A system for determining ambient temperature

Abstract

A mechanism for indicating ambient temperature (Ta) of an enclosure (14) from temperatures determined within the enclosure (14). The temperatures may be obtained from two or more sensors (12, 13, 18) at each of two or more locations within the enclosure (14). The enclosure (14) may include an apparatus (27) inside such as electronics of which power consumption may be determined. Data including temperatures (T1, T2) of two locations within the enclosure (14) at various electronics power consumption levels may be entered into a 2-D plot. An approximation of the 2-D plot may be effected with an appropriate equation to be solved for ambient temperature (Ta). The data of the 2-D plot plus temperatures (T3) of a third location and air flow levels in the enclosure (14) may be entered into a 3-D plot. An approximation of the 3-D plot may be effected with an appropriate equation to be solved for ambient temperature (Ta).

Description

A SYSTEM FOR DETERMINING AMBIENT TEMPERATURE Background The present invention pertains to temperature sensing and particularly to indirect temperature determination. Summary The invention is a mechanism for indicating an ambient temperature about an enclosure containing a device, from deteLmined temperatures within the enclosure. Brief Description of the drawing Figure 1 is a diagram of enclosure having possibly power consuming equipment and temperature sensors for providing temperatures from two locations in the enclosure; Figure 2 is a diagram of a straight line fitted to data from sensors in the enclosure plotted on a two- coordinate graph for determining ambient temperature from a fitted equation; Figure 3a a graph of a temperature of a first vicinity in the enclosure versus power; Figure 3b a graph of a temperature of a second vicinity in the enclosure versus power; Figure 3c is a graph resulting from a combining the graphs of Figures 3a and 3b into one of the first temperature of the first vicinity versus the temperature of the second vicinity of the enclosure; Figure 4 is a diagram of an enclosure of equipment having sensors for providing temperatures from three locations in the enclosure; 1 Date Regue / Date Received 2022-06-28 Figure 4a is a diagram of a processor with inputs from various sensors pertinent to the enclosure; Figure 5 a table of data from sensors for three locations in the enclosure for various air flows and power consumption levels in the equipment in the enclosure; Figure 6 is a three-coordinate graph having a plot of the data of Figure 5 which is plane-fitted with an equation; Figure 7 is a two-coordinate graph of cool versus warm temperatures; and Figure 8 is a three-coordinate graph having a plot of another set of data which is plane-fitted with an equation. Description Accurate ambient temperature sensing is needed in a thermostat application. Sensing temperature using thermistors, semiconductor temperature sensors, thermocouples or any other form of temperature sensors from within an enclosure of electronics or equipment may result in a temperature higher than the ambient air temperature surrounding the enclosure of the equipment or device. The term "ambient" used herein refers to the volume proximate to, external of and surrounding the enclosure. The difference between the ambient and the sensed temperature may vary and be affected by the amount of electrical energy needed to power the device, ventilation, how close or far the temperature sensors are from warm components of the device, air flow surrounding the enclosure and / or device, device materials and their thermal conductivities, and so forth. If the amount of heat generated inside the enclosure is low and constant, constant temperature compensation might be sufficient. 2 Date Regue / Date Received 2022-06-28 But when the heat generated inside the case or enclosure is high and variable, computing the ambient temperature may become very challenging. The invention may be used for enabling the device or a processor to calculate the ambient temperature by sensing two or more different temperature points within the enclosure. An algorithm used to calculate the ambient temperature may be independent of power consumption of the device. Two or more temperature sensors may be placed in different locations within the enclosure of the device. In theory, any two locations that have different temperatures in steady state under a given load should work. In practice, one temperature sensor "Thot" may be placed close to the heat generating components. The other temperature sensor "Tcooin may be placed in about the coldest location within the device. Under very stable ambient conditions, the temperatures may be sampled at different equipment or device power load conditions. The temperatures sampled may be used to generate equations in terms of power (by means of curve fitting). The equations may be regarded as approximations of two- dimensional and three-dimensional relationships which may be graphs, plots, representations, and / or the like. The equations may include the following. T0001 - Tambient f(x) > Tcool - determined cool temperature. x - power dissipated in the device. f(x) - heat rise with respect to power for the cool temperature sensor. Thot Tambient f(x) > That. = determined hot temperature. x = power dissipated in the device. f(x) - heat rise with respect to power for the hot temperature sensor. From the system of two equations, x and Tambient are unknowns. Once these equations are solved, Tcrubiem_ = facool, Th.J. And since Tc001 and Thot are determined values, ambient 3 Date Regue / Date Received 2022-06-28 temperature may be calculated from them. f(x) may be approximated (i.e., fitted) to a linear function, but it can also be non-linear for increased accuracy; however, in the latter case f(x) would be more complicated to implement. The present approach does not suggest sensing ambient temperature via one sensor, such as a thermistor, then sensing a warm temperature via another sensor and calculating an error to compensate for the sensed ambient temperature. The ambient temperature may be calculated from two different temperatures within an enclosure of a device or equipment, and therefore ambient temperature becomes a function of both temperatures or a function of additional temperatures if more than two sensors are used, where the additional temperatures and the initial two temperatures are averaged together into two or three temperatures within the enclosure. The present approach does not require special algorithms for special cases; it may work well even if there is no heat generated within the device. The sought temperature is not necessarily time dependent; the ambient temperature may be a function of the different temperatures and be calculated virtually instantaneously. The present system may use a two-dimensional (2-D) model with two or more temperature sensors in two groups of the sensors in an enclosure of some equipment, or a three-dimensional (3-D) model with three or more temperature sensors in three groups of sensors in the enclosure to determine the ambient temperature. Each group may provide an average temperature of the sensors in the group. The 3-D model may also be used to readily detect air flow. The equipment may be a piece of electronics that generates heat because the usage of power within the enclosure where the sensors are placed. 4 Date Regue / Date Received 2022-06-28 Although the equipment may be inactivated and the sensors detecting temperatures inside the enclosure of the equipment may themselves indicate the ambient temperature. Equations for determining ambient temperature from internal enclosure sensors may have a form of the following equation, T, - (T1-aT2-b) / (1-a), where Ta is ambient temperature, T1 may represent a hotter temperature and T2 may represent a colder temperature in the enclosure 14 containing equipment 27. Sensors 12 and 13 for T1 and T2, respectively, may be situated in two different places of the enclosure 14, as shown in Figure 1. Data may be taken and plotted on a two dimensional graph as shown in Figure 2. A classic form of the equation for a straight line fitted to a plot of temperature data may be y= ax -I- b. From the graph, the constant "a" may be the slope and the constant "b" may be the offset of the line 11 from the zero coordinates. The "constant" nomenclature "a", "b", and so on, may be lower or upper case. The graph may show T1 versus T2 for various ambient temperatures. There may instead be two or more sensors situated in a vicinity representing T1, and two or more sensors situated in another vicinity representing T2, rather than single sensors representing T1 and T2, respectively. An output average of the two or more sensors may be taken for Ti and an average of the other two or more sensors may be taken for T2. An additional third sensor or group of sensors may be used for averaging with one or more sensors or for T, and for determining air flow direction and / or magnitude. For Illustrative purposes, just two sensors 12 and 13 may be used in the enclosure 14. When the equipment or device 5 Date Regue / Date Received 2022-06-28 27 in the enclosure 14 is energized, one may have Tl > T2 > Ta. Tl may be regarded as the Thot and T2 may be regarded as Tccid= Using the equation, T. = (T1-aT2-b) / (1-a), with values provided for the constants, the ambient temperature T, may be determined. Values of the constants may be determined with data from empirical tests, simulation or calculations under conditions that the enclosure 14 is likely to be subject. Data may be taken from the temperature sensors and plotted in graphs 15 and 16 in Figures 3a and 3b for T1 versus power and T2 versus power, respectively. Data may be taken at different power levels of the equipment 27 in the enclosure 14. The ambient temperature may be held constant. The plots may be fitted with straight lines. The graphs 15 and 16 may be combined into a graph 17 in Figure 3c. The common power determinations or measurements of the graphs 15 and 16 may drop out, resulting in Tl versus T2 in a graph 17. The slope value of the solid line in graph 17 may be determined and substituted for "a- and the offset from graph 17 may be determined, measured or calculated and substituted for "b". One set of data as shown in Figures 3a-3c may be sufficient in a situation where the direction and magnitude of air flow, if any, remain the same for measurements or determinations, or are negligible, and thus the resultant equation should be adequate in determining the ambient temperature T.. Where air flow is changed, then a new set of data, like that in Figures 3a and 3b, should be taken for the equipment 27 of enclosure 14 situated in the new air flow. The new air flow may result in a different line (dashed) 19 in graph 17 of Figure 3c. The two-dimensional approach just noted herein may be extended to a three-dimensional approach with a third 6 Date Regue / Date Received 2022-06-28 sensor 18 situated in the enclosure 14, as illustratively shown in Figure 4. Figure 4a shows a processor 37 which may determine an ambient temperature proximate to the enclosure 14 based on outputs from temperature sensors 12, 18 and 13, an air flow sensor 35 proximate (external and / or internal) to the enclosure, and a power level sensor 36 connected to a power input to the electronics equipment 27 and / or processor 37. The ambient temperature may be indicated at an output 38 of the processor 37 or electronics 27. Electronics 27 or processor 37 may be configured for either the two- dimensional approach and / or the three-dimensional approach as noted herein. Processor 37 may be internal or external to enclosure 14. The 3-D approach may result in an equation which accommodates various air flows. The resultant plot of the data may result in a 3-D surface. The simplest form of this surface is a plane of a 3-axis coordinate system. The basic equation form may be ax + by + cz + d = O. For improved accuracy, a more complicated non-linear 3-D surface equation may be generated from the data. Three temperature readings for Ti sensor 12, T2 sensor 13 and T3 sensor 18 may be taken for each power level at various air flows or vice versa. The ambient temperature should be constant during the data taking. For an illustrative example of data taking and determining the values of the constants for the three equations of the three-dimensional approach, one may note tables of Figure 3. Each sensor and respective temperature may represent a coordinate axis of a 3-axis or 3-D graph 24 in Figure 6. In table 21, temperature determinations or measurements Ti, T2 and T3 from sensors 12, 13 and 18 for a first air flow and a first power 7 Date Regue / Date Received 2022-06-28 level may be 85, 78 and 74 degrees F, respectively; for the first air flow and second power level, the determinations or measurements may be 88, 79 and 76 degrees, respectively; and for the first air flow and third power level, the determinations or measurements may be 89, 84 and 79, respectively. In table 22, temperature determinations or measurements T1, T2, and T3 from sensors 12, 13 and 18 for a second air flow and the first power level may be 80, 76, and 71 degrees, respectively; for the second air flow and the second power level, the determinations or measurements may be 84, 78 and 75 degrees, respectively; and for the second air flow and the third power level the determinations or measurements may be 86, 81 and 77 degrees, respectively. In table 23, temperature determinations or measurements T1, T2, and T3 from sensors 12, 13 and 18 for a third air flow and the first power level, the determinations or measurements may be 91, 80 and 76 degrees, respectively; and for the third air flow and the second power level the determinations or measurements may be 93, 84, and 78 degrees, respectively; and for the third air flow and the second power level, the determinations or measurements may be 95, 88 and 82 degrees, respectively. Since the ambient temperature (TJ may be regarded as at 70 degrees F, during data determination or a taking of the empirical measurements, the data may be adjusted for Ta, resulting in data points for plotting on the 3- coordinate graph 24, as illustrated in Figure 6. The data points may be 15, 8, 4; 18, 9, 6; and 19, 14, 9; for air flow 1 and power levels 1, 2 and 3, respectively. Data points may be 10, 6, 1; 14, 8, 5; and 16, 11, 7; for air flow 2 and power levels 1, 2 and 3, respectively. Data points may be 21, 10, 6; 23, 14, 8; and 25, 18, 12; for air flow 3 and power levels 1, 2 and 3, respectively. 8 Date Regue / Date Received 2022-06-28 The data points from 15, 8, 4 through 25, 18, 12, as indicated herein, may be labeled A, Br C, D, E, F, G, H and I, respectively. The latter labels may be used in graph 24. One may plane fit the data points and come up with a plane 26 and a corresponding equation. These data points may be inserted in versions of the following equation, ax + by + cz + d = 0, to obtain values for the respective constants for the ultimate equation for obtaining T, from Ti, T2 and T3 at various air flows and power levels of the enclosure 14 and equipment 27. For an illustrative example, with respect to the 2-D model, the following temperatures were logged at 70 degrees F ambient condition. These are at 3 different load conditions. The cool temperatures are 73.95439, 74.14308 and 74.80374 degrees F. The warm temperatures are 81.49281, 82.11406 and 84.3687. From these temperatures, one may subtract temperatures from ambient and graph. The results from the cool temperatures are 3.95439, 4.14308 and 4.80374. The results from the warm temperatures are 11.49281, 12.11406 and 14.3687. The results for both sets of temperatures may be plotted as coordinate points 33 a graph 31 of Figure 7. One may generate a best curve fit 32. In this condition, it happens to be linear. Twarm Tambient = A* (Tcooi Tambient) B, where A= 2.9468 and B= 0. One may look to the plot 33 and linear curve 32 fitting in graph 31 of Figure 7. One may have Tamnient = (Twarm A* Tc001 B) / (1 - A) . After applying this equation to the original temperature, the calculated ambient temperatures are 70.08218, 70.04868 and 69.89057, respectively. As may be seen, the temperatures appear accurate. And since the above items 9 Date Regue / Date Received 2022-06-28 have been the extreme load conditions, different loads in between would generate temperatures that fall on the same curve and therefore the ambient temperature can be recovered. When the same device is exposed to different ambient temperatures, the temperature rise on the sensors is constant and the ambient temperature may be recovered. With an example at ambient temperature - 80 degrees, one may get cool temperatures of 84.03199, 83.59956 and 84.8985, and hot temperatures of 92.10085, 91.00635 and 94.71613. The calculated temperatures may be 79.88731, 79.79496 and 79.85554, respectively. With respect to a 3-D model, three given different temperature sensors will generate a 3-D surface equation, in the case of a linear approach, this would be a plane. For example, Ax + By + Cz + D = 0. Assuming that the plane crosses at (0,0,0), which means if no heat is generated within the device, then the temperature sensed by the sensors = ambient. Ax + By + Cz = 0, x,y,z are Tl - Lamb:mit, T2 ¨ T aubientr and T2 ¨ Tarnbientr respectively. TAmbient = (A*Ti + B*T2 + C*Ti) (A + B + C) where A, B and C are plane constants, and may be calculated algebraically or by the use of curve / surface fit software In some cases temperatures inside an enclosure might be affected by external environmental changes and a 2-D solution might not be sufficient to recover ambient temperature accurately. For instance, airflow direction or speed may cause some variation and constantly generate temperatures that do not fall on a 2-D dimensional curve. With a third sensor, temperature variations may be modeled with a surface of 3-D equation. A graph 41 in Figure 8 shows an example of that. In this example, the Date Regue / Date Received 2022-06-28 points 42 are surface fit to a plane 43, instead of a 2-D curve or a line 32 as in Figure 7. Determinations, measurements, plotting, graphs, curve-, line- and plane-fitting, calculations, approximations, relationships, representations, managing equations and getting solutions, obtaining values for constants and temperatures such as ambient, doing flow and power level determinations or measurements, and other items for effecting the present system, and so forth, may be effected electronically with a processor or the like, along with appropriate software as desired or needed. In the present specification, some of the matter may be of a hypothetical or prophetic nature although stated in another manner or tense. Although the invention has been described with respect to at least one illustrative example, many variations and modifications will become apparent to those skilled in the art upon reading the present specification. It is therefore the intention that the appended claims be interpreted as broadly as possible in view of the prior art to include all such variations and modifications. 11 Date Regue / Date Received 2022-06-28

Claims

What is claimed is:

1. A thermostat that functions to provide control signals to temperature control equipment to maintain a desired temperature in a space, comprising: a housing; one or more heat generating elements in the housing, wherein during operation of the thermostat, the one or more heat generating elements cause a first region within the housing to be warmer than a second region within the housing; a first temperature sensor for reporting a measure that is related to the temperature in the first region; a second temperature sensor for reporting a measure that is related to the temperature in the second region; a controller in communication with the first temperature sensor and the second temperature sensor, the controller determining a measure related to an ambient temperature outside of the housing based, at least in part, on the measure that is related to the temperature in the first region reported by the first temperature sensor and the measure that is related to the temperature in the second region reported by the second temperature sensor; and wherein: the thermostat uses the measure related to the ambient temperature outside of the housing to determine one or more control signals for controlling temperature control equipment; the thermostat is powered, at least in part, by electrical energy; the one or more heat generating elements generate heat by consuming the electrical energy; a level of electrical energy needed to power the thermostat changes over time; the first temperature sensor and / or the second temperature sensor report a measure that is related to the temperature in the first region or the second region, respectively, which changes over time in a rapid or slow manner, correspondingly, at least in part, to the changes of energy over time needed to power the thermostat incorporating the heat generating elements; and 12 Date Recue / Date Received 2022-06-28 the changes over time in a rapid manner are compensated so as to avoid affecting determination of ambient temperature changes over time in a slow manner of the first temperature sensor and / or the second temperature sensor which reports a measure that is related to the temperature in the first region or the second region, respectively.

2. The thermostat of claim 1, wherein the one or more heat generating elements comprises a display backlight which is at certain times turned on resulting in one or more changes in a rapid manner.

3. The thermostat of claim 1, wherein the controller compensates for the temperature in the first region or the second region, respectively, which changes over time in a rapid or slow manner, correspondingly, at least in part, to changes of energy needed over time to power one or more heat generating elements, to result in the controller determining the measure related to an ambient temperature outside of the housing, at least in part, on the measure that is related to the temperature in the first region reported by the first temperature sensor and the measure that is related to the temperature in the second region reported by the second temperature sensor.

4. The thermostat of claim 3, wherein the measure related to the ambient temperature determined by the controller is relatively independent of the level of the electrical energy needed to power the thermostat.

5. The thermostat of claim 3, wherein the controller determines the measure related to the ambient temperature outside of the housing based, at least in part, on a predetermined relationship between the measure related to the ambient temperature outside of the housing, the measure related to the temperature in the first region reported by the first temperature sensor and the measure related to the temperature in the second region reported by the second temperature sensor.

6. The thermostat of claim 5, wherein the thermostat is powered by a level of electrical energy that changes over time, and wherein the measure related to the ambient 13 Date Recue / Date Received 2022-06-28 temperature is relatively independent of the level of electrical energy powering the thermostat.

7. The thermostat of claim 3, wherein a change over time in a rapid manner is a rise of a measure of the first sensor or the second sensor of greater than a predetermined rate of X degrees Fahrenheit per second.

8. The thermostat of claim 3, further comprising: a third temperature sensor for reporting a measure that is related to the temperature in a third region within the housing; the controller determining a measure related to an air flow direction and / or air flow magnitude about the housing that is based, at least in part, on the measure related to the temperature in the third region reported by the third temperature sensor; and the controller using the measure related to the air flow direction and / or air flow magnitude about the housing when determining the measure related to the ambient temperature outside of the housing.

9. The thermostat of claim 3, further comprising: a third temperature sensor for reporting a measure that is related to the temperature in a third region within the housing; and wherein: the measure related to an ambient temperature outside of the housing based, at least in part, on the measure that is related to the temperature in the first region reported by the first temperature sensor, the measure that is related to the temperature in the second region reported by the second temperature sensor, and the measure that is related to the temperature in the third region reported by the third temperature sensor, is according to T Amlnent=c4 *T +B*T 2 +C *T 3 +E*(Final¨(Final¨Initia1)*e^(¨t / tau))+D) / (4+ B +C); Ti is the measure reported by the first temperature sensor; T2 is the measure reported by the second temperature sensor; T3 is the measure reported by the third temperature sensor; 14 Date Recue / Date Received 2022-06-28 E is a dynamic heat source factor; Final is a new heat source level; Initial is an old heat source level before a change; t is time that lapsed since a change; tau is a time constant; A, B, C, D and E are constants; a dynamic heat source is a heat generating element that is powered by changes of energy over time which results, at least in part, the temperature in the first, second and / or third region, changing over time in a rapid manner; and the rapid manner is greater than a predetermined rate of X degrees Fahrenheit per second.

10. A method for determining an ambient temperature outside an enclosure, comprising: detecting a first temperature over a period of time at a first location in an enclosure; detecting a second temperature over the period of time at a second location in the enclosure; determining a first change of the first temperature over the period of time, from the first temperature over the period of time; detecting a second change of the second temperature over the period of time, from the second temperature over the period of time; selecting from the first change of the first temperature and the second change of the second temperature, a greatest change of temperature, over the period of time; determining whether the greatest change of temperature is dynamic; a change of temperature is dynamic when the rate of change exceeds a predetermined rate of X degrees Fahrenheit per second; generating a relationship between an ambient temperature outside of the enclosure and the first temperature, the second temperature, the first change of temperature and the second change of temperature; and determining the ambient temperature from the relationship; and Date Recue / Date Received 2022-06-28 wherein the relationship incorporates compensation for the dynamic change of temperature.

11. The method of claim 10, wherein: the relationship is T A=G4*T 1 +B*T 2 +E*(Final¨(Final¨Initial)*e^(¨t / tau))+D)1(A+B); TA is ambient temperature; Ti is the first temperature over the period of time; T2 is the second temperature over the period of time; E is a dynamic heat source factor; w is a dynamic heat source level; Final is a new heat source level; Initial is an old heat source level before a change; t is time that lapsed since the change; tau is a time constant; and A, B, D and E are constants.

12. The method of claim 10, further comprising: detecting a third temperature over a period of time; determining a third change of the third temperature over the period of time; and identifying the change or changes of temperature that are dynamic, and wherein: the relationship is T A=0*T 1 +B*T 2 +C *T 3 +E*(Final¨(Final¨Initial)*e^(¨thau))+D) / (A+ B+C); TA is ambient temperature; Ti is the first temperature over the period of time; T2 is the second temperature over the period of time; T3 is the third temperature over the period of time; E is a dynamic heat source factor; Final is a new heat source level; 16 Date Recue / Date Received 2022-06-28 Initial is an old heat source level before a change; t is time that lapsed since the change; tau is a time constant; and A, B, C, D and E are constants.

13. The method of claim 12, wherein: values of the constants are determined with data of empirical tests, simulations and / or calculations under conditions of the enclosure; and data comprise first, second and third temperatures over a period of time.

14. The method of claim 12 wherein: the enclosure comprises a backlight; and turning on the backlight causes at least one of the first, second and third changes of temperature to be dynamic.

15. The method of claim 10, wherein: the controller comprises a thermostat connected to the sensors; and the controller determines one or more control signals for controlling temperature control equipment based, at least in part, on the ambient temperature.

16. A system for determining ambient temperature comprising: an enclosure; a first temperature sensor situated at a first location in the enclosure; a second temperature sensor situated at a second location in the enclosure which is spaced from the first location; a controller receiving a first temperature from the first temperature sensor and a second temperature from the second temperature sensor; and a dynamic heat generating element situated in the enclosure; and wherein the dynamic heat generating element, when turned on, causes at least in part, the first temperature and / or the second temperature to change greater than a predetermined rate of X degrees Fahrenheit per second; and 17 Date Recue / Date Received 2022-06-28 wherein the controller determines a measure related to an ambient temperature outside of the enclosure based, at least in part, on the first temperature and the second temperature, and on greater than the predetermined rate of X degrees Fahrenheit per second of temperature change of the first temperature and / or the second temperature.

17. The system of claim 16, wherein the measure is from an algorithm which determines the ambient temperature from the first temperature and the second temperature, and compensates for a temperature change of the first temperature and / or the second temperature greater than the predetermined rate of X degrees Fahrenheit per second.

18. The system of claim 16, wherein: the measure is from an algorithm comprising an equation, TA=(AT 1 +BT 2 +Ew+D)I(A+B); TA is ambient temperature; Ti is the first temperature; T2 is the second temperature; E is a dynamic heat source factor; w is a dynamic heat source level; and A, B, D and E are constants. 18 Date Recue / Date Received 2022-06-28 19. The system of claim 16, further comprising: a third temperature sensor situated at a third location in the enclosure, which is spaced from the first location and the second location; and wherein: the controller also receives a third temperature from the third temperature sensor; the dynamic heat generating element causes at least in part the first temperature, the second temperature and / or the third temperature to change greater than the predetermined rate of X degrees Fahrenheit per second; the controller determines a measure related to an ambient temperature outside of the enclosure based, at least in part, on the first temperature, the second temperature and the third temperature on greater than the predetermined rate of X degrees Fahrenheit per second of temperature change of the first temperature, the second temperature and / or the third temperature; the measure is from an algorithm comprising an equation, TA=(AT 1 BT 2 +CT 3 +Ew+D)1(A+B+C); TA is ambient temperature; Ti is the first temperature; T2 is the second temperature; T3 is the third temperature; E is a dynamic heat source factor; w is a dynamic heat source level; and A, B, C, D and E are constants. 19 Date Recue / Date Received 2022-06-28