISA | HMT4801 Heat and Mass Transfer
Question 1: Analytical vs Experimental Approach to Heat Transfer
Heat transfer as a discipline can be studied through two fundamentally different lenses: one
grounded in mathematical theory and the other anchored in physical observation (Cengel and
Ghajar, 2020). Each approach has its place, and in professional engineering practice, they
tend to complement rather than replace each other.
1.1 The Analytical Approach
The analytical approach relies on applying governing mathematical equations to model the
thermal behaviour of a system without physically building or testing it. It draws on the princi-
ples of thermodynamics and the three heat transfer mechanisms — conduction, convection,
and radiation — to derive mathematical expressions that describe how energy moves through
a system (Cengel and Ghajar, 2020).
Common tools in this approach include differential equations, integral energy balance meth-
ods, and numerical techniques such as finite element analysis (FEA) or finite difference meth-
ods. A simple example is Fourier’s law of heat conduction:
dT
Q̇ = −kA (1)
dx
where k is the thermal conductivity (W/m·K), A is the cross-sectional area (m2 ), and dT /dx is
the temperature gradient along the direction of heat flow.
The advantages of the analytical approach include:
• It is generally less expensive than physical testing since no equipment needs to be built.
• It allows engineers to evaluate many design configurations quickly by changing parame-
ters in equations.
• It provides a clear theoretical framework for understanding the underlying physics.
Its limitations are that it can become mathematically intractable for complex geometries
or boundary conditions, and results depend heavily on the accuracy of assumed material
properties (Incropera et al., 2011).
Page 1 of 18
,UNISA | HMT4801 Heat and Mass Transfer
1.2 The Experimental Approach
The experimental approach involves building physical setups and using instruments to mea-
sure heat transfer behaviour in real or controlled conditions. Temperature sensors, heat flux
meters, calorimeters, and flow meters are examples of the tools used to gather empirical
data (Holman, 2012).
This method is particularly valuable when:
• The geometry or boundary conditions are too complex to model analytically.
• Phase change, radiation, or combined-mode heat transfer introduces nonlinear behaviour.
• Verification of analytical or numerical models is needed before deploying a design.
The downside of this approach is that physical experiments can be expensive, time-consuming,
and prone to measurement uncertainties. Environmental variables such as ambient tempera-
ture changes or vibrations can influence results (Holman, 2012).
1.3 Comparison Summary
Table 1: Analytical vs Experimental Approach to Heat Transfer
Aspect Analytical Approach Experimental Approach
Basis Mathematical models and equa- Physical measurements and
tions observation
Method Differential equations, numerical Lab instruments, prototypes
methods
Cost Lower (no hardware required) Higher (equipment, setup, time)
Complexity limit Restricted by mathematical Can handle complex phenom-
tractability ena
Accuracy Depends on model assumptions Reflects real-world behaviour
Best use Design exploration, parametric Validation, complex systems
studies
Key Distinction
The analytical approach predicts thermal behaviour through mathematical models,
while the experimental approach measures it in practice. In modern engineering,
the two are used together: analytical models generate predictions, and experiments
validate or refine them (Incropera et al., 2011).
Page 2 of 18
,UNISA | HMT4801 Heat and Mass Transfer
Question 2: Heat Absorbed by Air in a House After Heating
This question applies the first law of thermodynamics and the ideal gas model to determine
how much energy the air in the house absorbs when heated from 10◦ C to 22◦ C at constant
pressure. Since some air escapes through cracks as the heated air expands, this is treated as
a constant-pressure open system.
2.1 Given Information
• Floor area: A = 200 m2
• Average height: h = 3 m
• Atmospheric pressure: P = 101.3 kPa
• Initial temperature: T1 = 10◦ C = 283 K
• Final temperature: T2 = 22◦ C = 295 K
• Cost of electricity: R0.075/kWh
2.2 Volume of the House
V = A × h = 200 × 3 = 600 m3 (2)
2.3 Mass of Air Initially in the House
Using the ideal gas law, P V = mRT :
PV
m= (3)
RT1
For air, the specific gas constant R = 0.287 kJ/kg · K.
101.3 × 600 60780
m= = ≈ 748.3 kg (4)
0.287 × 283 81.221
2.4 Heat Absorbed by Air at Constant Pressure
Since the process occurs at constant atmospheric pressure with some air escaping, the
enthalpy relation applies:
Page 3 of 18
, UNISA | HMT4801 Heat and Mass Transfer
Q = mcp (T2 − T1 ) (5)
For air at constant pressure: cp = 1.005 kJ/kg · K.
Q = 748.3 × 1.005 × (295 − 283) (6)
Q = 748.3 × 1.005 × 12 (7)
Q ≈ 9022 kJ (8)
2.5 Cost of Electricity
Converting to kWh:
9022
Q= ≈ 2.506 kWh (9)
3600
Cost = 2.506 × R0.075 = R0.19 (10)
Implementation Insight
In practice, South African residential buildings lose significant heat through poorly insu-
lated ceilings and walls. The SANS 10400-XA energy efficiency standard for buildings
recommends ceiling insulation with a minimum R-value to reduce this kind of heating
energy consumption. The actual electricity cost would be higher than R0.19 because
the heater must also compensate for heat losses through the building envelope (SABS,
2011).
Page 4 of 18
College of Science, Engineering and Technology
⋄
HMT4801 — ASSIGNMENT 01
Semester 1, 2026
⋄
Module Code: HMT4801
Module Name: Heat and Mass Transfer
Student Name: [Student Name]
Student Number: [Student Number]
Assignment No.: 01
Due Date: [Due Date]
Semester: Semester 1, 2026
Unique Number: [Unique Number]
,UNISA | HMT4801 Heat and Mass Transfer
Question 1: Analytical vs Experimental Approach to Heat Transfer
Heat transfer as a discipline can be studied through two fundamentally different lenses: one
grounded in mathematical theory and the other anchored in physical observation (Cengel and
Ghajar, 2020). Each approach has its place, and in professional engineering practice, they
tend to complement rather than replace each other.
1.1 The Analytical Approach
The analytical approach relies on applying governing mathematical equations to model the
thermal behaviour of a system without physically building or testing it. It draws on the princi-
ples of thermodynamics and the three heat transfer mechanisms — conduction, convection,
and radiation — to derive mathematical expressions that describe how energy moves through
a system (Cengel and Ghajar, 2020).
Common tools in this approach include differential equations, integral energy balance meth-
ods, and numerical techniques such as finite element analysis (FEA) or finite difference meth-
ods. A simple example is Fourier’s law of heat conduction:
dT
Q̇ = −kA (1)
dx
where k is the thermal conductivity (W/m·K), A is the cross-sectional area (m2 ), and dT /dx is
the temperature gradient along the direction of heat flow.
The advantages of the analytical approach include:
• It is generally less expensive than physical testing since no equipment needs to be built.
• It allows engineers to evaluate many design configurations quickly by changing parame-
ters in equations.
• It provides a clear theoretical framework for understanding the underlying physics.
Its limitations are that it can become mathematically intractable for complex geometries
or boundary conditions, and results depend heavily on the accuracy of assumed material
properties (Incropera et al., 2011).
Page 1 of 18
,UNISA | HMT4801 Heat and Mass Transfer
1.2 The Experimental Approach
The experimental approach involves building physical setups and using instruments to mea-
sure heat transfer behaviour in real or controlled conditions. Temperature sensors, heat flux
meters, calorimeters, and flow meters are examples of the tools used to gather empirical
data (Holman, 2012).
This method is particularly valuable when:
• The geometry or boundary conditions are too complex to model analytically.
• Phase change, radiation, or combined-mode heat transfer introduces nonlinear behaviour.
• Verification of analytical or numerical models is needed before deploying a design.
The downside of this approach is that physical experiments can be expensive, time-consuming,
and prone to measurement uncertainties. Environmental variables such as ambient tempera-
ture changes or vibrations can influence results (Holman, 2012).
1.3 Comparison Summary
Table 1: Analytical vs Experimental Approach to Heat Transfer
Aspect Analytical Approach Experimental Approach
Basis Mathematical models and equa- Physical measurements and
tions observation
Method Differential equations, numerical Lab instruments, prototypes
methods
Cost Lower (no hardware required) Higher (equipment, setup, time)
Complexity limit Restricted by mathematical Can handle complex phenom-
tractability ena
Accuracy Depends on model assumptions Reflects real-world behaviour
Best use Design exploration, parametric Validation, complex systems
studies
Key Distinction
The analytical approach predicts thermal behaviour through mathematical models,
while the experimental approach measures it in practice. In modern engineering,
the two are used together: analytical models generate predictions, and experiments
validate or refine them (Incropera et al., 2011).
Page 2 of 18
,UNISA | HMT4801 Heat and Mass Transfer
Question 2: Heat Absorbed by Air in a House After Heating
This question applies the first law of thermodynamics and the ideal gas model to determine
how much energy the air in the house absorbs when heated from 10◦ C to 22◦ C at constant
pressure. Since some air escapes through cracks as the heated air expands, this is treated as
a constant-pressure open system.
2.1 Given Information
• Floor area: A = 200 m2
• Average height: h = 3 m
• Atmospheric pressure: P = 101.3 kPa
• Initial temperature: T1 = 10◦ C = 283 K
• Final temperature: T2 = 22◦ C = 295 K
• Cost of electricity: R0.075/kWh
2.2 Volume of the House
V = A × h = 200 × 3 = 600 m3 (2)
2.3 Mass of Air Initially in the House
Using the ideal gas law, P V = mRT :
PV
m= (3)
RT1
For air, the specific gas constant R = 0.287 kJ/kg · K.
101.3 × 600 60780
m= = ≈ 748.3 kg (4)
0.287 × 283 81.221
2.4 Heat Absorbed by Air at Constant Pressure
Since the process occurs at constant atmospheric pressure with some air escaping, the
enthalpy relation applies:
Page 3 of 18
, UNISA | HMT4801 Heat and Mass Transfer
Q = mcp (T2 − T1 ) (5)
For air at constant pressure: cp = 1.005 kJ/kg · K.
Q = 748.3 × 1.005 × (295 − 283) (6)
Q = 748.3 × 1.005 × 12 (7)
Q ≈ 9022 kJ (8)
2.5 Cost of Electricity
Converting to kWh:
9022
Q= ≈ 2.506 kWh (9)
3600
Cost = 2.506 × R0.075 = R0.19 (10)
Implementation Insight
In practice, South African residential buildings lose significant heat through poorly insu-
lated ceilings and walls. The SANS 10400-XA energy efficiency standard for buildings
recommends ceiling insulation with a minimum R-value to reduce this kind of heating
energy consumption. The actual electricity cost would be higher than R0.19 because
the heater must also compensate for heat losses through the building envelope (SABS,
2011).
Page 4 of 18
