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Topics for the simulation competition
1. Conduction
2. Convection
3. Thermal conductivity
4. Convection Heat transfer Co-efficient
5. The Thermal Resistance Concept
6. Fourier’s Law of Thermal Conduction
7. Heat transfer through composite wall (Steady)
References:
Heat and Mass Transfer. Yunus A. Cengel. McGraw-Hill
Education, 2011. ISBN: 9780071077866. (page 128-137)
Compiled by Abu Raihan Ibna Ali
Fourier’s law of Thermal Conduction
Heat transfer processes can be quantified in terms of appropriate rate equations. The rate equation in
this heat transfer mode is based on Fourier’s law of thermal conduction. This law states that the
time rate of heat transfer through a material is proportional to the negative gradient in the
temperature and to the area, at right angles to that gradient, through which the heat flows. Its differential
form is:
Compiled by Abu Raihan Ibna Ali
Heat Flux
The rate of heat transfer per unit area normal to the direction of heat transfer is called heat flux.
Sometimes it is also referred to as heat flux density. In SI its units are watts per square metre
(W.m−2). It has both a direction and a magnitude, and so it is a vector quantity. The average heat flux is
expressed as:
where A is the heat transfer area. The unit of heat flux in English units is Btu/h·ft2. Note that heat flux
may vary with time as well as position on a surface.
In nuclear reactors, limitations of the local heat flux is of the highest importance for reactor safety.
Since nuclear fuel consist of fuel rods, the heat flux is there defined in units of W/cm (local linear heat
flux) or kW/rod (power per fuel rod).
Compiled by Abu Raihan Ibna Ali
Thermal Conductivity
The heat transfer characteristics of a solid material are measured by a property called the thermal
conductivity, k (or λ), measured in W/m.K. It is a measure of a substance’s ability to transfer heat through a
material by conduction. Note that Fourier’s law applies for all matter, regardless of its state (solid, liquid, or
gas), therefore, it is also defined for liquids and gases.The thermal conductivity of most liquids and solids
varies with temperature. For vapors, it also depends upon pressure. In general:
Most materials are very nearly homogeneous, therefore we can usually write k = k (T). Similar definitions are
associated with thermal conductivities in the y- and z-directions (ky, kz), but for an isotropic material the thermal
conductivity is independent of the direction of transfer, kx = ky = kz = k.
From the foregoing equation, it follows that the conduction heat flux increases with increasing thermal
conductivity and increases with increasing temperature difference. In general, the thermal conductivity of a solid
is larger than that of a liquid, which is larger than that of a gas. This trend is due largely to differences
in intermolecular spacing for the two states of matter. In particular, diamond has the highest hardness and
thermal conductivity of any bulk material.
Compiled by Abu Raihan Ibna Ali
Fourier’s Law and Thermal Resistance
Thermal resistance is the reciprocal of thermal
conductance. Just as an electrical resistance is
associated with the conduction of electricity, a thermal
resistance may be associated with the conduction of heat.
Consider a plane wall of thickness L and average thermal
conductivity k. The two surfaces of the wall are maintained
at constant temperatures of T1 and T2. For one-
dimensional steady heat conduction through the wall, we
have T(x). Then Fourier’s law of heat conduction for the
wall can be expressed as:
Compiled by Abu Raihan Ibna Ali
Thermal resistance is a heat property and a measurement of a temperature difference by which an
object or material resists a heat flow. The thermal resistance for conduction in a plane wall is defined
as:
Compiled by Abu Raihan Ibna Ali
L1 L2 L3
K1 K2 K3h1 h2
T1 T2 T3 T4 T5 T6
𝑄 =
𝑇1 − 𝑇6
1
ℎ1 𝐴
+
𝐿1
𝐾1 𝐴
+
𝐿2
𝐾2 𝐴
+
𝐿3
𝐾3 𝐴
+
1
ℎ2 𝐴
Where,
Q= Heat transfer
A= cross sectional area
K1,K2,K3= Thermal conductivity of material A,B, C
h1, h2 = convection heat transfer coefficient
L1,L2,L3=thickness of material A,B,C
T= Temperature
Heat transfer through composite wall
Compiled by Abu Raihan Ibna Ali
References:
Heat and Mass Transfer. Yunus A. Cengel. McGraw-Hill Education, 2011. ISBN:
9780071077866.
Compiled by Abu Raihan Ibna Ali

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Ansys simulation competition contents- Arranged by CSME CUET Chapter

  • 1.
  • 2. Topics for the simulation competition 1. Conduction 2. Convection 3. Thermal conductivity 4. Convection Heat transfer Co-efficient 5. The Thermal Resistance Concept 6. Fourier’s Law of Thermal Conduction 7. Heat transfer through composite wall (Steady) References: Heat and Mass Transfer. Yunus A. Cengel. McGraw-Hill Education, 2011. ISBN: 9780071077866. (page 128-137) Compiled by Abu Raihan Ibna Ali
  • 3. Fourier’s law of Thermal Conduction Heat transfer processes can be quantified in terms of appropriate rate equations. The rate equation in this heat transfer mode is based on Fourier’s law of thermal conduction. This law states that the time rate of heat transfer through a material is proportional to the negative gradient in the temperature and to the area, at right angles to that gradient, through which the heat flows. Its differential form is: Compiled by Abu Raihan Ibna Ali
  • 4. Heat Flux The rate of heat transfer per unit area normal to the direction of heat transfer is called heat flux. Sometimes it is also referred to as heat flux density. In SI its units are watts per square metre (W.m−2). It has both a direction and a magnitude, and so it is a vector quantity. The average heat flux is expressed as: where A is the heat transfer area. The unit of heat flux in English units is Btu/h·ft2. Note that heat flux may vary with time as well as position on a surface. In nuclear reactors, limitations of the local heat flux is of the highest importance for reactor safety. Since nuclear fuel consist of fuel rods, the heat flux is there defined in units of W/cm (local linear heat flux) or kW/rod (power per fuel rod). Compiled by Abu Raihan Ibna Ali
  • 5. Thermal Conductivity The heat transfer characteristics of a solid material are measured by a property called the thermal conductivity, k (or λ), measured in W/m.K. It is a measure of a substance’s ability to transfer heat through a material by conduction. Note that Fourier’s law applies for all matter, regardless of its state (solid, liquid, or gas), therefore, it is also defined for liquids and gases.The thermal conductivity of most liquids and solids varies with temperature. For vapors, it also depends upon pressure. In general: Most materials are very nearly homogeneous, therefore we can usually write k = k (T). Similar definitions are associated with thermal conductivities in the y- and z-directions (ky, kz), but for an isotropic material the thermal conductivity is independent of the direction of transfer, kx = ky = kz = k. From the foregoing equation, it follows that the conduction heat flux increases with increasing thermal conductivity and increases with increasing temperature difference. In general, the thermal conductivity of a solid is larger than that of a liquid, which is larger than that of a gas. This trend is due largely to differences in intermolecular spacing for the two states of matter. In particular, diamond has the highest hardness and thermal conductivity of any bulk material. Compiled by Abu Raihan Ibna Ali
  • 6. Fourier’s Law and Thermal Resistance Thermal resistance is the reciprocal of thermal conductance. Just as an electrical resistance is associated with the conduction of electricity, a thermal resistance may be associated with the conduction of heat. Consider a plane wall of thickness L and average thermal conductivity k. The two surfaces of the wall are maintained at constant temperatures of T1 and T2. For one- dimensional steady heat conduction through the wall, we have T(x). Then Fourier’s law of heat conduction for the wall can be expressed as: Compiled by Abu Raihan Ibna Ali
  • 7. Thermal resistance is a heat property and a measurement of a temperature difference by which an object or material resists a heat flow. The thermal resistance for conduction in a plane wall is defined as: Compiled by Abu Raihan Ibna Ali
  • 8. L1 L2 L3 K1 K2 K3h1 h2 T1 T2 T3 T4 T5 T6 𝑄 = 𝑇1 − 𝑇6 1 ℎ1 𝐴 + 𝐿1 𝐾1 𝐴 + 𝐿2 𝐾2 𝐴 + 𝐿3 𝐾3 𝐴 + 1 ℎ2 𝐴 Where, Q= Heat transfer A= cross sectional area K1,K2,K3= Thermal conductivity of material A,B, C h1, h2 = convection heat transfer coefficient L1,L2,L3=thickness of material A,B,C T= Temperature Heat transfer through composite wall Compiled by Abu Raihan Ibna Ali
  • 9. References: Heat and Mass Transfer. Yunus A. Cengel. McGraw-Hill Education, 2011. ISBN: 9780071077866. Compiled by Abu Raihan Ibna Ali