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2 Thermal Transmission through Buildings
2.1 Combined Modes of Heat Transfer
(a) heat transfer by convection Qch and
radiation Qrh from the hot air and surrounding surfaces to the wall surface,
(b) heat transfer by conduction through the
wall Qk,
(c) heat transfer by convection Qcc and radiation Qrc from
the wall surface to the cold air and surrounding surfaces.
 
Figure 3 Heat Exchange Configuration Figure 4 Thermal
Resistance Network
Under steady state conditions, the total rate of heat
transfer (Q) between the two fluids is:
 (7)
Combining Eqns. (5), (6) and (10), Eqn. (11) becomes:
 (8)
2.2 Analogy between Electrical and Thermal systems
Owing to the similarity in the mechanism of
electrical conductivity and thermal conductivity, an analogy (as shown in Figure 4) is
made between electric current transfer and heat transfer as follows:
For electric system,
 (9)
For thermal system,
 (10)
2.3 Thermal Transmission Terms
The following are some terms commonly used in describing
heat transmission through buildings:
2.3.1 Thermal Conductance
Thermal conductance (C) is the
thermal transmission through unit area of a slab of material, or of a structure, divided
by the temperature difference between the hot and cold faces in steady state conditions.
The unit is W/(m2 K).
2.3.2 Thermal Resistivity
Thermal resistivity is the reciprocal of thermal
conductivity. The unit is Km/W.
2.3.3 Thermal Resistance
Thermal resistance (R) is the reciprocal of
thermal conductance. It is a measure of the resistance to heat transmission across a
material, or a structure. The unit Km2/W.
Comparing Eqns (1) and (10), the conduction
thermal resistance is:
 (11)
Comparing Eqns (2) and (10), the convection thermal
resistance is:
 (12)
Comparing Eqns (6) and (10), the radiation thermal
resistance is:
 (13)
Figure 5 Conduction Thermal Resistance of a
Composite Plane Wall
 (14)
2.3.4 Surface Conductance
Surface conductance is the rate of transfer
of heat to or from unit area of a surface in contact with a fluid due to convection and
radiation per unit difference in temperature between the surface and the neighbouring
fluid.
2.3.5 Surface Resistance
 (15)
From Eqns (1) and (6)
 (16)
2.3.6 Resistance of Airspaces
The thermal resistance of airspaces depends mainly on the
following factors:
(a) Thickness of the airspace
Resistance of airspace increases with the thickness up to a
maximum at about 20 mm.
(b) Surface emissivity
Commonly used building materials have a
high emissivity and radiation accounts for two-thirds of the heat transfer through an
airspace with high emissivity surfaces. Lining the airspace with low emissivity material
such as aluminum foil increases the thermal resistance by reducing radiation.
(c) Direction of heat flow
A horizontal airspace offers higher
resistance to downward than to upward heat flow, because downward convection is small.
(d) Ventilation
Airspace ventilation provides an additional
heat flow path which decreases the effective airspace resistance.
2.3.7 Thermal Transmittance (U-value)
For a simple structure
without heat bridging, the thermal transmittance coefficient U is expressed as:
 (17)
The thermal transmission through a wall or
other building element is given by:
 (18)
2.4 Thermal Bridging
A metal or other high conductivity member
bridging a structure increases the heat loss. A thermal bridge, as
shown in Figure 6, is a portion of a structure at which the high thermal conductivity
lowers the overall thermal insulation of the structure and hence the effective U-value of
the structure.
Figure 6 Temperature Profile at Thermal
Bridge
Figure 7 Construction of Temperature
Gradient a Multi-layer Wall
2.5 Temperature Gradient
If two faces of a wall are exposed to
different but steady temperature conditions, a temperature gradient is established across
the thickness of the wall:
(a) The temperature gradient is linear
between the two surfaces for a homogenous wall.
(b) The slope of temperature gradient is
proportional to the resistances of individual layers for a composite structure.
The temperature gradient is either
constructed graphically or calculated.
2.5.1 Graphical Method (See Figure 7)
(a) Represent the overall resistance Rt by
a linear dimension (e.g. wall thickness) in a scale.
(b) Show all the component resistances to
the above scale.
(c) Establish an arbitrarily vertical
temperature scale where Ti and To are internal and external environmental temperatures
respectively.
(d) Mark points A and B corresponding to Ti
and To respectively.
(e) Connect A and B by a straight diagonal.
The intersection of this line with the boundary lines of each layer will indicate the
temperature at that point, according to the vertical scale.
(f) Project the intersection points across
to a cross-section of the wall drawn alongside to a physical scale to obtain the actual
temperature gradient.
2.5.2 Calculation
The gradient is determined by
(a) calculating the ratio (To - Ti)/Rt, and
(b) starting from the outside air,
calculating the temperature increment (D T) across each wall component by multiplying the
ratio calculated in (a) and the thermal resistance of that wall component., e.g. 
(c) calculating the temperature of each
layer of component, e.g. T = To - D Tso.
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