Mean Radiant Temperature (MRT) - Part I
Copyright (c) 2010, Robert Bean, R.E.T., P.L.(Eng.) and www.healthyheating.com

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Thermal Comfort: A Condition of Mind NEW!

Mean Radiant Temperature (MRT) - Part I: Introduction/theory
Mean Radiant Temperature (MRT) - Part II: Application of theory
Mean Radiant Temperature (MRT) - Part III: Spreadsheet tool for thermal bridging
Mean Radiant Temperature (MRT) - Part IV: Project examples & ASHRAE research
Mean Radiant Temperature (MRT) - Part V: Calculation example (REHVA GB #7)
 

Have you ever considered that we don't feel the heat loss from the building, but the heat loss from our skin, ergo we must understand the intimate infrared relationship our bodies have with the surrounding surfaces of the room (T_s) described by the mean radiant temperature (Tr , T_mr or MRT). Mean radiant is a dominant element in the thermal comfort equation which is an integral part of indoor environmental quality (see also radiant asymmetry) and building performance.
 

Figure 1. The mean radiant temperature (MRT) is a means of expressing the influence of surface temperatures on occupant comfort. It can be calculated many ways. In its simplest and least accurate form it is a homogenous steady state area weighted average of the uncontrolled or unconditioned surface temperatures (AUST) written as;

        T_mr = T₁A₁  + T₂A₂  + …+ T_NA_N  / ( A₁  + A₂  + …+ A_N  )

where,

        T_mr = mean radiant temperature, °R

        T_N = surface temperature of surface N, °R (calculated or measured)

       A_N = area of surface

This method does not reflect the geometric position, posture and facing orientation of the occupant nor ceiling height nor the thermal comfort influence of extraordinary items such as radiant asymmetry.
 

Figure 2. In practice the mean radiant temperature is ambiguous as the occupant moves about the space and as a result of different room geometries and changes to internal and external environmental conditions.

Mean radiant temperature and the angle factor
In a more advanced review of MRT, we can not only look at the individual surface temperatures and their area but also the distance of those surfaces from the occupant and whether that person is seated or standing. Why is this important? Well let's say you live in a cold climate and have a home office where your back will be facing a large northern facing window. That large cold window will have much greater influence on your perception of comfort more so than any other surface in that room regardless of the air temperature. Why? Because the radiant transfer from your warm body to that cold surface will invoke a cooling sensation from your back which will be perceived by your brain as being uncomfortable. The angle factor is a means to describe the geometric relationship an occupant has with each surface in the space.

When surfaces have a high emittance (ε), they can be assumed to be black and thus the following equation for mean radiant temperature can be used:
 

        T_mr⁴ = T₁⁴F_p-1  + T₁⁴F_p-1  + …+ T_N⁴F_p-N

where,

        T_mr = mean radiant temperature, °R

        T_N = surface temperature of surface N, °R

       F_p-N = angle factor between a person and surface N
 

When relatively small temperature differences exist between the surfaces of the enclosure the mean radiant temperature can be simplified to:
 

        T_mr = T₁F_p-1  + T₁F_p-1  + …+ T_NF_p-N

How does MRT fit in with thermal comfort?
Of course MRT is only one element of thermal comfort - and we would be naive to ignore the air temperature (dry bulb, T_db)...so the MRT and T_db must be combined after factoring in their respective heat transfer coefficients into what is known as the operative temperature, written as:
 

        T_o = ( h_rT_mr + h_cT_db ) / ( h_r + h_c )

Radiant based HVAC

We address the definition of radiant based HVAC systems throughout the site but suffice to say it is first and foremost the radiant influence as a result of the building enclosure and subsequent interior surface temperatures on the occupant. A low U-value enclosure will have warmer surfaces in winter and cooler surfaces in summer in comparison to an enclosure with higher U-values (ignoring discussions on internal gains). Because of the lower U-Value and reduced air leakage associated with a high performance building, there is lower heating and cooling loads and shorter periods of operating time. This leads to improved comfort and lower operating costs - both desirable for any building.

Figure 3. Radiant based HVAC system begin with the building enclosure (U) where its thermal performance determines the interior surface temperatures and thus the mean radiant temperature (click image to enlarge).

Figure 4. Mean radiant temperature can be controlled with enclosure performances as demonstrated above using FEA to model various walls.

Building and energy codes, MRT and operative temperature (T_o)

Ironically, most building and energy codes do not explicitly consider thermal comfort from thermal comfort metrics such as mean radiant and operative temperatures  - if they did... the minimum requirements for insulation and air leakage would be better than it is currently specified. The few building codes which do consider the radiant element, usually place the description in the appendix and most enforcing authorities don't know the clauses exists. Here's a sample statement from the National Building Code of Canada v2010: Section A-5.3.1.2.(1) Use of Thermal Insulation or Mechanical Systems for Environmental Control;

“In addition to controlling condensation, interior surface temperatures must be warm enough to avoid occupant discomfort due to excessive heat loss by radiation.”

The above clause is not a trivial statement as it is one of the only places we have found in building codes in North America, which recognizes the intimate radiant relationship between thermal comfort and building surface temperatures. Virtually an entire industry of manufacturers, suppliers, builders and trades people incorrectly equate thermal comfort with air temperatures.

Relationships between mean radiant and dry bulb temperatures (Figure 5), floor surface temperatures and flux (Figure 6) for various operative temperatures.

Figure 5 The sloped lines are the resulting operative temperatures with various combinations of mean radiant and dry bulb temperature (click image to enlarge).

Figure 6. Relationship between heating flux and surface temperatures at various operative temperatures (click image to enlarge).

The human body: a model for HVAC design

Figure 7. Your body already produces heat so it's only necessary to add or remove enough heat from a space to maintain a reasonable balance between the operative temperature and the occupant, and this can be accomplished very effectively first with a combination of architecture, interior design and then if needed high temperature radiant cooling and low temperature radiant heating systems.

Figure 8. Thermal Comfort Instrumentation (Courtesy of Innova) - measures mean radiant temperature, dry bulb temperature, humidity, air velocity, radiant asymmetry and other metrics of the ANSI/ASHRAE Standard 55 - Thermal Environmental Conditions for Human Occupancy.