Heat transfer occurs whenever there is a temperature difference between two objects, and it continues until both objects are in thermal equilibrium. According to a formulation of the Second Law of Thermodynamics known as the Clausius statement, heat cannot naturally flow from a colder temperature to a hotter temperature.
In other words, heat will always naturally flow from hot to cold. Heat is transferred in three ways: conduction, convection and radiation. A radiant cooling system uses all three modes of heat transfer.
Conduction is heat transfer between two solids that are in direct contact with each other. In radiant heating and cooling systems, conduction occurs between the PEX-a tubing and the concrete slab. The heat transfer rate is based on the conductivity of materials, the tubing surface, and the temperature difference between the tubing and the slab. Conduction also occurs between the cooled slab and the objects in the space that are in contact with the slab, including air film, furnishings and occupants. If a person is standing on a cooled slab, then a quantity of body heat will naturally flow via conduction to the slab.
The heat transfer rate is based on the cumulative thermal resistance (R-values) from footwear, the floor conductivity, and the temperature difference between the occupant and the floor surface. To prevent discomfort due to temperature differentials, ASHRAE Standard 55-2010 recommends that floor slab temperatures be above 66°F (18.9°C) for occupants wearing normal footwear in occupied spaces. It should be noted that in temperature ranges typical of radiant floor cooling systems, and in consideration of footwear R-values, the amount of conductive heat transfer from foot to slab is relatively low and, therefore, typically considered negligible.
Convection is heat transferred through a moving fluid or gas. In the case of radiant-based HVAC systems,
natural or “free” air convection occurs due to differences in air densities influenced through contact with warmed or cooled surfaces.
Natural convection is a design consideration with radiant-cooled ceilings as the layer of air in contact with the cool ceiling will drop due to its higher density, increasing air movement, and thus heat transfer, in the space. Forced convection occurs in the air handler, such as a dedicated outdoor air system (DOAS), where fans are used to force the cooled air into the space. Because convection deals with heat transfer through the movement of air, the air temperature is directly affected.
A Look at Radiation
Not surprisingly, the sensible heat transfer in a radiant cooling system is through radiation. Radiation is heat transfer through electromagnetic waves travelling through space. When the incident waves from a warmer surface come into contact with a cooler surface, the energy is absorbed, reradiated, reflected or transmitted.
An example of radiation is sunlight, which travels through the vacuum of space as short-wave radiation to warm the Earth’s surface. The heat-transfer rate is influenced by a number of factors, including the absorptivity, reflectivity and emissivity of the surfaces; wavelength; temperature and the spatial relationship between the cooled surface and the occupant (defined as the view and angle factors). In radiant cooling, the electromagnetic waves from the occupant are drawn toward the cooled surface, resulting in the occupant experiencing a cooling effect.
- Long-wave Radiation: Long-wave radiation is the heat flux that occurs between the conditioned surface and the unconditioned room surfaces; its quantity and wave length are temperature-dependent.
- Short-wave Radiation: The transfer of short-wave radiation upon room surfaces from solar gains or high-intensity lighting is not dependent on the temperature of the absorbing surface. Energy at this intensity upon a surface at room conditions will be absorbed, reflected and/or transmitted based upon the color and optical characteristics (reflectivity, absorptivity, transmissivity) of the receptor surfaces.
As previously discussed, the radiation within a space is usually separated into two groups: long-wave and short-wave. The long-wave radiation is that which occurs between room surfaces. The short-wave radiation upon a cooled floor should be considered; its incident energy will be absorbed, reflected and/or transmitted based upon the color and optical characteristics of the receptor surfaces.
The first law of thermodynamics: α + τ + ρ = 1
α= fraction of incident radiation absorbed (absorptance).
τ= fraction of incident radiation transmitted (transmittance).
ρ = fraction of incident radiation reflected (reflectance).
If the floor surface is opaque, then the transmittance of the floor surface τ= 0. For a black surface where α= 1, ρ = 0, τ= 0, all short-wave radiation reaching the surface will be absorbed by the black surface. For most surfaces, absorbtance for short-wave radiation (high-temperature radiation) is different than emittance for long-wave radiation (low-temperature radiation).
Solar absorptance can also vary with the size of windows. Absorptance can range from 0.90 for dark-colored spaces with small windows to 0.60 or less for light-colored spaces with large windows.
When using textile-based floor coverings, the slab temperature required to draw down the floor surface temperature must be evaluated to ensure it does not approach the dew point temperature.
A Final Word on Heat Transfer
Understanding the basics of convection, conduction and radiation is key to creating buildings that are sustainable and energy efficient. Conduction, convection, and radiation heat transfer take place almost everywhere we look. In a building envelope, conduction primarily takes place through opaque envelope assemblies, convection is usually the result of wind or pressure-driven air movement, and radiant heat transfer is primarily from the sun through fenestrations. Building HVAC systems are typically designed to provide comfort using convective or radiant modes of heat transfer.
Radiant cooling solutions focus primarily on radiation but also address the two remaining elements of heat transfer. DOAS is commonly used in conjunction with radiant cooling system to provide an energy efficient means of cooling.