## 08 June 2011

### Building Energy Transfers: Modes of Heat Transfer, Thermo-physical Properties of Materials, and Calculation of U-value

PAUL HAY Capital Projects

# Building Energy Transfers & Properties of Materials

Author:          Paul Hay
e-mail:            paul.hay@phcjam.com

## 1.0       INTRODUCTION TO ENERGY TRANSFERS & MODES OF TRANSFER

1.1       Majority of heat transfer in the tropics is through thermal radiation.

1.2       Heat transfer can be either "Steady State" or "Periodic" in nature.

1.3       Energy transfers primarily depend on (a) difference of the ambient air-temperature to the indoor air temperature, (b) thermo-physical properties of the construction materials, and (c) location of materials in the assembly of the building component.

## 2.0       PERIODIC HEAT TRANSFER

2.1       Periodic (or Non-Steady-State) Heat Transfer is the thermal condition in which temperature on at least one side of a material and distribution within the material fluctuate predictably.

2.2       Thermal Mass is the measure of a building component's ability to absorb heat while undergoing a temperature change.

2.3       (Volumetric) Heat Capacity is the measure of a material's ability to store or absorb heat while undergoing a temperature change.

3.1       Steady-State Heat Transfer is the thermal condition in which temperature on each surface of a material and distribution within the material is uniform and constant with time.
3.1.1    Surface Coefficients are thermo-physical properties of surfaces that assume the existence of steady-state heat transfer; and
3.1.2    Thermal Conductance is another thermo-physical property of a material that assumes the existence of steady-state heat transfer.

3.2       Rate of Heat Transfer (Q) through a building component is dependent on the temperature difference across its outermost surfaces, ventilation loss, its area and Overall Thermal Transmission Coefficient (i.e. U-value):
3.2.1    Overall Thermal Transmission Coefficient (U) is the overall (i.e. area-weighed) coefficient of heat transfer from air to air arising from conduction through a building component (eg. roof) [unit = W/m2.K];
3.2.2    The U-value depends on (a) the individual thermal conductance of its components and (b) the placement of components relative to each other;
3.2.3    The Jamaican Energy Efficiency Building Code [EEBC-94] stipulates a maximum U-value for specific climatic zones in Jamaica.

## 4.0   THERMO-PHYSICAL PROPERTIES OF MATERIALS

4.1       Thermal Conductivity (k) is the rate of heat flow through a unit area and unit thickness of an homogeneous material, under steady-state conditions, for a unit temperature gradient perpendicular to the area [unit = W/m-K].

4.2       Thermal Conductance (C) is the rate of heat flow through a unit area of a component from one of its bounding surfaces to the other for a unit temperature difference between the two surfaces, under steady state conditions [unit = W/m2-K]

4.3       Individual thermal conductance can be derived from the thickness of the component (t) and its conductivity (k) as follows:
C = k/t                                                                                                  [4.1]

4.4       Thermal Resistivity (r) is the reciprocal of the thermal conductivity [unit = m.K/W]:
r = 1/k                                                                                                  [4.2]
It indicates the thermo-physical property of a material as a thermal insulator.

4.5       Thermal Resistance (R) is the reciprocal of thermal conductance [unit = m2.K/W]:
R = 1/C = t/k                                                                                         [4.3]

It indicates the thermo-physical property of a component as a thermal insulator.

## 5.0       CALCULATION OF U-VALUE

Example:-  Calculate Ur for a roof constructed as per sketch

ho =     22.7 W/m2-K
hi =      6.14 W/m2-K
a. Subscript numbers conform to  identification of components.

Conductances at joists are as followsa:
C2 =     17.0 W/m2-K
C3 =     4.09 W/m2-K
C4 =     7.32 W/m2-K
C7 =     12.5 W/m2-K
C8 =     4.54 W/m2-K

Also,
k6 =     0.12 W/m-K
Therefore,
b.  Actual thickness of 200 mm (nom.) deep joist is 184 mm or 0.184 m.

C6 =     k6/t =   0.12/0.184b =   0.63 W/m2-K
And,
1/Uj =  1/ho + 1/C2 + 1/C3  + 1/C4 + 1/C6 + 1/C7 + 1/C8 + 1/hi
=     1/22.7 + 1/17 + 1/4.09 + 1/7.32 + 1/0.63 + 1/12.5 + 1/ 4.54 + 1/6.13
=     2.53 m2-K/W
So,
Uj   = 1/2.53 =             0.40 W/m2-K

c.  Conductance of air-space assumes heat-flow is downward, mean temperature = 32 EC & temp. difference = 5 K
Conductance at air-space is as follows:
C5 =     5.68 W/m2-K

And,
1/Us =  1/ho + 1/C2 + 1/C3  + 1/C4 + 1/C5 + 1/C7 + 1/C8 + 1/hi
=   1/22.7 + 1/17 + 1/4.09 + 1/7.32 + 1/5.68 + 1/12.5 + 1/4.54 + 1/6.13
=   1.12 m2-K/W

So,
Us   =                           1/1.12 =           0.89 W/m2-K

And,
Ur =     (Uj Aj + UsAs)/(Aj + As)
=     UjAj /(Aj + As) + UsAs /(Aj + As)
=     0.40 x 0.10 + 0.89 x 0.90
=     0.84 W/m2-K