Title:

Kind
Code:

A1

Abstract:

A method of predicting the amount of heat flowing into an object includes the steps of formulating a thermal circuit representing a heat flow into the object and an equation representing the thermal circuit; obtaining parameters for the equation; applying the parameters in the equation; and solving the equation to predict the amount of heat flowing into the object.

Inventors:

Kanamori, Hiroshi (Tokyo, JP)

Application Number:

11/482621

Publication Date:

01/25/2007

Filing Date:

07/07/2006

Export Citation:

Primary Class:

International Classes:

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Related US Applications:

Primary Examiner:

O MALLEY, MARY CATHERINE

Attorney, Agent or Firm:

LADAS & PARRY LLP (224 SOUTH MICHIGAN AVENUE
SUITE 1600, CHICAGO, IL, 60604, US)

Claims:

What is claimed is:

1. A method of predicting an amount of heat flowing into an object, comprising the steps of: formulating a thermal circuit representing a heat flow into the object and an equation representing the thermal circuit; obtaining parameters for the equation; applying the parameters in the equation; and solving the equation to predict the amount of heat flowing into the object.

2. The method of predicting the amount of heat as claimed in claim 1, wherein, when the heat flow into the object is i, a solar absorptance is a, a solar irradiance is I, an external temperature is T_{ex}, an internal temperature is T_{in}, a heat resistance of a structure between an exterior and an interior of the object is R_{c}, a heat transfer resistance of an internal structure is r_{in}, and a heat transfer resistance of an external structure is r_{ex}, the equation representing the thermal circuit is expressed as follows: i={(a×I×r_{ex})+(T_{ex}−T_{in})}/(R_{c}+r_{in}+r_{ex}).

3. The method of predicting the amount of heat as claimed in claim 1, wherein changes in the amount of heat are predicted by the steps of: (a) obtaining two or more sets of the parameters each set corresponding to a time point; (b) applying one of the sets of the parameters in the equation; (c) solving the equation and thereby obtaining the heat flow into the object at the corresponding time point; (d) obtaining the amount of heat at a subsequent time point based on the heat flow obtained in step (c); and (e) repeating the steps (b) through (d) for a number of the sets of the parameters.

4. The method of predicting the amount of heat as claimed in claim 1, wherein, when an internal temperature at a time point j is T_{in(j)}, an internal temperature at a time point (j+1) is T_{in(j+1)}, an external temperature at the time point j is T_{ex(j)}, parameters obtained by combining parameters relating to structural conditions and internal conditions of the object at the time point j are H_{(j)}′ and KS_{(j)}, and a heat capacity of the object is C_{t}, the internal temperature T_{in(j+1) }at the time point (j+1) is calculated as follows: T_{in(j+1)}=T_{ex(j)}+H_{(j)}′/KS_{(j)}−(T_{ex(j)}+H_{(j)}′/KS_{(j)}−T_{in(j)})exp(−KS_{(j)}/C_{t}).

5. The method of predicting the amount of heat as claimed in claim 4, wherein time interval between the time point j and the time point (j+1) is within a range between about ten minutes and about an hour.

6. A system to predict an amount of heat flowing into an object, wherein a thermal circuit representing a heat flow into the object and an equation representing the thermal circuit are used, comprising: an acquisition unit configured to obtain parameters for the equation; and a processing unit configured to apply the parameters in the equation and to solve the equation to predict the amount of heat flowing into the object.

7. The system to predict the amount of heat as claimed in claim 6, wherein, when the heat flow into the object is i, a solar absorptance is a, a solar irradiance is I, an external temperature is T_{ex}, an internal temperature is T_{in}, a heat resistance of a structure between an exterior and an interior of the object is R_{c}, a heat transfer resistance of an internal structure is r_{in}, and a heat transfer resistance of an external structure is r_{ex}, the equation representing the thermal circuit is expressed as follows: i={(a×I×r_{ex})+(T_{ex}−T_{in})}/(R_{c}+r_{in}+r_{ex}).

8. The system to predict the amount of heat as claimed in claim 6, wherein changes in the amount of heat are predicted by the steps of: (a) obtaining two or more sets of the parameters each set corresponding to a time point; (b) applying one of the sets of the parameters in the equation; (c) solving the equation and thereby obtaining the heat flow into the object at the corresponding time point; (d) obtaining the amount of heat at a subsequent time point based on the heat flow obtained in step (c); and (e) repeating the steps (b) through (d) for a number of the sets of the parameters.

9. The system to predict the amount of heat as claimed in claim 6, wherein, when an internal temperature at a time point j is T_{in(j)}, an internal temperature at a time point (j+1) is T_{in(j+1)}, an external temperature at the time point j is T_{ex(j)}, parameters obtained by combining parameters relating to structural conditions and internal conditions of the object at the time point j are H_{(j)}′ and KS_{(j)}, and a heat capacity of the object is C_{t}, the internal temperature T_{in(j+1) }at the time point (j+1) is calculated as follows: T_{in(j+1)}=T_{ex(j)}+H_{(j)}′/KS_{(j)}−(T_{ex(j)}+H_{(j)}′/KS_{(j)}−T_{in(j)})exp(−KS_{(j)}/C_{t}).

10. The system to predict the amount of heat as claimed in claim 9, wherein time interval between the time point j and the time point (j+1) is within a range between about ten minutes and about an hour.

11. A recording medium having a program embodied therein for causing a computer to predict an amount of heat flowing into an object, said program comprising: a first code unit for formulating a thermal circuit representing a heat flow into the object and an equation representing the thermal circuit; a second code unit configured to obtain parameters for the equation; a third code unit configured to apply the parameters in the equation; and a fourth code unit configured to solve the equation to predict the amount of heat flowing into the object.

12. The recording medium as claimed in claim 11, wherein, when the heat flow into the object is i, a solar absorptance is a, a solar irradiance is I, an external temperature is T_{ex}, an internal temperature is T_{in}, a heat resistance of a structure between an exterior and an interior of the object is R_{c}, a heat transfer resistance of an internal structure is r_{in}, and a heat transfer resistance of an external structure is r_{ex}, the equation representing the thermal circuit is expressed as follows: i={(a×I×r_{ex})+(T_{ex}−T_{in})}/(R_{c}+r_{in}+r_{ex}).

13. The recording medium as claimed in claim 11, wherein changes in the amount of heat are predicted by the steps of: (a) obtaining two or more sets of the parameters each set corresponding to a time point; (b) applying one of the sets of the parameters in the equation; (c) solving the equation and thereby obtaining the heat flow into the object at the corresponding time point; (d) obtaining the amount of heat at a subsequent time point based on the heat flow obtained in step (c); and (e) repeating the steps (b) through (d) for a number of the sets of the parameters.

14. The recording medium as claimed in claim 11, wherein, when an internal temperature at a time point j is T_{in(j)}, an internal temperature at a time point (j+1) is T_{in(j+1)}, an external temperature at the time point j is T_{ex(j)}, parameters obtained by combining parameters relating to structural conditions and internal conditions of the object at the time point j are H_{(j)}′ and KS_{(j)}, and a heat capacity of the object is C_{t}, the internal temperature T_{in(j+1) }at the time point (j+1) is calculated as follows: T_{in(j+1)}=T_{ex(j)}+H_{(j)}′/KS_{(j)}−(T_{ex(j)}+H_{(j)}′/KS_{(j)}−T_{in(j)})exp(−KS_{(j)}/C_{t}).

15. The recording medium as claimed in claim 14, wherein time interval between the time point j and the time point (j+1) is within a range between about ten minutes and about an hour.

1. A method of predicting an amount of heat flowing into an object, comprising the steps of: formulating a thermal circuit representing a heat flow into the object and an equation representing the thermal circuit; obtaining parameters for the equation; applying the parameters in the equation; and solving the equation to predict the amount of heat flowing into the object.

2. The method of predicting the amount of heat as claimed in claim 1, wherein, when the heat flow into the object is i, a solar absorptance is a, a solar irradiance is I, an external temperature is T

3. The method of predicting the amount of heat as claimed in claim 1, wherein changes in the amount of heat are predicted by the steps of: (a) obtaining two or more sets of the parameters each set corresponding to a time point; (b) applying one of the sets of the parameters in the equation; (c) solving the equation and thereby obtaining the heat flow into the object at the corresponding time point; (d) obtaining the amount of heat at a subsequent time point based on the heat flow obtained in step (c); and (e) repeating the steps (b) through (d) for a number of the sets of the parameters.

4. The method of predicting the amount of heat as claimed in claim 1, wherein, when an internal temperature at a time point j is T

5. The method of predicting the amount of heat as claimed in claim 4, wherein time interval between the time point j and the time point (j+1) is within a range between about ten minutes and about an hour.

6. A system to predict an amount of heat flowing into an object, wherein a thermal circuit representing a heat flow into the object and an equation representing the thermal circuit are used, comprising: an acquisition unit configured to obtain parameters for the equation; and a processing unit configured to apply the parameters in the equation and to solve the equation to predict the amount of heat flowing into the object.

7. The system to predict the amount of heat as claimed in claim 6, wherein, when the heat flow into the object is i, a solar absorptance is a, a solar irradiance is I, an external temperature is T

8. The system to predict the amount of heat as claimed in claim 6, wherein changes in the amount of heat are predicted by the steps of: (a) obtaining two or more sets of the parameters each set corresponding to a time point; (b) applying one of the sets of the parameters in the equation; (c) solving the equation and thereby obtaining the heat flow into the object at the corresponding time point; (d) obtaining the amount of heat at a subsequent time point based on the heat flow obtained in step (c); and (e) repeating the steps (b) through (d) for a number of the sets of the parameters.

9. The system to predict the amount of heat as claimed in claim 6, wherein, when an internal temperature at a time point j is T

10. The system to predict the amount of heat as claimed in claim 9, wherein time interval between the time point j and the time point (j+1) is within a range between about ten minutes and about an hour.

11. A recording medium having a program embodied therein for causing a computer to predict an amount of heat flowing into an object, said program comprising: a first code unit for formulating a thermal circuit representing a heat flow into the object and an equation representing the thermal circuit; a second code unit configured to obtain parameters for the equation; a third code unit configured to apply the parameters in the equation; and a fourth code unit configured to solve the equation to predict the amount of heat flowing into the object.

12. The recording medium as claimed in claim 11, wherein, when the heat flow into the object is i, a solar absorptance is a, a solar irradiance is I, an external temperature is T

13. The recording medium as claimed in claim 11, wherein changes in the amount of heat are predicted by the steps of: (a) obtaining two or more sets of the parameters each set corresponding to a time point; (b) applying one of the sets of the parameters in the equation; (c) solving the equation and thereby obtaining the heat flow into the object at the corresponding time point; (d) obtaining the amount of heat at a subsequent time point based on the heat flow obtained in step (c); and (e) repeating the steps (b) through (d) for a number of the sets of the parameters.

14. The recording medium as claimed in claim 11, wherein, when an internal temperature at a time point j is T

15. The recording medium as claimed in claim 14, wherein time interval between the time point j and the time point (j+1) is within a range between about ten minutes and about an hour.

Description:

1. Field of the Invention

The present invention generally relates to a heat amount prediction method, a heat amount prediction system, and a recording medium having a heat amount prediction program stored therein, and more particularly relates to a heat amount prediction method, a heat amount prediction system, and a recording medium having a heat amount prediction program stored therein which are used to measure the amount of heat flowing into an object.

2. Description of the Related Art

Solar heat reflecting coatings (heat shield coatings) for coating exterior surfaces of various structures receiving solar radiation, such as ships, buildings, automobiles, and electronic appliances, have been developed. A solar heat reflecting coating reflects sunlight, suppresses the rise in temperature inside structures, and protects the surfaces of structures. A solar heat reflecting coating thereby reduces consumption of energy required for, for example, air conditioning in structures and improves the durability of structures.

When using a solar heat reflecting coating for structures to achieve the above mentioned effects, it is important to measure the heat shielding effect of the solar heat reflecting coating.

Steady-state calculations used in architectural environmental engineering and other fields provide a simple method of calculating the heat load of a structure.

Also, a method of measuring the effects of a heat shield coating, which method also uses steady-state calculations, has been proposed. In this method, the solar reflectance of a heat shield coating is measured, the solar absorptance is calculated from the measured solar reflectance, the sol-air temperature is calculated from the calculated solar absorptance, and the amount of heat transfer is calculated from the calculated sol-air temperature.

[Patent document 1] Japanese Patent Application Publication No. 2002-39977

However, steady-state calculations used in architectural environmental engineering and other fields can calculate only the amount of heat in steady-state conditions, and cannot perform a predictive calculation of the amount of heat taking into account the changes in heat capacity and meteorological conditions. To calculate the amount of heat in non-steady state conditions taking into account the changes in heat capacity and meteorological conditions, a simulation program for heat load calculation running on a mainframe has been used. However, such a simulation program is very expensive and not easily available.

The present invention provides a heat amount prediction method, a heat amount prediction system, and a recording medium having a heat amount prediction program stored therein that substantially obviate one or more problems caused by the limitations and disadvantages of the related art.

A heat amount prediction method, a heat amount prediction system, and a recording medium having a heat amount prediction program stored therein according to embodiments of the present invention provide a simple and affordable way to calculate the amount of heat in non-steady state conditions.

According to an embodiment of the present invention, a method of predicting the amount of heat flowing into an object includes the steps of formulating a thermal circuit representing a heat flow into the object and an equation representing the thermal circuit; obtaining parameters for the equation; applying the parameters in the equation; and solving the equation to predict the amount of heat flowing into the object.

According to an aspect of the present invention, when the heat flow into the object is i, solar absorptance is a, solar irradiance is I, external temperature is T_{ex}, internal temperature is T_{in}, heat resistance of a structure between the exterior and the interior of the object is R_{c}, heat transfer resistance of the internal structure is r_{in}, and heat transfer resistance of the external structure is r_{ex}, the equation representing the thermal circuit is expressed as follows:

i={(*a×I×r*_{ex})+(*T*_{ex}*−T*_{in})}/(*R*_{c}*+r*_{in}*+r*_{ex}).

According to an aspect of the present invention, changes in the amount of heat are predicted by the steps of (a) obtaining two or more sets of the parameters each set corresponding to a time point; (b) applying one of the sets of the parameters in the equation; (c) solving the equation and thereby obtaining the heat flow into the object at the corresponding time point; (d) obtaining the amount of heat at a subsequent time point based on the heat flow obtained in step (c); and (e) repeating the steps (b) through (d) for the number of sets of parameters.

According to an aspect of the present invention, when an internal temperature at a time point j is T_{in(j)}, an internal temperature at a time point (j+1) is T_{in(j+1)}, an external temperature at the time point j is T_{ex(j)}, parameters obtained by combining parameters relating to structural conditions and internal conditions of the object at the time point j are H_{(j)}′ and KS_{(j)}, and the heat capacity of the object is C_{t}, the internal temperature T_{in(j+1) }at the time point (j+1) is calculated as follows: T_{in(j+1)}=T_{ex(j)}+H_{(j)}′/KS_{(j)}−(T_{ex(j)}+H_{(j)}′/KS_{(j)}−T_{in(j)})exp(−KS_{(j)}/C_{t}).

According to an aspect of the present invention, the time interval between the time point j and the time point (j+1) is within a range of about ten minutes and about an hour.

According to an embodiment of the present invention, a system to predict the amount of heat flowing into an object, wherein a thermal circuit representing a heat flow into the object and an equation representing the thermal circuit are used, includes an acquisition unit configured to obtain parameters for the equation; and a processing unit configured to apply the parameters in the equation and to solve the equation to predict the amount of heat flowing into the object.

An embodiment of the present invention provides a recording medium having a program stored therein for causing a computer to predict the amount of heat flowing into an object, which program includes a first code unit for formulating a thermal circuit representing a heat flow into the object and an equation representing the thermal circuit; a second code unit configured to obtain parameters for the equation; a third code unit configured to apply the parameters in the equation; and a fourth code unit configured to solve the equation to predict the amount of heat flowing into the object.

In a heat amount prediction method according to an embodiment of the present invention, heat flowing into an object through different parts of the object are calculated by steady-state calculations and are summed to obtain the total heat load of the object. With the calculated heat load and the equations as described above, changes in the internal temperature of the object, for example, can be predicted taking into account changing meteorological conditions.

FIG. 1 is a block diagram illustrating an exemplary system configuration according to an embodiment of the present invention;

FIG. 2 is a flowchart illustrating an exemplary process of a heat load calculation program according to an embodiment of the present invention;

FIG. 3 is a table showing exemplary parameters used in a heat load calculation;

FIG. 4 is a drawing used to describe a method of calculating the heat load of a building;

FIG. 5 is a flowchart illustrating an exemplary process of a heat load calculation;

FIG. 6 is a table showing structural conditions of a building used in an exemplary simulation;

FIG. 7 is a table showing internal conditions of a building used in an exemplary simulation;

FIG. 8 is a table showing exemplary meteorological conditions at a place where a building used in an exemplary simulation is located;

FIG. 9 is a drawing illustrating a calculation process in an exemplary simulation;

FIG. 10 is a graph showing the results of an exemplary internal temperature simulation; and

FIG. 11 is a drawing illustrating an exemplary method of calculating the heat load of a road.

Preferred embodiments of the present invention are described below with reference to the accompanying drawings.

[System Configuration]

FIG. 1 is a block diagram illustrating an exemplary system configuration according to an embodiment of the present invention.

A heat amount prediction system **100** of this embodiment is implemented as a personal computer system including an input apparatus **111**, a processing unit **112**, a storage apparatus **113**, a memory **114**, a display apparatus **115**, and a communication apparatus **116**.

The input apparatus **111** includes, for example, a mouse and a keyboard, and is used to input information such as the location, dimensions, and an internal temperature setting of an object, for example, a structure.

The processing unit **112** includes a CPU and executes a heat load calculation program stored in the storage apparatus **113**.

The storage apparatus **113** includes a disk drive such as a hard disk drive or a CD-ROM drive. A heat load calculation program is installed in the storage apparatus **113**. The storage apparatus **113** is also used to store, for example, the information on an object and calculation results.

The memory **114** is implemented with a volatile memory such as a RAM and is used as a temporary storage area for the processing unit **112**.

The display apparatus **115** is implemented, for example, with a CRT or an LCD, and used to display, for example, input information and calculation results.

The communication unit **116** is connected to a network such as the Internet and is used to access, for example, a database of a meteorological bureau and obtain meteorological information.

[Heat Load Calculation Program]

FIG. 2 is a flowchart illustrating an exemplary process of a heat load calculation program according to an embodiment of the present invention. In the descriptions below, a building is used as an example of an object.

When a heat load calculation program is started in step S**1**-**1**, the processing unit **112**, in step S**1**-**2**, displays a screen requesting the location of a building according to the heat load calculation program.

When the location of a building is input by a user in step S**1**-**3**, the processing unit **112** obtains corresponding meteorological information from a database of a meteorological bureau in step S**1**-**4**.

In step S**1**-**5**, the processing unit **112** displays a screen requesting the orientation and dimensions of the building. When the orientation and dimensions of the building are input by a user in step S**1**-**6**, the processing unit **112** obtains the input orientation and dimensions of the building in step S**1**-**7**.

In step S**1**-**8**, the processing unit **112** displays a screen requesting internal information including conditions such as the internal temperature of the building. When internal information is input in step S**1**-**9**, the processing unit **112** obtains the internal information in step S**1**-**10**.

In step S**1**-**11**, the processing unit **112** calculates parameters used in a heat load calculation. For example, the processing unit **112** calculates the amount of solar radiation from the location of the building, the surface area of the building from its dimensions, and the heat capacity of the building from the internal information. Parameters such as the amount of solar radiation may be easily calculated by steady-state calculations using formulas commonly employed in architectural environmental engineering or other fields. For example, such formulas are described in Environmental Engineering Text (Kankyo Kougaku Kyokasho) Second Edition, written and edited by Environmental Engineering Text Study Group, and published by Shokokusha Publishing Co., Ltd.

FIG. 3 is a table showing exemplary parameters used in a heat load calculation.

Parameters obtained from meteorological information include the external temperature T_{ex }[° C.], the roof surface solar irradiance I_{r }[W/mˆ2], the wall surface solar irradiance I_{w }[W/mˆ2], and the wind velocity v [m/s]. The external temperature T_{ex }[° C.] is obtained by identifying a local meteorological station based on the location of the building and by obtaining meteorological information of the local meteorological station from a database, for example, of a meteorological bureau. The communication apparatus **116** accesses, for example, via the Internet a meteorological bureau or a meteorological information service company to obtain meteorological information.

The roof surface solar irradiance I_{r }[W/mˆ2] and the wall surface solar irradiance I_{w }[W/mˆ2] are calculated from the average atmospheric transmittance and the duration of sunshine obtained from meteorological information of a local meteorological station identified based on the location of the building, and the latitude and longitude of the local meteorological station.

When the solar constant 1.37 [kW/mˆ2] is J_{0}, the solar altitude [degree] is h, and the atmospheric transmittance is P, the amount of normal direct solar radiation J_{D }is obtained by the following equation (1) according to Buga's formula:

*J*_{D}=0.5*×J*_{0}*×P*ˆ cosec(*h*) (1)

and, the amount of horizontal diffuse solar radiation J_{s }is obtained by the following equation (2):

*J*_{s}=0.5*×J*_{0}×sin(*h*)·(1*−Pˆ cosec(**h*))/(1−1.4×ln(*P*)) (2)

The amount of horizontal direct solar radiation I_{H}, which is the amount of solar radiation directly reaching the roof or rooftop of the building, is obtained by the following equation (3):

*I*_{H}*=J*_{D}×sin(*h*) (3)

The amount of vertical direct solar radiation I_{v}, which is the amount of solar radiation directly reaching a wall surface of the building, is obtained by the following equation (4):

*I*_{v}*=J*_{D}×cos(*h*)×cos(α−*A*_{v}) (4)

In the equation (4), A_{v }denotes an azimuth angle [degree] of a wall surface.

The horizontal actual solar irradiance is calculated from the amount of horizontal direct solar radiation and the duration of sunshine; and the vertical actual solar irradiance is calculated from the amount of vertical direct solar radiation and the duration of sunshine. The duration of sunshine may be obtained from meteorological information of a local meteorological station.

The horizontal actual solar irradiance corresponds to the roof surface solar irradiance I_{r }[W/mˆ2] and the vertical actual solar irradiance corresponds to the wall surface solar irradiance I_{w }[W/mˆ2].

The wind velocity v [m/s] may be obtained from meteorological information of a local meteorological station.

Parameters obtained from structural conditions of the building include the roof surface solar absorptance a_{r }[%], the roof surface area S_{r }[mˆ2], the roof heat transfer resistance r_{rex }[mˆ2k/W], the roof structure heat resistance R_{rc }[mˆ2k/W], the ceiling heat transfer resistance r_{rin }[mˆ2k/W], the wall surface solar absorptance a_{w }[%], the external wall heat transfer resistance r_{wex }[mˆ2k/W], the wall structure heat resistance R_{wc }[mˆ2k/W], and the internal wall heat transfer resistance r_{win }[mˆ2k/W].

The roof surface solar absorptance a_{r }[%] is determined, for example, according to JIS R 3106 or JIS A 5759. The roof surface area S_{r }[mˆ2] is obtained from the dimensions of the building.

The roof heat transfer resistance r_{rex }[mˆ2k/W] is calculated from the wind velocity v [m/s].

The roof structure heat resistance R_{rc }[mˆ2k/W] is calculated based on the roof structure of the building and the heat conductivity and thickness of each roof component.

For the ceiling heat transfer resistance r_{rin }[mˆ2k/W], a normal value in air conditioning engineering is used.

As in the case of the roof surface solar absorptance a_{r }[%], the wall surface solar absorptance a_{w }[%] is determined, for example, according to JIS R 3106 or JIS A 5759.

For the external wall heat transfer resistance r_{wex }[mˆ2k/W], a normal value in air conditioning engineering is used.

The wall structure heat resistance R_{wc }[mˆ2k/W] is calculated based on the wall structure of the building and the heat conductivity and thickness of each wall component.

For the internal wall heat transfer resistance r_{win }[mˆ2k/W], a normal value in air conditioning engineering is used.

Parameters obtained from internal conditions of the building include the internal temperature T_{in }[° C.], the internal air volume V_{air }[mˆ3], the internal air volumetric specific heat capacity c_{air }[Wh/mˆ3k], the ventilation rate N [number of times/h], and the internal heat source H [W].

The internal temperature T_{in }[° C.] is a fixed value which is an air conditioning temperature (target temperature).

The internal air volume V_{air }[mˆ3] is calculated from the capacity of the building.

For the internal air volumetric specific heat capacity c_{air }[Wh/mˆ3k], a physical property value of air is used.

The ventilation rate N [number of times/h] is a value estimated based on the status of use of the interior of the building.

The internal heat source H [W] is a value estimated based on the power consumption of equipment used in the building and the number of people in the building.

The above described parameters may be entered by a user or stored in the storage apparatus **113**.

In step S**1**-**12**, the processing unit **112** applies the above parameters in equations representing thermal circuits, solves the equations by steady-state calculations, and thereby obtains the heat load of the building. In step S**1**-**13**, the processing unit **112** displays the calculated heat load.

[Heat Load Calculation]

FIG. 4 is a drawing used to describe a method of calculating the heat load of a building, which is used as an example of an object in the descriptions below.

The exemplary building has a roof composed of a roof base **211**, a coating **212**, and a ceiling structure heat insulator **213**; and walls each composed of a wall base **221**, a coating **222**, and a wall structure insulator **223**.

In the thermal circuit of the roof of the building described above, the roof heat transfer resistance r_{rex}, the roof structure heat resistance R_{rc}, and the ceiling heat transfer resistance r_{rin }are connected in series between the external temperature T_{ex }and the internal temperature T_{in}. The heat flow (a_{r}×I_{r}) obtained by multiplying the roof surface solar irradiance I_{r }and the roof surface solar absorptance a_{r }flows into a connecting point between the roof heat transfer resistance r_{rex }and the roof structure heat resistance R_{rc}. The heat flow into the building through the roof can be obtained from the steady-state solution of an equation representing the above thermal circuit using Kirchhoff's law.

The temperature difference between the external temperature T_{ex }and the internal temperature T_{in }is expressed by (T_{ex}−T_{in}). When i_{r }denotes the heat flow into the building through the roof, the heat flow out of the building is expressed as follows:

{(a_{r}×I_{r})−i_{r}} (8)

Therefore,

(*T*_{ex}*−T*_{in})=*i*_{r}×(*R*_{rc}*+r*_{in})−{(*a*_{r}*×I*_{r})−*i*_{r}*}r*_{rex }

=*i*_{r}×(*R*_{rc}*+r*_{in}*+r*_{rex})−(*a*_{r}*×I*_{r}*×r*_{rex}) (9)

Therefore,

(*T*_{ex}*−T*_{in})+(*a*_{r}*×I*_{r}*×r*_{rex})=*i*_{r}×(*R*_{rc}*+r*_{in}*+r*_{rex}) (10)

Thus, the heat flow into the building is obtained by the following equation:

*i*_{r}={(*a*_{r}*×I*_{r}*×r*_{rex})+(*T*_{ex}*−T*_{in})}/(*R*_{rc}*+r*_{in}*+r*_{rex}) (11)

The roof surface temperature T_{rs }is obtained by the following equation using the heat flow i_{r}:

*T*_{rs}*=T*_{in}*+i*_{r}×(*R*_{rc}*+r*_{in}) (12)

The ceiling temperature T_{rc }is obtained by the following equation using the heat flow i_{r}:

*T*_{rc}*=T*_{in}*+i*_{r}*×r*_{rin} (13)

In the thermal circuit of each of the walls of the building described above, the external wall heat transfer resistance r_{wex}, the wall structure heat resistance R_{wc}, and the internal wall heat transfer resistance r_{win }are connected in series between the external temperature T_{ex }and the internal temperature T_{in}. The heat flow (a_{w}×I_{w}) obtained by multiplying the wall surface solar irradiance I_{w }and the wall surface solar absorptance a_{w }flows into a connecting point between the external wall heat transfer resistance r_{wex }and the wall structure heat resistance R_{wc}. As in the case of the heat flow i_{r}, the heat flow i_{w }flowing into the building through each of the walls is obtained from the steady-state solution of an equation representing the above thermal circuit using Kirchhoff's law.

Each of the heat flows i_{r }and i_{w }is a heat flow per unit area. Therefore, the heat flows through the roof and the north, south, east, and west walls can be calculated separately. When i_{r }is the heat flow per unit area of the roof, i_{wE }is the heat flow per unit area of the east wall, i_{wW }is the heat flow per unit area of the west wall, i_{wS }is the heat flow per unit area of the south wall, i_{wN }is the heat flow per unit area of the north wall, S_{r }is the roof surface area, S_{wE }is the east wall surface area, S_{wW }is the west wall surface area, S_{wS }is the south wall surface area, and S_{wN }is the north wall surface area,

the heat flow through the entire roof is obtained by

i_{r}×S_{r} (14)

the heat flow through the east wall is obtained by

i_{wE}×S_{wE} (15)

the heat flow through the west wall is obtained by

i_{wW}×S_{wW} (16)

the heat flow through the south wall is obtained by

i_{wS}×S_{wS} (17)

and, the heat flow through the north wall is obtained by

i_{wN}×S_{wN} (18)

The heat flow Q_{air }caused by ventilation is normally obtained by the following equation using the above described parameters:

*Q*_{air}*=C*_{air}*·V*_{air}·(*T*_{ex}*−T*_{in})·N (19)

The heat from the internal heat source is indicated by H.

The amount of heat I flowing into the building is obtained by adding the results of formulas (14) through (18), the heat flow Q_{air}, and the heat H from the internal heat source. The equation is expressed as follows:

*I*=(*i*_{r}*×S*_{r})+(*i*_{wE}*×S*_{wE})+(*i*_{wW}*×S*_{wW})+(*i*_{wS}*×S*_{wS})+(*i*_{wN}*×S*_{wN})+*Q*_{air}*+H* (20)

The amount of heat I flowing into the building is obtained by the above equation (20). The above parameters and the solutions of the equations representing the thermal circuits can be easily obtained by steady-state calculations.

How to obtain the internal temperature T_{in }when the heat flow is 0 is described below.

From the equation (11), the internal temperature T_{in }is obtained as follows:

*T*_{in}*=T*_{ex}+(*a*_{r}*×I*_{r}*×r*_{rex})−*i*_{r}·(*R*_{rc}*+r*_{in}*+r*_{rex})

When the internal heat source H and the heat flow caused by ventilation is taken into account, the internal temperature T_{in(j) }at the time point j is obtained by the following equation (21):

*T*_{in(j)}*=T*_{ex(j)}+H_{(j)}*+Σ{S*_{i}*·a*_{i}*·I*_{i(j)}*·r*_{iex}/(*r*_{ex}*+R*_{ic}+r_{iin})}/c_{air}*·V*_{air}*·N*_{(j)}*+Σ{S*_{i}/(*r*_{iex}*+R*_{ic}*+r*_{iin})} (21)

In the equation (21), Σ denotes the sum of the results of performing calculations in corresponding parentheses for each of the roof and the north, south, east, and west walls.

In the equation (21), the heat capacity of the building is not taken into account. To improve the measurement accuracy, the heat capacity of the building is preferably taken into account.

When the roof structure heat capacity is C_{r}, the wall structure heat capacity is C_{w}, the internal air heat capacity is C_{air}, and the internal furniture heat capacity is C_{f}, the building heat capacity C_{t }is normally obtained by the following equation (22):

*C*_{t}={(*C*_{r}*+C*_{w})/2*}+C*_{air}*+C*_{f} (22)

When the internal temperature at the time point j is T_{in(j)}, the external temperature is T_{ex(j)}, and the roof surface solar irradiance is I_{r(j)}, the heat flow i_{r(j) }flowing through the roof into the interior of the building is obtained from the equation (11) as follows:

*i*_{r(j)}={(*a*_{r}*×I*_{r(j)}*×r*_{rex})+(*T*_{ex(j)}*−T*_{in(j)})}/(*R*_{rc}*+r*_{in}*+r*_{rex}) (23)

When the following equation (24) is used for simplification

*r*_{rex}*+R*_{rc}*+r*_{rin}=1*/k*_{r} (24)

the equation (23) is expressed as follows:

*i*_{r(j)}*=k*_{r}×{(*a*_{r}*×I*_{r(j)}*×r*_{rex})+(*T*_{ex(j)}*−T*_{in(j)})} (25)

The heat flows i_{wE(j)}, i_{wW(j)}, i_{wS(j)}, and i_{wN(j) }at the time point j through the north, south, east, and west walls can be separately obtained in a similar manner.

When the ventilation rate is N, the heat flow Q_{air(j) }caused by ventilation at the time point j is obtained by the following equation (26):

*Q*_{air(j)}*=C*_{air}(*T*_{ex(j)}*−T*_{in(j)})·*N*_{(j)} (26)

From the equation (20), the amount of heat I_{(j) }flowing into the building at the time point j is obtained by the following equation (27):

*I*_{(j)}=(*i*_{r(j)}*×S*_{r})+(*i*_{wE(j)}*×S*_{wE})+(*i*_{wW(j)}*×S*_{wW})+(*i*_{wS(j)}*×S*_{wS})+(*i*_{wN(j)}*×S*_{wN})+*Q*_{air(j)}*+H*_{(j)} (27)

When the following equation is used for simplification

(*i*_{r(j)}*×S*_{r})+(*i*_{wE(j)}*×S*_{wE})+(*i*_{wW(j)}*×S*_{wW})+(*i*_{wS(j)}*×S*_{wS})+(*i*_{wN(j)}*×S*_{wN})=Σ(*i*_{i(j)}*×S*_{i})

the equation (27) is expressed as follows:

*I*_{(j)}=(*i*_{i(j)}*×S*_{i})+*Q*_{air(j)}*+H*_{(j)} (28)

From the equations (25) and (26), the equation (28) is expressed as follows:

*I*_{(j)}*=Σk*_{i}*×S*_{i}×{(*a*_{i}*×I*_{i(j)}*×r*_{iex})+(*T*_{ex(j)}*−T*_{in(j)})}+{*C*_{air}(*T*_{ex(j)}*−T*_{in(j)})·*N*_{(j)}*}+H*_{(j)} (29)

The external temperature T_{ex }and the solar irradiance on each surface I_{i }vary continuously depending on meteorological conditions between the time point j and the time point j+1. However, the external temperature T_{ex }and the heat flow I at the time point (j+1) which is approximate to the time point j are substantially the same as those at the time point j.

Therefore, when

T_{ex(j)}=T_{ex(j+1) }

I_{i(j)}=I_{i(j+1) }

and when the building heat capacity is C_{t}, the rise Δ T_{in(j) }of the internal temperature between the time point j and the time point j+Δ t (0<Δ t<1) is expressed as follows:

*C*_{t}*·ΔT*_{in(j)}*=[Σk*_{i}*×S*_{i}×{(*a*_{i}*×I*_{i(j)}*×r*_{iex})+(*T*_{ex(j)}*−T*_{in(j)})}+{*C*_{air}(*T*_{ex(j)}*−T*_{in(j)})·*N*_{(j)}*}+H*_{(j)}*]·Δt* (30)

When (T_{ex(j)}−T_{in(j)})=x, the equation (30) is expressed in the form of a differential equation as follows:

{Σ*k*_{i}*×S*_{i}*×a*_{i}*×I*_{i(j)}*×r*_{iex}*+H*_{(j)}*}−{Σk*_{i}*×S*_{i}*+C*_{air}*×N*_{(j)}*}×x=C*_{t}·(*dx/dt*) (31)

When the following equations (32) and (33) are used for simplification

Σ*k*_{i}*×S*_{i}*×a*_{i}*×I*_{i(j)}*×r*_{iex}*+H*_{(j)}*=H*_{(j)}′ (32)

Σ*k*_{i}*×S*_{i}*+C*_{air}*×N*_{(j)}*=KS*_{(j)} (33)

the equation (31) is expressed as follows:

*H*_{(j)}*′+KS*_{(j)}*×x=C*_{t}·(*dx/dt*) (34)

The equation (34) can be transformed into the following equation (34-1):

*dx/{H*_{(j)}*′+KS*_{(j)}*×x}=*1*/C*_{t}*·dt* (34-1)

Multiplying both sides of the equation (34-1) by KS_{(j) }provides the following equation (34-2):

*dx/{H*_{(j)}*′/KS*_{(j)}*+x}=KS*_{(j)}*/C*_{t}*·dt* (34-2)

The equation (34-2) can be further transformed into the following equation (34-3):

*dx*/{−(*H*_{(j)}*′/KS*_{(j)})*−x*}=−(*KS*_{(j)}*/C*_{t})*·dt* (34-3)

When both sides of the equation (34-3) are integrated by using the following integral formula (34-4),

∫{*dx*/(*a−x*)}=−{ln(*a−x*)+ln*C*} (C is an integral constant) (34-4)

and when Δt=0 and the integral constant C is such that T_{in(j)}=T_{in(j+Δt)}, the following equation (35) is obtained:

*T*_{in(j+1)}*=T*_{ex(j)}*+H*_{(j)}*′/KS*_{(j)}−(*T*_{ex(j)}*+H*_{(j)}*′/KS*_{(j)}*−T*_{in(j)})*exp*(−*KS*_{(j)}*/C*_{t}*·Δt)* (35)

When Δt=1, the equation (35) is expressed as follows:

*T*_{in(j+1)}*=T*_{ex(j)}*+H*_{(j)}*′/KS*_{(j)}*−(T*_{ex(j)}*+H*_{(j)′}*/KS*_{(j)}*−T*_{in(j)})*exp*(−*KS*_{(j)}*/C*_{t}) (36)

Changes in the internal temperature can be simulated by assigning an appropriate initial value to the internal temperature T_{in }in the equation (36). The time interval between the time point j and the time point (j+1) is preferably between about ten minutes and about one hour.

When the building heat capacity C_{t }is not taken into account, the following equation (37) can be used to simulate the internal temperature T_{in}:

*T*_{in(j)}*=T*_{ex(j)}*+H*_{(j)}*′/KS*_{(j)} (37)

The equation (37) is obtained by rewriting the equation (21) by using the equations (24), (32), and (33).

Changes in the roof surface temperature T_{rs }can be simulated by using the following equation (38) obtained from the equation (12):

*T*_{rs(j)}*=T*_{in(j)}*+i*_{r(j)}×(*R*_{rc}*+r*_{rin}) (38)

Changes in the ceiling temperature T_{rc }can be simulated by using the following equation (39) obtained from the equation (13):

*T*_{rc(j)}*=T*_{in(j)}*+i*_{r(j)}*×r*_{rin} (39)

[Heat Load Calculation Process]

An exemplary process of a heat load calculation is described below.

FIG. 5 is a flowchart illustrating an exemplary process of a heat load calculation.

In step S**2**-**1**, the processing unit **112** calculates the coefficient (1/k_{i}) by combining obtained heat resistance values. The coefficient (1/k_{i}) is obtained by applying the obtained heat resistance values r_{iex}, R_{ic}, and r_{iin }in the equation (24). _{i }stands for _{r }indicating the roof, _{wE }indicating the east wall, _{wW }indicating the west wall, _{wS }indicating the south wall, and _{wN }indicating the north wall.

In step S**2**-**2**, the processing unit **112** calculates the building heat capacity C_{t }by combining obtained heat capacity values. The building heat capacity C_{t }is calculated by assigning obtained heat capacity values to C_{r}, C_{w}, and C_{f }in the equation (22).

In step S**2**-**3**, the processing unit **112** combines parameters including the coefficient (1/k_{i}), which is obtained by combining the heat resistances, and the building heat capacity C_{t }by using the equations (32) and (33).

In step S**2**-**4**, the processing unit **112** resets the time point j to 0.

In step S**2**-**5**, the processing unit **112** obtains a parameter at the time point j. In step S**2**-**6**, the processing unit **112** applies the obtained parameter in the equation (36) and thereby calculates the internal temperature T_{in(j+1) }at the time point j+1.

In step S**2**-**7**, the processing unit **112** determines whether all calculations are completed. If not, the processing unit **112** increments the value of j in step S**2**-**8**, and repeats the steps from step S**2**-**5**. When all calculations are completed, the processing unit **112** displays the results.

[Simulation Results]

An example of a simulation performed using the above described heat prediction system is described below.

FIG. 6 is a table showing structural conditions of a building used in the exemplary simulation. FIG. 7 is a table showing internal conditions of a building used in the exemplary simulation. FIG. 8 is a table showing exemplary meteorological conditions at a place where a building used in the exemplary simulation is located. FIG. 9 is a drawing illustrating a calculation process in the exemplary simulation. FIG. 10 is a graph showing the results of an exemplary internal temperature simulation.

A warehouse in Koriyama City, Fukushima Prefecture, Japan is used in this exemplary simulation. An internal temperature of 18.5° C. measured at 24:00 on June 13th is used as an initial value.

The parameter (1/k_{i}), which is the sum of heat resistances, is obtained by applying the structural conditions shown in FIG. 6 in the equation shown in FIG. 9 (A).

The building heat capacity C_{t }is obtained by applying the internal conditions shown in FIG. 7 in the equation shown in FIG. 9 (B).

The parameters H_{(j=0)}′ and KS_{(j=0) }are obtained by applying the parameters at the time point j=0 in the equations (32) and (33) as shown in FIG. 9 (C).

The internal temperature T_{in(j=1) }at a time point 1 hour (Δ t) from the time point j=0 is obtained by applying the initial internal temperature T_{in(j=0)}=18.5° C. and parameters H_{(j=0)}′ and KS_{(j=0)}, which parameters are obtained in FIG. 9 (C), in the equation (36) shown in FIG. 9 (D). As shown above, the internal temperature T_{in(j=1) }at the time point j=1 (at 1:00 on June 14th) can be predicted by using the parameters at the time point j=0 (at 24:00 on June 13th).

In a similar manner, the internal temperature T_{in(j=2) }at the time point j=j+1=2 can be obtained by applying the parameters at the time point j=1 in the equation (an equivalent of the equation (36)) shown in FIG. 9 (E). Further, the internal temperature T_{in(j) }at subsequent time points j can be predicted similarly.

In FIG. 10, ◯ marks indicate the hourly prediction results of the above exemplary internal temperature simulation.

The results of the exemplary internal temperature simulation according to this embodiment show approximately the same temperature changes as the actual measurements indicated by ● marks in FIG. 10. Such results show that the heat amount prediction method according to an embodiment of the present invention enables accurate internal temperature simulation. In the same graph, Δ marks show the results of an internal temperature simulation performed without taking the building heat capacity into account, which results are quite different from the actual measurements and therefore inaccurate. As is evident from the above results, parameters such as meteorological conditions and the heat capacity of the building should be taken into account for an accurate simulation. The line in the graph shows the changes in the external temperature T_{ex}.

Prediction of changes in the temperature T_{in }enables the evaluation of the coatings **212** and **222**.

[Effectiveness]

In a heat amount prediction method according to an embodiment of the present invention, which method uses thermal circuits for calculation, the heat flows through the roof and the north, south, east, and west walls, the heat flow caused by ventilation, and the heat flow from the internal heat source are calculated separately; and those calculated heat flows are summed to obtain the total heat load of an object. With such a heat amount prediction method, heat flows can be calculated very easily by steady-state calculations.

[Others]

In the above embodiment, the internal temperature T_{in }is simulated. However, a heat amount prediction method according to an embodiment of the present invention may be applied to simulations of, for example, the ceiling temperature and the wall surface temperature which temperatures can be calculated using thermal circuits. Also, power consumption of air-conditioning equipment can be calculated from the results of a heat flow simulation.

In the above embodiment, the heat load of a building is calculated. However, the present invention may also be applied to a calculation of the heat load of any other structure such as a road.

FIG. 11 is a drawing illustrating an exemplary method of calculating the heat load of a road.

The exemplary road shown in FIG. 11 has a layered structure where a road bed **312** is laid on soil **311**, a road base **313** is laid on the road bed **312**, a base pavement **314** and a surface pavement **315** are laid on the road base **313**, and a coating **316** is formed on the surface pavement **315**.

In an exemplary thermal circuit of the road shown in FIG. 6, the soil heat resistance Rr**1**, which is the heat resistance of the soil **311**, the road bed structure heat resistance Rr**2**, the road base heat resistance Rr**3**, which is the heat resistance of the road base **313**, the pavement structure heat resistance Rr**4**, and the surface heat transfer resistance r_{rex }are connected in series between the external temperature T_{ex }and the underground temperature T_{in}. With the above thermal circuit, the heat flow through the layers of the road can be predicted in a manner similar to that of a building. Prediction of the heat flow through the layers of the road enables the evaluation of the coating **316**.

As described above, embodiments of the present invention enable prediction of temperature changes, heat flows, and the like not only in a building but also in any other object such as a road.

The present invention is not limited to the specifically disclosed embodiments, and variations and modifications may be made without departing from the scope of the present invention.

The present application is based on Japanese Priority Application No. 2005-198760, filed on Jul. 7, 2005, the entire contents of which are hereby incorporated herein by reference.