1. Introduction
Sol-air temperature is a critical concept in thermal engineering, particularly in building design, HVAC system optimization, and other engineering applications.
In this article, we will explore the concept of “sol-air temperature”, its significance in building design, the formula for its calculation, and common mistakes to avoid when incorporating it into HVAC and architectural strategies.
By understanding and applying sol-air temperature, engineers and architects can design buildings with improved thermal performance, energy efficiency, and occupant comfort.
To simplify the analysis, only the vertical surface (wall), is taken into consideration for Sol-air temperature. However, for cooling load calculation (using Carrier HAP) both wall and roof surfaces have been considered
2. Conduction Heat Transfer Rate Through External Wall
In HVAC system design, the cooling/heating load calculation is one of the major and prime calculations that must be completed in the project’s initial phase. The calculation outputs will be the basis for the rest of the design activities (such as duct, and pipe sizing, equipment selection, MTOs, procurement of equipment/items, etc.).
The cooling load components of the room/space are as below:
- Internal loads (lighting, equipment, people)
- External loads (Wall, roof, floor, partition, window, door, infiltration)
To understand the concept of “Sol-air temperature”, we will consider the conduction heat transfer through the external wall only.
Normally we use the following equation for calculating the conduction heat transfer rate through the external wall:
Q = U x A x ΔT (Watts)
Where,
U = Overall heat transfer coefficient of the wall construction, (W/m2.K)
A = Surface area of the wall, (m2)
ΔT = Temperature difference, (OC)
Now the question arises of which temperature difference should be used?.
Consider the following wall arrangement:
In manual calculations, for the above wall construction and temperature scenarios, most of us use the temperature difference between outdoor ambient air temperature (To) and conditioned room air temperature (TR), i.e. ΔT= TO-TR, and below equation will be used for calculating the heat transfer rate.
Q = (1/(1/hi+L1/K1+L2/K2+1/h0)) x A x (TO-TR)
Note that this equation is correct for the below temperature profile between the outdoor ambient and room temperature (where TO> TS). In this case, heat transfer will occur only in one direction, from external ambient air to indoor room/space.
However, during summer, the outer surface of the walls becomes significantly hotter than the surrounding air temperature (i.e., TS>TO. Refer below picture for the temperature profile). This phenomenon is noticeable when we touch external surfaces, such as walls or metal objects like a car’s exterior, which feel much warmer compared to the ambient air. This occurs due to the absorption of solar radiation, which causes these surfaces to heat up beyond the ambient temperature.
Note that in this scenario, the maximum temperature occurs at the outer surface of the wall and both the room temperature and ambient air temperature are lower than the surface temperature. So, heat transfer occurs in both directions (i.e., from the external wall surface towards the room by conduction & from the external wall surface towards ambient air by convection and radiation)
So, for calculating the heat transfer rate the ΔT of TS-TR (and associated resistances) should be used rather than TO-TR.
In the coming sections, we will learn about, the concept of “Sol-air temperature, and how to calculate the surface temperature of the external wall. This surface temperature is called “Sol-air Temperature”, Te.
3. What is Sol-Air Temperature?
ASHRAE definition of Sol-air temperature is given below:
“Sol-air temperature is the outdoor air temperature that, in the absence of all radiation changes gives the same rate of heat entry into the surface as would the combination of incident solar radiation, radiant energy exchange with the sky and other outdoor surroundings, and convective heat exchange with outdoor air.”
The formula for sol-air temperature is:
Te = TO + (α x Et / hO) – (Ɛ x ΔR / hO)
Where:
To = Ambient air temperature, (OC)
α = Absorptivity of the external surface (dimensionless, 0 to 1)
Et = Total solar radiation incident on surface, (W/m²)
h0 = External surface heat transfer coefficient, (W/m²K)
Ɛ = Emissivity of the surface (dimensionless, 0 to 1)
ΔR = Difference between long-wave radiation incident on the surface from sky and surroundings and radiation emitted by a blackbody at outdoor air temperature, W/m2
For horizontal surfaces (roof) that receive long-wave radiation from the sky only, the value of ΔR is about 63 W/m2, so if Ɛ = 1 and ho = 17 W/(m2·K), the long-wave correction term (=Ɛ x ΔR / h0) is about 4 K.
For vertical surfaces (wall), When solar radiation intensity is high, the surface temperature is higher than the outdoor air, so its long-wave radiation compensates to some extent for the sky’s low emittance, the correction term, Ɛ x ΔR / h0, is normally assumed zero.
So, the simplified equation for the vertical surface (wall) is:
Te = To + (α x Et / ho)
Absorptivity (α)
The following factors affect the absorptivity of the surface:
- Color of the surface
- Material of the surface
- Surface Texture
Total solar radiation incident on surface (Et)
It is the function of the following factors:
1) Direct solar heat gain, which is a function of:
- Location of the building (Latitude, longitude)
- Orientation of the wall
- Time
- Atmospheric clearance number
2) Ground reflection, soil conductivity
4. Sol-air Temperature (Te) Calculations
Consider the vertical wall with the following design temperature conditions and parameters:
To = 46 OC (Consider design ambient DBT for Dubai, UAE)
h0 = 17 W/m2.K (from Carrier HAP software)
Et = 780 W/m2. (Et varies with time, location, and orientation, ground reflection value, atmospheric clearance, soil conductivity). The specified value has been considered for analysis. However note that based on orientation this value can reach about 70 W/m2
The simplified equation is given below:
Te = To + (α x Et / ho)
= 46 + (α x 780/17)
= 46 + (α x 45.88)
For various surface colors, the Sol-air temperature of the wall is given below :
For easy understanding, the changes in Sol-air temperature with absorptivity value have been shown in the bar chart:
5. Cooling Load calculation
For a sample room with the design parameters outlined below, cooling loads were calculated for varying wall and roof absorptivity (α), while maintaining all other parameters constant.
• Room Size:
Room size: 10 x 10 m, height = 6 m
• Weather Input:
• Space Input: Lighting load = 10 W/m2, People = 4 Nos, seated at rest, no window. Wall exposure: All the sides (N, S, W, E), 60 sq. m. No ventilation rate.
• System Input: Room temperature: 24 OC, Design Safety factors: 5 % on both sensible and latent.
Refer to the bar chart between absorptivity and total cooling load.
Conclusion
Note that just by changing the color of the external wall, the cooling load can be reduced significantly. In this example, compared with a black matte-colored wall (Absorptivity of 0.94), the heat transfer rate is reduced by about 23 % when using a white acrylic paint-colored wall (Absorptivity of 0.26).
6. Significance of Sol-Air Temperature
• Thermal Load Calculations
• Building Envelope Design
• Energy Efficiency
• Indoor Comfort
• Sustainable Building Practices
7. Common Mistakes in Using Sol-Air Temperature
Ignoring Surface Properties
Many designers overlook the importance of surface absorptivity (α) and emissivity (Ɛ). These properties vary significantly with material type, color, and finish. For example, dark surfaces absorb more solar radiation than light-colored ones, leading to higher sol-air temperatures. Ignoring these variations can lead to inaccurate thermal load calculations.
Solution: Always use material-specific values for absorptivity and emissivity when calculating Sol-air temperature.
Using Average Solar Radiation Values
Some practitioners use average solar radiation values instead of location-specific or time-specific data. Solar radiation varies based on geographic location, season, and time of day, and using generalized data can lead to errors in calculations.
Solution: Incorporate site-specific and time-dependent solar radiation data for more accurate results.
Neglecting Longwave Radiation Effects
The temperature difference due to longwave radiation exchange (ΔR) is often omitted or underestimated. This component accounts for heat loss from the surface to the sky and can significantly impact the sol-air temperature.
Focusing Solely on Peak Conditions
While peak sol-air temperatures are critical for extreme conditions, focusing solely on these values may lead to overdesigning HVAC systems, increasing costs unnecessarily.
Solution: Balance peak and average conditions in the design process to optimize performance and cost-effectiveness. Alternatively ,use Computer based software like carrier HAP for the calculation
Neglecting Thermal Lag
Thermal lag, or the time delay between solar radiation absorption and heat transfer into the interior, is often ignored. This can lead to discrepancies in predicting indoor temperature fluctuations.
Solution: Consider the thermal mass of building materials and the associated time lag in energy modeling.
Failing to Integrate Sol-Air Data into Energy Models
Some energy modeling tools and simulations fail to incorporate sol-air temperature, relying solely on ambient air temperature. This omission can lead to underestimating thermal loads and energy requirements.
Solution: Ensure that sol-air temperature is integrated into energy modeling software and simulations for accurate results.
8. Real-Time Applications
White coloured surface (having low absorptivity) is used in the below applications to reduce the Sol-air temperature and thus reduce the heat transfer rate.
1) Whited-washed South Indian homes
2) White colors oil storage tanks
3) White clothing
4) White-colored water tanks
9. Conclusion
Sol-air temperature is an essential parameter in building design and HVAC system optimization, providing a more comprehensive understanding of external thermal conditions. By incorporating it into thermal load calculations, material selection, and energy modeling, designers can enhance building performance, improve occupant comfort, and achieve sustainability goals.
10. References
1) ASHRAE Handbook – Fundamental, Chapter “Physical Properties of Materials”
2) ASHRAE Handbook, Fundamentals, Chapter, Nonresidential Cooling and Heating Load Calculations
3) Carrier HAP Software, “Wall”, for Outside Surface Resistance (Converted to inside and outside convective heat transfer coefficient (h) by taking the reciprocal)
11. Abbreviations
| ASHRAE | American Society of Heating, Refrigerating, and Air-Conditioning Engineers |
| DBT | Dry Bulb Temperature |
| HAP | Hourly Analysis Program |
| HVAC | Heating, Ventilation, and Air Conditioning |
| MTO | Material Take-Off |
| UAE | United Arab Emirates |