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HEAT TRANSFER SIMPLIFIED

Fundamentals

Heat transfer is the movement of energy in the form of heat and always moves from a higher to a lower temperature. There are three modes of energy transfer:

• Conduction
• Convection
• Radiation 

All heat transfer processes involve one or more of these modes.
Conduction is accomplished by means of molecular interaction, where a higher energy molecule imparts energy to adjacent lower energy molecules.
Heat transfer due to convection is accomplished by the movement of a fluid (liquid or gas) and also involves the energy exchange between a surface and an adjacent fluid. The exact mechanism of radiant energy transfer is not completely understood, but unlike conduction and convection, no medium is required for its propagation. In fact, energy transfer by radiation is maximised when the two surfaces exchanging energy are separated by a perfect vacuum. The purpose of insulation is to reduce the rate of energy transfer, thereby reducing the rate of heat gain or heat loss to or from a body. The effectiveness of an insulant is determined by its thermal resistance, R, defined by:

R=x-Equation (1)
    k

Where: x is the thickness of the material in metres.
k is the thermal conductivity of the material, defined as the rate of heat flow through one metre of a homogenous material and is measured in Watts per metre Kelvin (W/mK).

Thermal conductivities of various materials can be found in reference literature, e.g. the ASHRAE Handbook of Fundamentals. 
From the above it can be seen that thermal resistance is increased with increasing thickness of products with low thermal conductivities. 

Thermal Resistance of Systems 
Buildings typically consist of various elements in their construction. To determine the heat loss or heat gain through a typical structural unit, the thermal resistance of each element in the composite structure must be taken into consideration. In such a case, the total thermal resistance of the structure, RTOT is the sum of the resistance of the individual elements comprising the system. 

i.e. RTOT = R1 +R2+R3+R4+... 

Manufacturers of bulk insulation products typically quote the thermal conductivity, k, and thickness, x, of their products. Applying equation (1) above yields the thermal resistance of the insulation alone, which is only one of the elements necessary to determine the overall thermal resistance of the system. Confusion arises when suppliers of radiant barrier insulation quote thermal resistance values which are inclusive of air gaps. Such thermal resistance values are in fact the resistance of a total system and cannot be compared to individual product R-values.
Radiant barriers, e.g. foil laminates, are typically very thin with high thermal conductivities, and in accordance with equation (1) thus have a very poor thermal resistance. For this reason, radiant barriers always quote an associated air gap. Thus the thermal resistance of radiant barriers, inclusive of air gaps, is the sum of five resistance elements:

• the upper air gap,
• the upper laminar boundary layer,
• the foil laminate itself,
• the lower laminar boundary layer,
• the lower air gap. 

By contrast, the thermal resistance of bulk insulation products refers to the product alone, to which must be added the effects of the upper and lower boundary layers as well as any air gaps.

A word of caution must be sounded with respect to air gaps. Although it is acknowledged that static air is a very good insulator owing to its very low thermal conductivity, it must be borne in mind that thermal gradients can induce natural convection, in which case convection becomes the main mechanism of heat transfer and not conduction. When this takes place, the thermal performance of air gaps is drastically reduced. 

Many published system thermal resistances for radiant barriers are based on "trapped" air gaps above and below the barrier, which is impossible to achieve in practical installations. Thus thermal resistance values, inclusive of air gaps, determined under ideal, experimental conditions, tend to overstate the performance of the system. 

In closing, it is thus recommended that the total thermal resistance of systems be calculated on the basis of internationally accepted standards and procedures to ensure that the required thermal performance is achieved and can be guaranteed. After all, our current energy resources are finite and care must be taken to ensure that such resources are conserved to ensure longer-term prosperity for all.