Theoretical Minimum Thermal Load in Buildings

Abstract

Space conditioning for thermal comfort within buildings is one of the largest sources of greenhouse gas emissions globally, creating an urgent need to realize deep energy reductions in this energy service to meet climate goals. Our current approach to providing thermal comfort relies on conditioning large spaces. In this perspective, we show that this approach is inherently energy inefficient by introducing and calculating the TMTL needed to keep building occupants thermally comfortable. The TMTL is approached when the space conditioning volume aligns with the immediate volume occupied by the individual. We show that such an approach could deliver 10× reductions in energy use for space conditioning in buildings and homes in the US. To investigate near-term solutions to approaching the TMTL, we develop a simple approximate model to calculate the energy savings from increasing zonal control of buildings and homes. We use this model to show that increasing the number of zones in a building to 10 with modest temperature setbacks can deliver up to a 70% energy reduction. We highlight technologies available today that could facilitate increased zonal control. We also identify long-term technology development needs, highlighting current research that supports approaching the TMTL. Specifically, we highlight advances and research needs in thermally adaptive clothing, radiative heating, and thermal energy storage combined with thermal switches that could further facilitate the TMTL. Building cooling and heating accounts for a large portion of total global energy use and requires commensurate amounts of resources, which contribute significantly to global warming. Traditionally, addressing this issue has meant improving the efficiency of equipment supplying the thermal energy, reducing envelope heat transfer, and reducing air infiltration. However, this approach is already reaching practical limits. In this perspective, we explore (1) how to reduce thermal load in buildings theoretically and (2) how to achieve that reduction and dramatically lower the energy required to support building loads practically. First, we discuss our framework developed for calculating the theoretical minimum thermal load (TMTL) in buildings. Our analysis shows that current thermal loads in buildings are more than an order of magnitude higher than the TMTL. We also introduce an approximate formula to calculate energy savings from zonal control of thermal load, which shows that the majority of zonal control benefits can be achieved with fewer than 10 zones. Then, we discuss pros and cons of various approaches and strategies to achieve the TMTL. We conclude our perspective with some longer-term R&D ideas, such as thermally adaptive clothing and thermal storage to help approach the TMTL, while providing the additional benefit of interacting with the renewable grid of the future. Building cooling and heating accounts for a large portion of total global energy use and requires commensurate amounts of resources, which contribute significantly to global warming. Traditionally, addressing this issue has meant improving the efficiency of equipment supplying the thermal energy, reducing envelope heat transfer, and reducing air infiltration. However, this approach is already reaching practical limits. In this perspective, we explore (1) how to reduce thermal load in buildings theoretically and (2) how to achieve that reduction and dramatically lower the energy required to support building loads practically. First, we discuss our framework developed for calculating the theoretical minimum thermal load (TMTL) in buildings. Our analysis shows that current thermal loads in buildings are more than an order of magnitude higher than the TMTL. We also introduce an approximate formula to calculate energy savings from zonal control of thermal load, which shows that the majority of zonal control benefits can be achieved with fewer than 10 zones. Then, we discuss pros and cons of various approaches and strategies to achieve the TMTL. We conclude our perspective with some longer-term R&D ideas, such as thermally adaptive clothing and thermal storage to help approach the TMTL, while providing the additional benefit of interacting with the renewable grid of the future. The limit of energy efficiency is often viewed from the lens of maximizing the efficiency of technologies used to meet energy demand. While this approach has realized substantial energy and cost benefits, it only addresses half of the problem. Here, we examine the fundamental limits of energy demand, which could transform the approach to reduce energy use and unlock benefits far beyond what was previously imagined. Nowhere is this change in focus needed more than the heating and cooling (thermal energy) of buildings. We examine the fundamental premise for why thermal energy is used in buildings (i.e., occupant comfort) and, in doing so, we identify the physical limit of minimum thermal energy demand. This limit presents a new baseline for how thermal energy is used in buildings and highlights the associated energy savings opportunities. Heating and cooling of buildings is directly attributed to more than 10% of global energy consumption and anthropogenic CO2 emissions.1Ürge-Vorsatz D. Cabeza L.F. Serrano S. Barreneche C. Petrichenko K. Heating and cooling energy trends and drivers in buildings.Renew. Sustain. Energy Rev. 2015; 41: 85-98Crossref Scopus (427) Google Scholar Current energy consumption trends project that the share of CO2 emissions attributable to buildings will continue to grow in coming years, as heating and cooling loads are forecast to increase globally to more than 50% of building energy demand.2Editorial The heat is on.Nat. Energy. 2016; 1: 16193Crossref Scopus (7) Google Scholar For example, in developing countries, air-conditioning demand is expected to increase >4.5x.3Davis L.W. Gertler P.J. Contribution of air conditioning adoption to future energy use under global warming.Proc. Natl. Acad. Sci. U. S. A. 2015; 112: 5962-5967Crossref PubMed Scopus (248) Google Scholar Biardeau et al.4Biardeau L.T. Davis L.W. Gertler P. Wolfram C. Heat exposure and global air conditioning.Nat Sustain. 2020; 3: 25-28Crossref Scopus (35) Google Scholar recently conducted an analysis of cooling degree days of 219 countries and found that highly populous countries such as India have a very high number of cooling degree days, leading to a higher energy demand. Waite et al.5Waite M. Cohen E. Torbey H. Piccirilli M. Tian Y. Modi V. Global trends in urban electricity demands for cooling and heating.Energy. 2017; 127: 786-802Crossref Scopus (73) Google Scholar analyzed the impact of this trend on both peak and annual energy demand globally. In terms of heating, it is expected that due to cheaper renewable electricity generation, heating in developed countries will switch to heat pumps.2Editorial The heat is on.Nat. Energy. 2016; 1: 16193Crossref Scopus (7) Google Scholar Waite et al. pointed out that in many subtropical cities, heating is being delivered by resistive heating, which will further exacerbate electricity generation and delivery concerns. Global warming is accelerated by refrigerants used in air conditioners (ACs) and heat pumps; these refrigerants have global warming potential more than 2,000 times that of CO2.6Velders G.J. Fahey D.W. Daniel J.S. McFarland M. Andersen S.O. The large contribution of projected HFC emissions to future climate forcing.Proc. Natl. Acad. Sci. U. S. A. 2009; 106: 10949-10954Crossref PubMed Scopus (246) Google Scholar Although there are active research and policy efforts to reduce the high global warming potential of refrigerants, the overall market growth of ACs and heat pumps is expected to increase dramatically, as mentioned above. The contribution from these refrigerants to greenhouse gas (GHG) emissions will be significantly more than 10% of total GHG emissions in the future.6Velders G.J. Fahey D.W. Daniel J.S. McFarland M. Andersen S.O. The large contribution of projected HFC emissions to future climate forcing.Proc. Natl. Acad. Sci. U. S. A. 2009; 106: 10949-10954Crossref PubMed Scopus (246) Google Scholar This confluence of factors brings building heating and cooling energy loads to the forefront of efforts to meet GHG emission reduction targets. Given the magnitude of the problem, a new way to think about energy use and energy savings in buildings is needed. The R&D community has traditionally concentrated its efforts on (1) improving the energy efficiency of the technologies and equipment that supply thermal energy and (2) reducing heat transfer across the building thermal envelope through conduction as well as air infiltration. For example, efforts have focused on optimizing the coefficient of performance (COP) of ACs/heat pumps and the annual fuel utilization efficiency (AFUE) of residential furnaces. Improving COP and performance of ACs/heat pumps have captivated both fundamental scientists and practitioners for decades, as the COP theoretical limit is governed by the Carnot limit and is deeply rooted in the second of law of thermodynamics.7Briley G. A history of refrigeration.ASHRAE J. 2004; 46: S31-S34Google Scholar Similarly, using the first law of thermodynamics as a benchmark, the R&D community has been able to increase the AFUE of natural-gas-burning furnaces to greater than 90%, meaning that more than 90% of the enthalpy of natural gas can be transferred into the building as heat.8Wheeler J. The 1990s: technological breakthroughs and higher efficiencies.Air Cond. Heat. Refrig. News. 2001; 214: 78https://www.achrnews.com/articles/87036-the-1990s-technological-breakthroughs-and-higher-efficienciesGoogle Scholar However, we believe one area that needs further investigation is whether there is a theoretical minimum building thermal load that the energy supply technology must provide for occupant comfort. Analogous to how the Carnot limit provides guidance to heat pump manufacturers on the opportunity for energy efficiency improvements relative to the theoretical limit, the theoretical minimum building thermal load can provide guidance to building designers on the energy reduction opportunity relative to current building thermal loads, while still providing a comfortable environment for people. Although a demand-side minimum theoretical load has not been established in the literature, there has been a significant progress in modeling and technologies to reduce whole-building energy demand.9Langevin J. Harris C.B. Reyna J.L. Assessing the potential to reduce U.S. Building CO2 emissions 80% by 2050.Joule. 2019; 3: 2403-2424Abstract Full Text Full Text PDF Scopus (33) Google Scholar, 10Cullen J.M. Allwood J.M. Borgstein E.H. Reducing energy demand: what are the practical limits?.Environ. Sci. Technol. 2011; 45: 1711-1718Crossref PubMed Scopus (89) Google Scholar, 11DeBoeck L. Verbeke S. Audenaert A. De Mesmaeker L. Improving the energy performance of residential buildings: a literature review.Renew. Sustain. Energy Rev. 2015; 52: 960-975Crossref Scopus (143) Google Scholar, 12U.S. Department of EnergyChapter 5. Increasing efficiency of building systems and technologies. September 2015.in: Quadrennial technology review: an assessment of energy technologies and research opportunities. 2015https://www.energy.gov/sites/prod/files/2017/03/f34/qtr-2015-chapter5.pdfGoogle Scholar The central premise of these studies is to achieve deep energy use reductions by minimizing undesired interactions between the building and the outside environment and by supplying energy to the building at efficiencies approaching thermodynamic limits. In general, this includes maximizing equipment efficiency, improving building envelopes, and implementing advanced control systems. For example, the U.S. Department of Energy (DOE) estimates that operating equipment at their thermodynamic limit (i.e., Carnot limit) and perfectly sealing and insulating building envelopes would lead to a 59% and 62% reduction in U.S. commercial and residential building energy consumption, respectively, depending on the thermal resistance of the envelope and other characteristics.13U.S. Department of EnergyQuadrennial technology review 2015.in: Chapter 5 supplemental information. 2015Google Scholar Purely from a theoretical point of view, modeling thermal demand based on solving the coupled heat transfer (conduction, convection, and radiation) equation has been achieved through many sophisticated analytical and numerical models over the past 50 years.14Harish V.S.K.V. Kumar A. A review on modeling and simulation of building energy systems.Renew. Sustain. Energy Rev. 2016; 56: 1272-1292Crossref Scopus (303) Google Scholar These models have been used in the development of various building codes/standards such as ENERGY STAR®, ASHRAE 90.1, the International Energy Conservation Code, and Title 24 in California. The focus of these studies has been to understand the impact of envelope thermal properties on reducing whole-building demand. However, the basic question of the minimum theoretical thermal load in a building with a given set of parameters, such as building type, properties (e.g., thermal insulation of the envelope, solar heat gain coefficient of windows), and ambient conditions, has not been answered. In this perspective, we establish a framework for determining the theoretical minimum thermal load (TMTL), which still maintains occupant comfort in buildings. In doing so, we identify a physical limit for reduced thermal energy use. Knowledge of this limit is used to highlight technology opportunities that can have a dramatic influence on the future of one of the most important and fastest growing energy services worldwide: space conditioning in buildings. The concept of the TMTL is important for both energy technology researchers and practitioners. For example, a material scientist currently developing next-generation thermal textile materials for personalized cooling/heating will now have a framework to determine the performance metrics required to approach the TMTL. Additionally, energy system and building designers will be able to design buildings with thermal loads that approach the TMTL (e.g., distributed instead of centralized heating, ventilating, and air-conditioning [HVAC] systems). A framework for developing a theoretical limit can be determined by first considering the primary purpose for delivering thermal energy in buildings—to provide comfort to occupants. However, the current paradigm requires conditioning the entire/partial building space to meet individual occupant comfort needs (see Figure 1). A theoretical limit would focus on only providing thermal energy sufficient to meet the needs of the occupant, which can be defined as the minimum thermal energy required to maintain the human body at 37°C for a given set of boundary conditions and thermal properties. In this framework, no thermal energy is actively supplied nor removed from the ambient building space via an HVAC system. Fundamentally, thermal energy is only needed to maintain the human body at a natural and healthy temperature. We define this as TMTL. Human thermal comfort is a well-studied topic15Van Hoof J. Forty years of Fanger’s model of thermal comfort: comfort for all?.Indoor Air. 2008; 18: 182-201Crossref PubMed Scopus (407) Google Scholar and serves as the basis for widely used building standards like the ANSI/ASHRAE Standard 5516ASHRAEANSI/ASHRAE Standard 55–2016: Thermal Environmental Conditions for Human Occupancy.2016Google Scholar and ISO 7730.17International standard ISO 7730, Third Edition. (2005-11-15).Google Scholar The standard is fundamentally based on an energy balance around people; energy transfers are calculated based on metabolism, clothing and activity levels, humidity, and building temperature. The resulting calculation, combined with statistical correlations about people’s perception of comfort, provides a method to assess whether the prescribed conditions are “comfortable” for an average person. However, the standard does not directly address the amount of energy that must be added or removed to turn an “uncomfortable” set of conditions into a “comfortable” set of conditions. In practice, achieving comfort is typically accomplished by changing the building conditions themselves (most often the temperature) to create a “comfortable” environment. This means that the whole or part of the building must be cooled or heated, which leads to thermal conditioning of the physical building as well as its contents, including unoccupied parts of the building. This results in supplying much more thermal energy than is minimally required to keep occupants comfortable. Recent research providing more localized heating and cooling18U.S. Department of Energy Advanced Research Projects Agency – Energy (ARPA-E)Delivering efficient local thermal amenities (DELTA).https://arpa-e.energy.gov/technologies/programs/delta#:∼:text=Delivering%20Efficient%20Local%20Thermal%20Amenities&text=ARPA%2DE's%20DELTA%20projects%20include,reductions%20in%20greenhouse%20gas%20emissionsDate: 2014Google Scholar is an initial step toward minimizing thermal energy while maintaining comfort. However, the concept of a theoretical minimum, or achievable energy minimum for localized heating and cooling while maintaining comfort, has not been addressed. The purpose of the TMTL is to determine a theoretical minimum thermal energy for localized heating and cooling while maintaining personal comfort. Thermal comfort is still a hotly debated topic;19Wang Z. de Dear R. Luo M. Lin B. He Y. Ghahramani A. Zhu Y. Individual difference in thermal comfort: A literature review.Build. Environ. 2018; 138: 181-193Crossref Scopus (197) Google Scholar,20Kingma B. van Marken Lichtenbelt W. Energy consumption in buildings and female thermal demand.Nature Clim. Change. 2015; 5: 1054-1056Crossref Scopus (105) Google Scholar however, the basis for our framework is the model used by ANSI/ASHRAE Standard 55 and ISO 7730, which provide recommended building set point temperatures based on the classic Fanger Model,21Fanger P.O. Calculation of thermal comfort: introduction of a basic comfort equation.ASHRAE Trans. 1967; 73: III.4.1-III.4.20Google Scholar a widely used methodology for estimating thermal comfort both in the US and internationally. In our framework for the calculation of the TMTL, we make the following assumptions:(1)Occupants are inside the building.(2)Heating and cooling equipment of the buildings are turned off.(3)Internal heat gain from other equipment such as light bulbs and refrigerators are included in the calculation of building temperature (See Supplemental Information for details).(4)The energy balance on a person is carried out using a localized control volume, as shown in Figure 2. With the heating and cooling equipment off, the building temperature (TBuilding) and relative humidity (RHBuilding) change according to fluctuating ambient temperature and relative humidity, as well as internal gains and other energy transfers between the building and the environment (Figure 2). For this analysis, the building temperature is calculated on an hourly basis for different climate zones (see Supplemental Information for details), using the building energy modeling tool EnergyPlus™.22Crawley D. Lawrie L. Pedersen C. Winkelmann F. Energy plus: energy simulation program.ASHRAE J. 2000; 42: 49-56Google Scholar In the energy balance on the localized control volume (Figure 2), various types of heat losses and gains are calculated based on standard equations in ANSI/ASHRAE Standard 55 and ISO 7730. Pertinent heat loss and gain components per unit area of the body in the localized control volume based on Fanger model23Fanger P.O. Thermal Comfort: Analysis and Applications in Environmental Engineering. McGraw-Hill, 1972Google Scholar are QSkin, QRespiration_L, QRespiration_D, QSweat, QRadiation, and QConvection, which are defined as follows:(1)Heat loss (QSkin) due to water diffusion through the skin is given by QSkin=hwm(psk−pb), where hw is the latent heat of vaporization of water, m the permeance coefficient of the skin, psk the saturated vapor pressure at skin temperature and pb is the vapor pressure inside the building which can be calculated from TBuilding and RHBuilding.(2)Breathing leads to latent (QRespiration_L) and sensible (QRespiration_D) heat loss from the body. Latent heat loss is given by QRespiration_L=hwV(Wex−Win), where V is the pulmonary ventilation rate, Wex is the humidity ratio of the expiration air, and Win is the humidity ratio of the inspiration air (depends on TBuilding and RHBuilding). Similarly, sensible heat loss is determined by QRespiration_D=cpV(Tex−Tin), where cp is the specific heat of dry air at constant pressure, and Tex and Tin are the temperatures of the expiration and inspiration air, respectively. In our analysis, we define Tin = TBuilding.(3)Heat loss due to sweating (QSweat) for thermal comfort is given by QSweat=0.42(M−58.2), where M is the metabolic rate.(4)Heat loss/gain by radiation (Qr) from the clothed body is given by QRadiation=fefffclϵσ(Tcl4−Tmrt4), where feff is the effective radiation area factor (view factor), fcl is the ratio of surface area of the clothed body to the surface area of the nude body, ϵ the emissivity of the outer surface of clothing, Tcl the temperature of the outer surface of the clothing, and Tmrt is the mean radiant temperature.(5)Heat loss/gain by convection (Qc) from the clothed body is given by QConvection=fclhc(Tcl−TBuilding), where hc is the convective heat transfer coefficient. Note that Tcl is dependent on the thermal resistance of clothing and can be calculated by equating the energy flow between the skin and clothing to the energy flow between clothing and the ambient. Assuming thermal equilibrium, the skin temperature (Tsk), measured in °C, required for thermal comfort is given by24Doherty T.J. Arens E. Evaluation of the physiological bases of thermal comfort models.ASHRAE Trans. 1988; 94: 1371-1385Google ScholarTsk=35.7−0.0275M(Equation 1) and energy conservation for the control volume shown in Figure 2 leads to the thermal neutrality equation:QMET−QSkin−QRespiration_L−QRespiration_D−QSweat−QRadiation−QConvection+QTMTL=0(Equation 2) where QMET is the metabolic heat generation ( = M) and QTMTL is the energy theoretically added or removed to the localized control volume to maintain thermal comfort. It should be noted that in Fanger’s original formulation, QTMTL does not exist making it equal to 0 and thermal neutrality is maintained only by adjusting TBuilding and RHBuilding (strategy used in current practice). In our formulation shown in Equation 2, TBuilding and RHBuilding are floating parameters decided by the characteristics of the building. Furthermore, thermal neutrality is maintained by adding or removing QTMTL from the localized control volume shown in Figure 2. Addition of QTMTL to the localized control volume and treating TBuilding and RHBuilding as floating parameters is the main difference between our formulation and Fanger’s formulation. A positive value of QTMTL means that heat is added to the person (i.e., heating), and a negative value means that heat is removed (i.e., cooling). Equation 2 assumes a complete thermal balance. However, standard practices such as ANSI/ASHRAE 55 are based on Fanger’s predicted mean vote (PMV) methodology that instead determines a range of conditions where thermal comfort is met. ANSI/ASHRAE 55 defines a building space as “comfortable” when the PMV ranges between -0.5 and 0.5. In this range, the PMV methodology predicts 80% of building occupants will be comfortable. When PMV = 0, thermal neutrality is met (i.e., Equation 2); however, for other values of PMV there is a net thermal load (L) on the body. As a result, the thermal balance for the localized control volume that incorporates QTMTL is given byL=M−QSkin−QRespirationL−QRespirationD−QSweat−QRadiation−QConvection+QTMTL,(Equation 3) where PMV is related to L byPMV=TS×L(Equation 4) and TS is the thermal sensation coefficient. Based on data collected on human subjects, Fanger empirically determined TS as:TS=0.303×e(−0.036M)+0.028.(Equation 5) From Equations 4 and 5, L is calculated for PMV = −0.5 and 0.5 for various values of metabolic rate, M, which sets a range for acceptable thermal comfort conditions. Consequently, thermal comfort can now be maintained by adjusting QTMTL or TBuilding and RHBuilding to meet the range of thermal load conditions as defined in Equation 3. In standard practice, thermal comfort is maintained by adjusting TBuilding and RHBuilding through centralized cooling/heating of the whole building or large control volume (e.g., room), and localized thermal control is not considered (i.e., QTMTL = 0), leading to significantly higher thermal load than is necessary to achieve thermal comfort. Alternatively, QTMTL can be adjusted while leaving TBuilding and RHBuilding constant; details on how QTMTL is iteratively calculated are given in the Supplemental Information. Note that the PMV methodology leads to a less stringent requirement of QTMTL as compared with the thermal equilibrium defined by Equation 2. This is because 0.5 < PMV < 0.5 ensures 80% of occupants are comfortable, while Equation 2 ensures15Van Hoof J. Forty years of Fanger’s model of thermal comfort: comfort for all?.Indoor Air. 2008; 18: 182-201Crossref PubMed Scopus (407) Google Scholar ∼95% of the occupants are comfortable. In this perspective, we have chosen to use the PMV methodology to be consistent with existing widely used standards. Although we have chosen Fanger’s PMV method, we acknowledge the range of debate on thermal comfort; therefore, it warrants some discussion. Equation 5 is empirical as well the relationship between PMV and the predicted percentage of dissatisfied people. The current PMV model is based on data collected on students and people in sedentary activity,15Van Hoof J. Forty years of Fanger’s model of thermal comfort: comfort for all?.Indoor Air. 2008; 18: 182-201Crossref PubMed Scopus (407) Google Scholar whereas real buildings involve much larger and more diverse samples of occupants. Fanger also found that women were more sensitive to fluctuations in optimum temperature than men. For precise comfort assessments, a precise measurement of metabolic rate is needed because the empirical coefficient in TS (Equation 5) depends on the value of metabolic rate, M, used to fit the data. In a recent paper, Kingma et al.20Kingma B. van Marken Lichtenbelt W. Energy consumption in buildings and female thermal demand.Nature Clim. Change. 2015; 5: 1054-1056Crossref Scopus (105) Google Scholar concluded that M for women can be off by as much as 30% when compared with the values recommended in ASHRAE for certain activities. Furthermore, there are also questions on whether the PMV model is applicable to naturally ventilated residential buildings.25Rupp R.F. Kim J. Ghisi E. de Dear R. Thermal sensitivity of occupants in different building typologies: the Griffiths constant is a variable.Energy Build. 2019; 200: 11-20Crossref Scopus (30) Google Scholar,26Peeters L. de Dear R. Hensen J. D’haeseleer W. Thermal comfort in residential buildings: comfort values and scales for building energy simulation.Appl. Energy. 2009; 86: 772-780Crossref Scopus (248) Google Scholar According to ISO 7730, the PMV model cannot be used without error for naturally ventilated buildings, because it only partly accounts for thermal adaptation to the indoor environment.15Van Hoof J. Forty years of Fanger’s model of thermal comfort: comfort for all?.Indoor Air. 2008; 18: 182-201Crossref PubMed Scopus (407) Google Scholar Therefore, a model of adaptive thermal comfort has been proposed for naturally ventilated buildings, which relates the neutral temperature indoors to the monthly average temperature outdoors.27de Dear R. Brager G.S. Developing an adaptive model of thermal comfort and preference de dear and Brager.ASHRAE Trans. 1998; 104: 1Google Scholar Van Hoof15Van Hoof J. Forty years of Fanger’s model of thermal comfort: comfort for all?.Indoor Air. 2008; 18: 182-201Crossref PubMed Scopus (407) Google Scholar has provided a comprehensive review of controversy related to the PMV model by Fanger. Furthermore, these correlations were also developed for centralized cooling/heating systems as compared with the localized control volume shown in Figure 2. Given the existing debate on PMV, if someone wanted to remove the empiricism and other related concerns inherent in the PMV methodology, the TMTL could still be calculated based on the thermal neutrality Equation 2, because it is derived from first principles without any empiricism. It is worth noting that unlike the Carnot limit, which only depends on the temperature of the cold and hot reservoirs, TMTL depends on the properties of various components, such as clothing resistance and convection heat transfer coefficient. It is also dependent on the building’s characteristics and design, since TBuilding and RHBuilding are a function of building characteristics. Therefore, it is important to remember that boundary conditions and thermal properties must be specified to provide proper context for TMTL. As a result, TMTL is the theoretical minimum thermal load for a given set of boundary conditions and properties. The parameters used to calculate QTMTL for the United States are given in Table 1; these values are representative of a person quietly seated in an indoor environment for summer (clo = 0.5) and winter (clo = 1.0). These values are based on ANSI/ASHRAE Standard 55. Parameter values given in Table 1 are considered nominal values. We have also performed a sensitivity study of QTMTL for various parameters such as clo, met, and air velocity. A flow chart for the calculation of TMTL