TCVN 9313:2012 ISO 7345:1987 Thermal insulation – Physical quantities and definitions

Foreword

TCVN 9313:2012 is fully equivalent to ISO 7345:1987

TCVN 9313:2012 is converted from TCXDVN 299:2003 (ISO 7345:1987) in accordance with clause 1, Article 69 of the Law on Standards and Technical Regulations and point a), clause 1, Article 7 of Decree 127/2007/ND-CP detailing the implementation of some articles of the Law on Standards and Technical Regulations.

TCVN 9313:2012 is compiled by the Institute of Architecture, Urban and Rural Planning, proposed by the Ministry of Construction, appraised by the Directorate for Standards, Metrology and Quality, and promulgated by the Ministry of Science and Technology.

1. Scope

This standard defines physical quantities used in the field of thermal insulation and provides the corresponding symbols and units.

NOTE: As the scope of this standard is limited to the field of thermal insulation, some definitions given in Clause 2 differ from those given in TCVN 7870-5:2007. To distinguish this difference, an asterisk (*) is placed before the terms.

2. Physical quantities and definitions

Table 1 – Physical quantities

Name	Quantity	Unit
2.1. Heat, quantity of heat	Q	J
2.2. Heat flow rate: The quantity of heat transferred to or from a system divided by time:	Φ	W
2.3. Heat flux density: The heat flow rate divided by area: NOTE: The term “density” may be replaced by “surface density” when confusion with “linear density” (see 2.4) is possible.	q	W/m²
2.4. Linear heat flux density: The heat flow rate divided by length:	q_l	W/m
2.5. Thermal conductivity: The quantity defined by the equation: NOTE: For a precise concept of thermal conductivity, see Annex A. This concept also relates to the use of the thermal conductivity concept for isotropic or anisotropic porous materials, the effect of temperature and test conditions.	λ	W/(m.K)
2.6. Thermal resistivity: The quantity defined by the equation: NOTE: For a precise concept of thermal resistivity, see Annex A.	r	(m.K)/W
2.7. Thermal resistance ¹⁾: The temperature difference divided by the heat flux density under steady state conditions. NOTE: 1) For a planar layer when using the thermal conductivity concept and when the properties are constant or linear with temperature (see Annex A), then: Where: d is the thickness of the planar layer. These definitions assume the definition of two reference temperatures T₁, T₂ and an area through which the heat flux density is uniform. The thermal resistance may relate to a material, a structure or a surface. If T₁ or T₂ is not the temperature of a solid surface but that of a fluid, the reference temperature shall be specified in each particular case (with reference to free or forced convection and thermal radiation from surrounding objects, etc.). When specifying a thermal resistance value, T₁ and T₂ shall be known. 2) “Thermal resistance” may be replaced by “surface thermal resistance” when confusion with “linear thermal resistance” (see 2.8) is possible.	R	(m².K)/W
2.8. Linear thermal resistance: The temperature difference divided by the linear heat flux density under steady state conditions: NOTE: The definition assumes two reference temperatures T₁, T₂ and a length along which the linear heat flux density is uniform. If within the system T₁ or T₂ is not the temperature of a solid surface but that of a fluid, the reference temperature shall be specified in each particular case (with attention to free or forced convection and thermal radiation from surrounding surfaces, etc.). When specifying a linear thermal resistance value, T₁ and T₂ shall be known.	R_l	(m.K)/W
2.9. Surface heat transfer coefficient: The heat flux density at the surface under steady state conditions divided by the temperature difference between that surface and the surrounding environment. NOTE: The definition assumes a heat transfer surface, a surface temperature T_s, and a defined air temperature T_a (with reference to free or forced convection and radiation from surrounding surfaces, etc.).	h	W/(m².K)
2.10. Thermal conductance: The reciprocal of the thermal resistance from one surface to another under conditions of uniform heat flux density. NOTE: “Thermal conductance” is replaced by “surface thermal conductance” when confusion with “linear thermal conductance” is possible.	A	W/(m².K)
2.11. Linear thermal conductance: The reciprocal of the linear thermal resistance from one surface to another under conditions of uniform linear heat flux density.	Λ₁	W/(m.K)
2.12. Thermal transmittance: The heat flow rate under steady state conditions divided by the product of the area and the temperature difference of the environments on either side of the system: NOTE: 1) The definition assumes a defined system, two reference temperatures T₁, T₂ and specified boundary conditions. 2) “Thermal transmittance” is replaced by “surface thermal transmittance” when confusion with “linear thermal transmittance” (see 2.13) is possible. 3) The reciprocal of the thermal transmittance is the total thermal resistance between the environments on either side of the system.	U	W/(m².K)
2.13. Linear thermal transmittance: The heat flow rate under steady state conditions divided by the product of the length and the temperature difference of the environments on either side of the system: NOTE: 1) The definition assumes a defined system, two reference temperatures T₁, T₂ and specified boundary conditions. 2) The reciprocal of the linear thermal transmittance is the total linear thermal resistance between the environments on either side of the system.	U_l	W/(m.K)
2.14. Heat capacity: The quantity defined by the following equation: NOTE: When the temperature of a system is increased by an amount dT due to the addition of a small quantity of heat dQ, the quantity dQ/dT is called the heat capacity.	C	J/K
2.15. Specific heat capacity: The heat capacity divided by mass	c	J/(kg.K)
2.15.1. Specific heat capacity at constant pressure	c_p	J/(kg.K)
2.15.2. Specific heat capacity at constant volume	c_v	J/(kg.K)
*2.16. Thermal diffusivity:** The thermal conductivity divided by the product of density and specific heat capacity. NOTE: 1) For liquids, the appropriate specific heat capacity is cp. 2) This definition assumes a homogeneous, opaque medium. 3) The thermal diffusivity relates to transient conditions and can be measured directly or calculated from the above formula from separately measured quantities. 4) In addition, the thermal diffusivity takes into account the change in temperature inside the material when the surface temperature changes. The higher the thermal diffusivity of the material, the more sensitive the internal temperature is to changes in surface temperature.	a	m²/s
2.17. Thermal effusivity: The square root of the product of thermal conductivity, density and specific heat capacity. NOTE: 1) For liquids, the appropriate specific heat capacity is cp. 2) This property relates to transient conditions. It can be measured or calculated from the above formula from separately measured quantities. Furthermore, the thermal effusivity represents the change of surface temperature of a material when the heat flux density through the surface changes. The lower the thermal effusivity of a material, the more sensitive the surface temperature is to changes in the heat flux at the surface.	b	J/(m².K.s^1/2)

3. Energy characteristics of buildings

Table 2 – Energy characteristics

Name	Quantity	Unit
3.1. Heat loss coefficient by volume: The heat flow from a building divided by the product of the volume and the temperature difference between the internal and external environments: NOTE: The heat flow may include: heat transfer effects through the building envelope, ventilation system, solar radiation, etc. The quantity volume V shall be specified. When applying the heat loss coefficient by volume, definitions of internal temperature, external temperature, volume and other heat effects causing the heat flow rate are assumed.	F_v	W/(m³.K)
3.2. Heat loss coefficient by area: The heat flow from a building divided by the product of the area and the temperature difference between the internal and external environments: NOTE: The heat flow may include: heat transfer effects through the building envelope, ventilation system, solar radiation, etc. The area may be the envelope area, floor area, etc. When applying the heat loss coefficient by volume, definitions of internal temperature, external temperature, volume and other heat effects causing the heat flow rate are assumed.	F_s	W/(m².K)
3.3. Air change rate: The number of times the air is changed within a defined volume divided by time. NOTE: The unit of air change rate (h^-1) is not an SI unit. However, the number of air changes per hour is generally accepted to express the air change rate.	n	h^-1

4. Symbols and units of other quantities

Table 3 – Symbols and units of other quantities

Name	Quantity	Unit
4.1. Thermodynamic temperature	T	K
4.2. Celsius temperature	θ	°C
4.3. Thickness	d	m
4.4. Length	l	m
4.5. Width	b	m
4.6. Area	A	m²
4.7. Volume	V	m³
4.8. Diameter	D	m
4.9. Time	t	S
4.10. Mass	m	Kg
4.11. Density	ρ	kg/m³

5. Subscripts

To avoid confusion, subscripts or other identifications should be used. Their meaning should then be made clear.

The following subscripts are recommended:

– Interior:	i
– Exterior:	e
– Surface:	s
– Interior surface:	si
– Exterior surface:	se
– Conduction:	cd
– Convection:	cv
– Radiation:	r
– Contact:	c
– Gas (air) space:	g
– Ambient:	a

ANNEX (Informative) CONCEPT OF THERMAL CONDUCTIVITY

A.0. Introduction

To clarify the concept of thermal conductivity when applied, this annex gives a more precise mathematical explanation.

A.1. Temperature gradient (grad T) at a point P

This is a vector normal to the isothermal surface containing point P. Its magnitude equals the derivative of the temperature T with respect to the distance from P along the normal direction n, the unit vector being .

By this definition:

g r a d T \vec{e_{n}} = \frac{\partial T}{\partial n}

(A.1)

A.2. Heat flux density q, at a point P (on a surface through which heat is transmitted)

Defined as:

q = (\frac{d ϕ}{d A})_{P}

(A.2)

When referring to heat exchange by conduction at any point of a body where conduction exists, the quantity q depends on the orientation of the surface (i.e. on the direction of the normal at point P to the area A) and it is possible to find the normal direction n to the area A_n containing point P, for which the value of q is maximum and denoted by the vector :

\vec{q} = (\frac{\partial ϕ}{\partial A_{n}})_{P} \vec{e_{n}}

(A.3)

For any surface area A_s passing through point P, the heat flux density q is a component of vector in the normal direction to that surface at point P.

The vector is called the “heat flux density” (not the heat flux). Whenever the vector cannot be defined (for convective heat transfer and most cases of radiative heat transfer), only the terms “heat flow rate” and “surface heat flux density” are used.

A.3. Thermal resistivity r at a point P

This is the quantity which allows the calculation of the vector grad T at the point P from the vector at the point P by Fourier’s law. The simplest case (isotropic material) is when grad T and are parallel and oppositely directed, then r is defined at each point as the ratio between the vectors grad T and .

g r a d T = - r \vec{q}

(A.4)

In this case r is also the inverse ratio between the components of grad T and at the same point along any direction s and is independent of the direction s chosen.

In the general case (isotropic or anisotropic material), one of the three components defining grad T is linearly related to the components of the vector . The thermal resistivity is therefore defined by the tensor [] of nine coefficients of these linear dependencies according to:

g r a d T = - ⌊ \vec{\vec{r}} ⌋ \times \vec{q}

(A.5)

If the thermal resistivity r or [] is invariant with respect to the coordinates and time, it can be considered a thermal characteristic at a given temperature.

A.4. Thermal conductivity l at a point P

This is the quantity which allows the calculation of the vector at the point P from the vector grad T at the point P, which means that the product of the thermal conductivity and the thermal resistivity equals one or a unit tensor.

If and grad T are parallel and oppositely directed, then:

\vec{q} = - λ \cdot g r a d T

λr = 1 (A.6)

As for the thermal resistivity, the thermal conductivity is in most cases a tensor [] of nine coefficients of the linear dependencies of the components of grad T which define each component of according to:

\vec{q} = - \vec{\vec{λ}} g r a d T

(A.7)

Thus [] can be defined by inversing [] and vice versa. If the thermal conductivity l or [] is invariant with respect to the coordinates and time, it can be considered as a thermal characteristic at a given temperature.

The thermal conductivity may be a function of the temperature and of the direction (anisotropic material). It is therefore necessary to know the relationship to these parameters.

Let us consider a body of thickness d limited by two parallel and isothermal plane faces, at temperatures T₁ and T₂, each having an area A.

The lateral edges surrounding the principal faces of this body are supposed to be adiabatic and perpendicular to them. Let us suppose that the body is constituted by a stable, homogeneous and isotropic material (or anisotropic with an axis of symmetry perpendicular to the principal faces). Under such conditions the following relations derived from Fourier’s law under steady state conditions will apply if the thermal conductivity l or [], or the thermal resistivity r or [] is independent of temperature:

λ = \frac{1}{r} = \frac{ϕ d}{A (T_{1} - T_{2})} = \frac{d}{R}

(A.8)

If all the above conditions are met (except that the thermal conductivity l or [] is a linear function of temperature), the above relations still apply but the thermal conductivity is evaluated at the mean temperature.

T_{m} = \frac{T_{1} + T_{2}}{2}

Similarly, if a body of length l is limited by two isothermal, cylindrical, coaxial faces at temperatures T₁ and T₂ and of diameters Di and De respectively, and if the ends of the body are plane adiabatic faces perpendicular to the cylinders, and the material is stable, homogeneous and isotropic, the following relations derived from Fourier’s law under steady state conditions will apply if the thermal conductivity l or the thermal resistivity r is independent of temperature:

λ = \frac{1}{r} = \frac{ϕ l n \frac{D_{e}}{D_{i}}}{2 π l (T_{1} - T_{2})} = \frac{\frac{D}{2} l n \frac{D_{e}}{D_{i}}}{R}

(A.10)

R = \frac{(T_{1} - T_{2}) \frac{π}{D}}{ϕ} = \frac{1}{λ} \frac{D}{2} l n \frac{D_{e}}{D_{i}} = r \frac{D}{2} l n \frac{D_{e}}{D_{i}}

(A.11)

Where D may be the external or internal diameter or some other defined diameter.

If all the above conditions are met except that the thermal conductivity l is a linear function of temperature, the above relations still apply but the thermal conductivity is evaluated at the mean temperature given by:

T_{m} = \frac{T_{1} + T_{2}}{2}

With the above limitations, equations (8) and (10) are commonly used to determine the thermal conductivity of opaque, homogeneous media from quantities measured at the mean temperature T_m.

Similarly, equations (A.8) and (A.10) are commonly used to determine the thermal characteristics of porous media from measured quantities for which the overall heat transfer process comprises the three modes of transfer: radiation, conduction and sometimes convection.

The measured thermal characteristic representing all the above modes of heat transfer is called the thermal conductivity (sometimes also called apparent, equivalent or effective thermal conductivity) of the homogeneous porous medium when it is independent of the geometrical dimensions of the test specimen, the radiative properties of the limiting surfaces of the specimen and the temperature difference (T₁ – T₂).

When these conditions are not satisfied, the surface thermal resistance should be used to characterize the specimen with its given geometrical dimensions, temperature difference (T₁ – T₂) and given radiative properties of the lateral faces of the specimen.

BIBLIOGRAPHY

[1] TCVN 7870-5:2007, Quantities and units – Part 5: Thermodynamics.