Thermal Transmission through Buildings
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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)

 

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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.

 

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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

 

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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.