Fundamentals Handbook Research Articles

Innovative airspace reflective tool for different building applications, part I: tool development

The current methods such as ISO-6946 provide thermal resistances for horizontal and vertical enclosed airspaces. Additionally, hot-box results from the U.S. National Bureau of Standards (now NIST) were used to provide the thermal resistances in the ASHRAE Handbook of Fundamentals (HOF) for horizontal, vertical and 45-degree angle airspaces. The thermal resistances in the HOF are available for three temperature differences and four values for mean temperatures. Thus, thermal resistances in the HOF include a limited number of climatic conditions and construction techniques that exist around the globe. The effect of the aspect ratio on airspace thermal resistances is not included in ISO-6946 or the ASHRAE HOF. Many studies including this one have shown that the aspect ratio of enclosed airspace has a significant impact on thermal resistance. This has motivated the development of a tool for accurately determining thermal resistances of enclosed airspaces for a wide variety of conditions. In this paper, a validated numerical model has been used to obtain the necessary thermal resistances values (about one million) of various enclosed airspaces, subjected to different operating conditions. Thereafter, the calculated thermal resistances were used to develop a tool, called “Airspace Reflective Tool, ART”. The capabilities of this tool for evaluation, optimization and design are explored in this paper.

Innovative airspace reflective tool for different building applications, part II: parametric study

Enclosed airspaces of different dimensions and inclinations that exist in buildings include double-pane windows, curtain walls, skylight devices, and reflective insulation assemblies for walls and roofing systems. Evaluating the energy performance of buildings requires accurate determination of the thermal resistance of enclosed airspaces in different climates. The parameters that affect enclosed airspace thermal resistances include the physical properties of air, the temperatures and emittances of airspace surfaces, airspace dimensions, and heat-flow direction. The Airspace Reflective Tool (ART) was developed for determining the thermal resistances of enclosed airspaces for a wide variety of conditions. In this article, for enclosed airspaces of various orientations and heat flow directions, the ART has been used to conduct a parametric study to quantify the effect on thermal resistance of: effective emittance, operating conditions such as temperature, orientation, dimensions (aspect ratio) and heat flow-direction. The calculated thermal resistances from the ART were compared with those in the ASHRAE Handbook of Fundamentals or calculated using ISO-6946 that are currently being used to obtain thermal resistances of enclosed airspaces and show the importance of the factors being considered.

Thermal Resistance of 30° Sloped, Enclosed Airspaces Subjected to Upward Heat Flow

Heat transmission across an enclosed space is determined by the type of filling gas, the temperatures and long-wave emissivities of all surfaces that define the space, and the heat flow direction. The ASHRAE Handbook of Fundamentals provides the thermal resistances (R-values) of enclosed airspaces with only five effective emittance values (E) for vertical, horizontal, and 45° airspaces. ASHRAE R-values do not include the case of 30° sloped airspaces. In addition, ASHRAE R-values ignore the impact of the airspace aspect ratio (A) on R-values. However, many previous studies, as well as this study, have shown that A can have a significant effect on the R-value. Previously, correlations were developed for determining the R-values for vertical (90°) airspaces subjected to horizontal heat flow, horizontal (0°) airspaces subjected to up and down heat flow, 45° airspaces subjected to up and down heat flow, and 30° airspaces subjected to downward heat flow. To the authors’ knowledge, no such correlation existed for determining the R-value of 30° airspaces subjected to upward heat flow, which is developed in this paper. The potential increase in R-value by placing a thin layer of varied emittance on both sides in the middle of the airspace was also considered. Architects and building designers can use the developed correlation to compute the R-values of airspaces of various values for A and E and various operating conditions. This correlation along with the previous correlations can be included in the current energy models (e.g., EnergyPlus, ESP-r, DOE, and Design Builder).

Advanced Modeling of Enclosed Airspaces to Determine Thermal Resistance for Building Applications

Enclosed airspaces to reduce heat flow have been recognized for well over 100 years. Airspaces with one or more reflective surfaces define reflective insulation (RI) assemblies, a product type used in walls, roofs, windows with multiple panes, curtain walls and skylights. The thermal resistance (R value) of airspaces depends on the emittance of all surfaces, airspace dimensions and orientation, heat flow direction and surfaces temperatures. The modeling of RI now includes CFD coupled with radiation to quantify the total heat transfer. This study compares a validated model for airspace R values with existing methods such as ISO 6946 and hot-box results that provide the R values in the ASHRAE Handbook of Fundamentals. The existing methods do not include an airspace aspect ratio. This study showed that the aspect ratio can impact the R value by a factor of two. The impact of aspect ratio was calculated for double airspaces variation such as that for single airspaces. The present calculations are two-dimensional and also consider all the bounding airspace surfaces, while previous methods are one-dimensional and do not include surface temperature variations or detailed radiative transport.

Practical correlation for thermal resistance of 45° sloped-enclosed airspaces with upward heat flow for building applications

Assessing the energy performance of building components with enclosed airspaces requires accurate determination of the thermal resistance ( R-value) of the airspaces. The R-value of enclosed airspace depends on its size and orientation, direction of heat transfer through the airspace, and temperatures and emissivities of all surfaces that define the airspace. In previous studies, practical correlations were developed to determine the R-values for vertical enclosed airspaces, horizontal enclosed airspaces with upward heat flow and downward heat flow, and 30° and 45° sloped-enclosed airspaces with downward heat flow. However, to the authors’ best knowledge, there is no such practical correlations available to determine the R-values for wide ranges of dimensions and operating conditions for 30° and 45° sloped-enclosed airspaces with upward heat flow. This paper focused on the thermal performance of 45° sloped-enclosed airspaces with upward heat flow, and the predicted R-values were compared with the R-values provided in ASHRAE Handbook of Fundamentals at different conditions. The dependence of the R-value on the aspect ratio of the enclosed airspaces was also investigated. As well, considerations were given to quantify the potential increase in the R-value of enclosed airspace when a thin sheet having different values of emissivity on both sides was placed in the middle of the airspace. The results showed that depending on the value of the effective emittance and the thickness of the airspace, the R-value could be tripled by incorporating thin a sheet in the middle of the enclosed airspace. Finally, practical correlation were developed to determine the effective R-values of 45° sloped-enclosed airspaces with upward heat flow for wide ranges of aspect ratio, temperature difference across the airspace, mean temperature, and effective emittance. The results showed that the calculated R-values using this correlation were in good agreement with the predicted R-values.

Energy Efficiency Calculation and Air Handling Unit Design Based on Cooling Load Capacity at MASTEK Mosque

The rate of development growth in Indonesia has resulted in an increase of energy demand. In addition, most power generation systems still use fossil fuels of nearly 50%, in other words this fuel can run out within the next 18 years. The electricity needs in the building come from the use of lighting, computers, office equipment, heating, ventilation, air conditioning and also air conditioning systems (AHU). This paper aims to investigate energy efficiency based on cooling load capacity to reduce energy use and design an air conditioning system. A well-designed HVAC system will have a great impact on indoor air conditions. Room comfortability will be realized throughout the year and also the outside environment if cared for properly according to the procedures of the American Society of Heating, Refrigerating, and Air Conditioning Engineers (ASHRAE) Handbook of Fundamentals. Mastek Mosque required 167,151,241 Btu/h. The ducting design for central air conditioning systems uses 12 x 8 pipes for the main ducting and 10 x 6 for the ducting suction with 12 nozzles and 10 x 6 and 10 x 8 return ducting sizes. This system has the advantages of efficient, silent cooling and increased comfort for prayer.

The fundamental handbook for analytical spectroscopy. Release of the second edition of ‘Chemometrics in spectroscopy’ by Howard Mark and Jerry Workman, Jr. and its impact on the spectroscopic community

In the last year, an event of a marked significance for the spectroscopic community had taken place. The second edition of Chemometrics in spectroscopy, by Howard Mark and Jerry Workman, Jr. has been published. In relation to its first edition, this plausibly the most renowned chemometric-based tutorial book has been significantly expanded with new content covering the substantial progress that has occurred in the field over the last decade. The comprehensive tutorial has been augmented by both the revised and newly added sections exploring the most recent hot topics in analytical spectroscopy. These include, but are not limited to, aspects directly and indirectly corresponding to calibration and spectral transfer, principal components, regression models, classical least squares, units of measure in spectroscopy, clinical data analysis, and other highly relevant topics. In the present short review, we sketch the features and improvements introduced in the re-released epic handbook for chemometricians and spectroscopists, providing the reader with a summary of essential information helpful in deciding whether this book should land in his library shelf.

Equipment power consumption and load factor profiles for buildings’ energy simulation (ASHRAE 1742-RP)

In most office buildings, plug loads are one of the main contributors to the building’s overall energy consumption and therefore need to be considered in load calculations. The heat gains from different office equipment deviate from their peak values due to both user and equipment behavior. The variation in the heat gains of different office equipment can be presented by average weekday and weekend power consumption profiles. These power consumption profiles serve as an input to the energy simulation programs for the purpose of load calculation. In this article, weekday and weekend power consumption profiles are developed for different office equipment. In addition, load factor profiles are developed for some typical office spaces and are compared against the peak load factors listed in the ASHRAE Handbook of Fundamentals (2017). Recommendations for the minimum number of testing days necessary to obtain the equipment peak heat gain are also made.

Measurement of solar factor of glazing and shading devices using a solar calorimeter

This paper reports an evaluation of the accuracy of a solar calorimeter for the determination of the solar factor of glass samples and window shading devices. The first step of the assessment consisted of the use of internationally recognized mathematical procedures: ISO 9050 and the ASHRAE Fundamentals Handbook. The results obtained with the solar calorimeter for three types of glass and four solar protection devices were compared with the theoretical values given in these standards. In the second step of the assessment, the measurement results were compared with those obtained using the computer simulation program WINDOW7. Based on the results, it can be observed that the solar factor for the 6 mm clear glass showed a difference of less than 6% when compared to theoretical values obtained from standards. For 6 mm green glass and 8 mm silver glass the differences in relation to the theoretical results were close to 17% and 33%, respectively. The results obtained from WINDOW7 were found to be significantly different for the external shading (up to 40%). However, it was noted that the WINDOW7 results were closer to the values measured with the solar calorimeter than to the theoretical results given in the ASHRAE Handbook Fundamentals.

Experimental methodology and results for heat gains from various office equipment (ASHRAE RP-1742)

Recent advances in building envelope systems and fenestration have resulted in improved building envelopes, reducing both the air leakage and the heat transfer with the surroundings. At the same time, the power consumption of the heating, ventilation, and air-conditioning systems is reduced due to the improvement in their energy efficiency. This leaves plug and miscellaneous loads as one of the main contributors to the overall energy consumption of buildings, accounting for up to 50% of the building's total energy consumption (NBI 2012). As a result of this, it is important to accurately assess the energy consumed by plug loads as overestimation can result in oversized HVAC systems increasing capital and operating cost while undersized systems result in thermal comfort problems for occupants. The ASHRAE Fundamental Handbook heat gain tables were last updated in 2009. Since then, equipment's power management capabilities improved tremendously and many new types of office equipment were introduced. ASHRAE, therefore, funded research project RP-1742 to update heat gain tables. The current article outlines the experimental methodology used in RP-1742 to measure heat gain values for different office equipment. The peak heat gain values for various office equipment are listed in different tables in the result section of the article and will be included in the 2017 ASHRAE Fundamentals Handbook.

Update to office equipment diversity and load factors (ASHRAE 1742-RP)

The current article gives an overview of methods used for the determination of updated recommended diversity factors for various office equipment. The update to the diversity factors was required because of the introduction of new types of office equipment, such as laptop docking stations, and both increased equipment performance as well as improved power management. The present study, in particular, investigates the effects of the number of tested pieces of equipment as well as the interval duration for data reduction. Analysis and results on the effect of the different number of tested pieces of equipment and averaging intervals on the diversity factor are presented. Load factors for various office types are calculated using heat gain and diversity factor values of various office equipment. These updated office load factor values are included in the 2017 edition of the ASHRAE Fundamentals Handbook are found to be 10% to 33% lower than those published in the previous ASHRAE Fundamentals Handbook (2013). The article also presents recommendations for minimum equipment count required to determine diversity factors for various office equipment in a typical office space. For most tested equipment, 8 to 9 pieces of equipment tested in parallel appears to give acceptable results, for example, ±6% of the predicted value for diversity factor within the predicted 95% confidence interval.

Measurements of grease emission and heat generation rates of electric countertop appliances (RP-1631, part 1)

The main objectives of this research were to improve the understanding of the characteristics of the grease emission and heat generation from electric countertop appliances, and to determine the amount of grease particulate/vapor production as well as sensible and latent heat gains from 20 commercial electric countertop appliances under cooking conditions. The grease particulate and vapor were captured by a Type II hood, and the concentrations were measured using EPA Method 5 in the exhaust duct under an exhaust flowrate of 0.24 m3/s (500 cfm). An energy balance protocol was used to determine the heat generation of these appliances during both idle and cooking conditions. The results indicate that the rate of grease particle and vapor emissions concentration for the 20 appliances tested ranged from 0.12 to 8.27 mg/m3. Only three appliances, the hot plate range, rapid cook oven (cooking with chicken wings or pizzas), and hot dog roller, generated more than 5 mg/m3 of grease at 0.24 m3/s (500 cfm) exhaust flow rate (i.e., 1.18 mg/s in emission rate), which is the threshold of the requirement to use a Type I hood by ASHRAE Standard 154 and UL 710B. The grease particulate matter caught by the EPA Method 5 was itemized by weight and analyzed as follows: filter catch, probe (acetone) catch, impinger (DI water) catch, and solvent extract (dichloromethane). The cooking sensible convective heat had a similar trend as the cooking energy consumption rate, except for the deep fryer and steamer countertop. However, the cooking latent convective heat depended more on the food material and whether or not steam was used to heat the food. The largest cooking latent convective heat was given by the steamer countertop, and the lowest was given by the hot plate and rice cooker. The effects of the duration of the test and the cooking time on the test results were also studied. It was found that three replicate tests with about 40 minutes each could generate similar reults as a 4-hour long test, hence a longer test duration (such as the 8-hour cooking test specified in UL 710B) may not be necessary. The study provides previously unavailable data of grease emission and heat generation rates for the design and analysis of kitchen spaces with countertop electrical appliances. They are used to update the current Table 5A; Recommended rates of radiant and convective heat gain from unhooded electric appliances during idle (ready to cook) conditions of chapter 18 in the ASHRAE Handbook of Fundamentals.

Content and teaching of Platonism in the second century

The aim of this paper is to reconstruct the content and teaching methods of Platonism in the second century. For this purpose, the Didaskalikos of Alcinous will be the primary instrument that we use to define the origin, influences and convergences of Middle Platonism, along with other parallel texts in timing and content. The survival of this entire work offers us an excellent opportunity to reconstruct accurately the general nature of Middle Platonism as one of the most crucial – and at the same time one of the most unknown – times in the development and expansion of Platonism. The works of Apuleius, Arius Didymus, Numenius of Apamea, Anonymous comments of Theaetetus and Antiochus of Ascalon will help us to complete the content of Didaskalikos as the fundamental handbook of Platonism in the second century. Keywords: Alcinous, Didaskalikos , Middle Platonism, Albinus, handbook.

Prediction Equations for Energy Consumption Through Surveys on Energy Consumption in Apartment Buildings

This study presents energy consumption prediction equations developed by conducting multiple regression analyses of data collected in surveys of actual states of energy consumption in apartment buildings in their operational stage. Surveys of actual states of average energy consumption per unit show that 1) the largest component of energy consumption is room heating, followed by electricity, hot water supply, and gas, in that order; 2) energy consumption increases with household area; 3) among exposures, energy consumption is highest in households facing east or northeast and lowest in those facing south or southwest; 4) among height types, energy consumption is highest in super-high-rise apartment buildings (50 stories or higher), followed by semi-super-high-rises, high-rises, and medium-high-rises, in that order; and 5) among plan types, tower-type apartment buildings use approximately 17% – 20% more energy than flat types. The goodness-of-fit criterion stated in the 2009 ASHRAE Fundamentals Handbook (SI) Edition is shown to be satisfied for the equations presented in this paper for the prediction of energy consumption of apartment buildings in their operational stage. These equations were developed through multiple regression analysis using the areas and heat transmission coefficients of structures as independent variables and using energy consumption as the dependent variable.

Practical correlation for thermal resistance of horizontal enclosed airspaces with downward heat flow for building applications

The 2009 ASHRAE Handbook of Fundamentals (Chapter 26) provides a table that contains the thermal resistances (R-values) of enclosed airspaces for different values of airspace thickness, effective emittance, mean airspace temperature, and temperature differences across the airspace. This table is extensively used by modelers, architects, and building designers in the design for thermal resistance of building enclosures. The effect of the airspace aspect ratio (length/thickness) on the R-value is not accounted for in the ASHRAE (American Society of Heating, Refrigerating and Air-Conditioning Engineers) table. However, in previous studies, it was shown that the aspect ratio of the airspace can affect its R-value. In this article, the previous studies by the author who focused on determining the R-value for vertical enclosed airspaces and horizontal enclosed airspace under upward heat flow condition are extended to investigate the effect of the aspect ratio on the R-value of horizontal enclosed airspaces under a downward heat flow condition for different airspace thicknesses and having a wide range of values for effective emittance, mean temperature, and temperature differences across the airspaces. The R-values predicted from numerical simulation are compared with those provided in the ASHRAE table. Considerations were also given to investigate the potential increase in the R-values of enclosed airspaces when a thin sheet is placed horizontally in the middle of the airspace and whose surfaces have different values of emissivity. Thereafter, practical correlation was developed for determining the R-values of horizontal enclosed airspaces for future use by modelers, architects, and building designers. The simplicity of this correlation derived for horizontal airspaces under downward heat flow condition together with those that were previously developed for vertical airspaces and horizontal airspaces under upward heat flow condition suggests that these correlations could be included in the ASHRAE Handbook of Fundamentals.

Practical correlation for thermal resistance of 45° sloped enclosed airspaces with downward heat flow for building applications

A table is provided in the 2009 ASHRAE Handbook of Fundamentals (Chapter 26) that contains the thermal resistances (R-values) of enclosed airspaces. The ASHRAE table provides the R-values for enclosed airspaces of different thicknesses, effective emittances, mean airspace temperatures, and temperature differences across the airspaces. This table is extensively used by modelers, architects and building designers in the design for the R-values of building enclosures. The effect of the airspace aspect ratio (length/thickness) on the R-value is not accounted for in the ASHRAE table. However, previous studies showed that the aspect ratio of the airspace can affect its R-value. In this paper, the previous studies that focused on determining the R-values for vertical enclosed airspaces and horizontal enclosed airspaces with upward and downward heat flow are extended to investigate the effect of the aspect ratio on the R-values of 45° sloped enclosed airspaces under downward heat flow for different airspace thicknesses and having a wide range of values for the effective emittance, mean temperature, and temperature differences across the airspaces. The predicted R-values are compared with those provided in the ASHRAE table. Considerations are also given to investigate the potential increase in the R-values of enclosed airspaces when a thin sheet is placed in the middle of the airspace and whose surfaces have different values of emissivity. Thereafter, practical correlation is developed for determining the R-values of 45° sloped enclosed airspaces for future use by modelers, architects and building designers. The simplicity of this correlation for the sloped enclosed airspaces along with those that were previously developed for vertical and horizontal airspaces suggests that these correlations could be included in the ASHRAE Handbook of Fundamentals.

Practical correlations for thermal resistance of horizontal enclosed airspaces with upward heat flow for building applications

The thermal resistance (R-value) of an enclosed airspace depends on the emissivity of all surfaces that bound the airspace, the size and orientation of the airspace, the direction of heat transfer through the airspace, and the respective temperatures of all surfaces that define the airspace. A table is provided in the 2009 ASHRAE Handbook of Fundamentals (Chapter 26) that contains the R-values of enclosed airspaces. The ASHRAE table is extensively used by modellers, architects and building designers in the design for thermal resistance of building enclosures. This table provides R-values for enclosed airspaces for different values of airspace thickness, effective emittance, mean airspace temperature, and temperature differences across the airspace. The effect of the airspace aspect ratio (length/thickness) on the R-value is not accounted for in the ASHRAE table. However, in previous studies, it was shown that the aspect ratio of the airspace can affect its R-value.In this paper, previous studies undertaken by the author that focused on determining the R-value for vertical enclosed airspaces and horizontal enclosed airspaces with downward heat flow are extended to investigate the effect of the aspect ratio on the R-value of horizontal enclosed airspaces under an upward heat flow condition for different airspace thicknesses and having a wide range of values for effective emittance, mean temperature, and temperature differences across the horizontal airspaces. The R-values predicted from numerical simulation are compared with those provided in the ASHRAE table. Considerations were also given to investigate the potential increase in the R-values of enclosed airspaces when a thin sheet is placed horizontally in the middle of the airspace and whose surfaces have different values of emissivity. Thereafter, practical correlations are developed for determining the R-values of horizontal enclosed airspaces for future use by modellers, architects and building designers. The simplicity of these correlations for horizontal airspaces with upward heat flow along with those that were previously developed for vertical airspaces and horizontal airspaces with downward heat flow suggests that these correlations could be included in the ASHRAE Handbook of Fundamentals.

Analysis of Heat Gain in Computer Laboratory and Excellent Centre by using CLTD/CLF/SCL Method

Performance of air conditioning system is closely related to heat gain that generated inside the particular room. The amount of heat that generated in the particular room is depend on several factors such as position of the room relative to solar orientation, wall material, electric appliances and number of human occupied in the room. In order to determine heat gain in a room, these parameters have considered and presented in this paper. The method of heat gain determination is using Cooling Load Temperature Differential (CLTD) and Cooling Load Factors (CLF) based on ASHRAE 1997 Fundamental Handbook and then verified by data provided by contractor of building. The case study of the present work is only focused on two rooms specifically Computer Laboratory Room and Excellent Centre Room in Faculty of Mechanical Engineering, University Malaysia Pahang. From this calculation, it has been obtained that the highest heat gain in Computer Laboratory Rom and in Excellent Centre Room is 20458.6 W and 33541.3 W respectively. The assessment of cooling capacity produced by air conditioning system showed that the air conditioning produced over cooling for 23.7 and 25.8 percent for Computer Laboratory and Excellent Centre rooms. Management should reduce the cooling capacity produced by the air conditioning in order to reduce energy consumption.

Practical correlations for the thermal resistance of vertical enclosed airspaces for building applications

Many parts of the building envelope contain enclosed airspaces. The thermal resistance (R-value) of an enclosed airspace depends on the emissivity of all surfaces that bound the airspace, the size and orientation of the airspace, the direction of heat transfer through the airspace, and the respective temperatures of all surfaces that define the airspace. The 2009 ASHRAE Handbook of Fundamentals (Chapter 26) provides a table that contains the R-values for an enclosed airspace. The ASHRAE table is extensively used by modelers, architects and building designers in the design of building enclosures. This table provides R-values for enclosed airspaces for different values of the thickness of the airspace, effective emittance, mean airspace temperature, and temperature differences across the airspace. The effect of the airspace aspect ratio (height/thickness of airspace) on the R-value is not included in the ASHRAE table. However, in a recent study on the R-value of reflective insulations using a numerical simulation model, it was shown that the aspect ratio of the airspace can affect the R-value of the enclosed airspace. The numerical simulation model used in this study had been benchmarked against experimental data obtained using two standard test methods: ASTM C-518 and ASTM C-1363.In this paper, a numerical simulation study was conducted, that was based on previous work focused on enclosed airspaces, to investigate the effect of the aspect ratio on the R-value of vertical enclosed airspaces of different thicknesses and having a wide range of values for effective emittance, mean temperature, and temperature differences across the airspace. The R-values predicted from numerical simulation are compared with those provided in the ASHRAE table. Considerations were also given to investigating the potential increase in R-values of enclosed airspaces when a thin sheet is placed vertically in the middle of the airspace and whose surfaces have different values of emissivity. Finally, practical correlations are developed for determining the R-values of an enclosed airspace for future use by modelers, architects and building designers. The simplicity of these correlations suggests that these could be included in the ASHRAE Handbook of Fundamentals.

A frequency domain estimation of wall conduction transfer function coefficients

This article describes a novel method to evaluate the series of wall thermal response factors for multi-layer walls, values which give the surface heat flows at hourly intervals due to a triangular pulse of external temperature (base 2h, height 1K). Here, the pulse is resolved into its Fourier components, each component is linked with the sinusoidal response of the wall at the corresponding frequency and the sums of the products provide the response factors. The approach is conceptually and computationally simple; for high accuracy it entails summation of a large number n of products but when n is large they can be handled in blocks of 200, then 1000,… Response factors can readily be transformed to wall conduction transfer coefficients (TCs) and the method is illustrated through analysis of one of the 41 walls whose transfer coefficients are listed in various editions of the ASHRAE Handbook of Fundamentals. It extends the ASHRAE values (a) by providing more terms and to higher accuracy, so as to remove an anomaly in their presentation, (b) it provides TCs for same-side excitation (additional to the current cross-excitation values), and (c) it demonstrates that such values are appropriate for use with a heat source in the room.