simultaneous heat and moister transfer in soil

8/14/2019 Simultaneous heat and moister transfer in soil

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G.H. dos Santos, N. Mendes/ Energy and Buildings 38 (2006) 303314304

Nomenclature

Ai area of the i-th surface (m2)

Aj,f area of j-th control volumes of the floor sur-

face discretized by using the finite-volume

method (m2

)c specific heat (J/(kg K))

cm mean specific heat (J/(kg K))

cw wall specific heat (J/(kg K))

cair air specific heat (J/(kg K))

DTl liquid phase transport coefficient associated to

a temperature gradient (m2/(s K))

DTv vapor phase transport coefficient associated to

a temperature gradient (m2/(s K))

Dul liquid phase transport coefficient associated to

a moisture content gradient (m2/s)

Duv vapor phase transport coefficient associated to

a moisture content gradient (m2/s)

DT mass transport coefficient associated to atemperature gradient (m2/(s K))

Du mass transport coefficient associated to a

moisture content gradient (m2/s)

Et energy flow that crosses the room control

surface (W)

Eg internal energy generation rate (W)

hm mass convection coefficient (m/s)

hmf floor mass convection coefficient (m/s)

hms soil mass convection coefficient (m/s)

h convection coefficient (W/(m2 K))

hint internal convection heat transfer coefficient

between internal surfaces and room air(W/(m2 K))

hext external convection heat transfer coefficient

between external surfaces and external air

(W/(m2 K))

hroof external convection heat transfer coefficient

for the rooftop (W/(m2 K))

hD the floor mass transfer coefficient (kg/m2 s),

H depth of the ground (m)

jv vapor flow (kg/(m2 K))

jl liquid flow (kg/(m2 K))

j total flow (kg/(m2 K))

L latent heat of vaporization (J/kg)

minf mass flow by infiltration (kg/s)

mvent mass flow by ventilation (kg/s)

mb water vapor flow from the breath of occupants

(kg/s)

mger internal water-vapor generation rate (kg/s),

M molecular mass (kg/kmol)

m number of surfaces

n number of control volumes of the floor surface

discretized by using the finite-volume method

Ps saturated pressure (Pa)

prev previous iteration

qr solar radiation (W/m2)

R universal gas constant (J/(kmol K))

Rlw long-wave radiation (W/m2)

T temperature (8C)

T0 temperature calculated at the previous time

step (8C)

Ti temperature of each surface of the building

envelope (8C)

Tint room air temperature (8C)

Text external air temperature (8C)

Ty=H temperature of the ground or floor surfaces

(8C)

Tx=0 temperature on the external surfaces (8C)

Tx=e temperature on the internal surfaces (8C)

Tprev temperature calculated at the previous itera-

tion (8C)

Tsur temperature of internal surfaces of surround-

ing walls (8C)

t time (s)Vair room volume (m

3)

W0 humidity ratio calculated at the previous time

step and (kg water/kg dry air)

Wext external humidity ratio (kg water/kg dry air)

Wint internal humidity ratio (kg water/kg dry air)

Wv,f the humidity ratio of each control volume (kg

water/kg dry air)

as soil solar absorptivity

aw wall solar absorptivity

es soil emissivity

ef floor emissivity

e

wwall emissivity

eroof roof emissivity

fv view factor

f relative humidity

fext external relative humidity

l thermal conductivity (W/(m2 K))

lf floor (concrete) thermal conductivity

(W/(m K))

ls soil thermal conductivity (W/(m K))

lw wall thermal conductivity (W/(m K))

lroof roof thermal conductivity (W/(m K))

r density (kg/m3)

r0 solid matrix density (kg/m3)

rl water density (kg/m3)pv,1 vapor density in the surrounding air far from

the soil surface (kg/m3)

Pv,y=H vapor density at the upper surface of the soil

domain (kg/m3)

rair air density (kg/m3)

u volume basis moisture content (m3/m3)

uprev volume basis moisture content calculated at

the previous iteration (m3/m3)

s StefanBoltzmann constant (W/(m2 K4))


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been developed by Blomberg [6]. These codes can be used

for analyses of thermal bridge effects, heat transfer through

the corners of a window and heat loss from a house to the

ground. However, the moisture presence has been ignored.

Matsumoto et al. [7] described a program for ground

temperature data generation, using the finite-element

method. Latent heat losses by evaporation at the groundsurface and snow cover on the surface are considered in their

program.

Krarti [8] discussed the effect of spatial variation of soil

thermal properties on slab-on-ground heat transfer by using

the Interzone Temperature Profile Estimation (ITPE)

technique.

In the works mentioned above, the conductivity and the

thermal capacity are considered constant and the moisture

effect is ignored. However, the presence of moisture in the

ground implies an additional mechanism of transport: in the

pores of unsaturated soil, liquid water evaporates at the

warm side, absorbing latent heat of vaporization, while, due

to the vapor-pressure gradient, vapor condenses on the

coldest side of the pore, releasing latent heat of vaporization

[9]. This added or removed latent heat can cause great

discrepancies on the prediction of room air temperature and

relative humidity, when compared to values obtained by pure

conduction heat transfer [2].

Moreover, Brink and Hoogendoorn [10] analyzed

groundwater losses due to conduction and natural convec-

tion heat transfer modes and verified that convection heat

losses are mainly dependent on soil permeability.

Freitas and Prata [11] elaborated a numerical methodol-

ogy for thermal performance analysis of power cables under

the presence of moisture migration in the surrounding soil.They utilized a two-dimensional finite-volume approach to

solve the governing equations and the boundary conditions

did not take any phase-change effect into account.

Ogura et al. [12] analyzed the heat and moisture behavior

in underground space in a two-dimensional model using the

quasi-linearized method. The outdoor temperature, relative

humidity, solar radiation and precipitation were investigated

as outdoor conditions.

Some simplified models can be also found in the

literature such as the model utilized by the MOHID program

[13]. This code, using the Richardss equation, is utilized for

simulating marine processes, quality processes in reservoirs

and water flow in unsaturated media.

Combined heat and moisture transfer in soils may require

the use of very short time steps, especially at highly

permeable surfaces, which may prohibit the use of long time

step for long-term simulations. Galbraith [14] noticed the

influence of the spatial discretization on the accuracy of the

numerical simulation on the heat and mass transport in

porous media. It was observed that in one-dimensional

discretization, the two-way model, based on the technique of

control volume, can be used to avoid refined meshes.

Due to the numerical instabilities caused by the effect of

latent heat at the boundaries, Wang and Hagentoft [15]

presented a numerical method based on an algorithm that

combines an explicit model with relaxation schemes. In this

model, a criterion for time step determination is developed

to improve numerical stability.

For ensuring numerical stability in the present model, the

linearized set of equations was obtained by using the finite-

volume method and the MultiTriDiagonal-Matrix Algorithm[16] to solve a three-dimensional model to describe the

physical phenomena of heat and mass transfer in sandy-silt

and sandy porous soils. In this way, the code has been

conceived to be numerically robust with a fast-simulating

procedure. The heat and moisture transfer in soils was based

on the theory of Philip and De Vries [17], which is one of the

most disseminated and accepted mathematical formulation

for studying heat and moisture transfer through porous soils,

considering both vapor diffusion and capillary migration.

Janssen et al. [18] elaborated an analysis of heat loss

through a basement and presented as false a generally

accepted postulate in building simulation: the combined heat

and mass transfer in ground can be ignored for the heat flow

calculation through the building foundation. In this context,

Onmura et al. [19] investigated the evaporative cooling

effect of roofs lawn gardens and observed a reduction of up

to 50% on the heat flux through the ceiling.

In soil simulation, some parameters such as the boundary

conditions, initial conditions, simulation time period

(including warm-up), simulation time step and grid

refinement have to be carefully chosen and combined in

order to reach accuracy without using excessive computa-

tional processing.

In this way, it is presenteda mathematicalmodel in order to

test the hygrothermal performance of buildings by consider-ing the combined three-dimensional heat and moisture

transport through the ground for capillary unsaturated porous

soils. Heat diffusion through building envelope (walls and

roof) was calculated by using the Fouriers law. The

importance of considering a three-dimensional approach

for the soil domain for low-rise buildings was verified by

Santos and Mendes [20], using a simply conductive model for

ground heat transfer calculation.

The room can be submitted to loads of solar radiation,

inter-surface long wave radiation, convection, infiltration and

internal gains from light, equipment and people. A lumped

approach for energy and water vapor balances is used to

calculate the room air temperature and relative humidity.

2. Mathematical model

The physical problem is divided into three domains:

ground, building envelope (walls and roof) and room air. At

the external surfaces, the heat transfer due to short wave

radiation and convection were considered as boundary

conditions and the long-wave radiation losses were taken

into account only at horizontal surfaces, i.e., ground and

roof. At the internal surfaces, besides the convection heat

G.H. dos Santos, N. Mendes/ Energy and Buildings 38 (2006) 303314 305


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transfer, long-wave radiation exchange between the surfaces

was considered and for the ground and floor a combined heat

and mass transfer model was used.

2.1. Soil and floor domain

The governing equations, based on the theory of Philipand De Vries [17], to model heat and mass transfer through

porous media, are given by Eqs. (1) and (2). The energy

conservation equation is written in the form:

r0cmT; u@T

@t r lT; urT LTr jv (1)

and the mass conservation equation as:

@u

@t r

j

rl

; (2)

where r0 is the solid matrix density (m3/kg); cm, the mean

specific heat (J/(kg K)); T, temperature (8

C); l, thermalconductivity (W/(m K)); L, latent heat of vaporization (J/

kg); u, volumetric moisture content (m3/m3); jv, vapor flow

(kg/(m2 K)); j, total flow (kg/(m2 K)); rl is the water density

(kg/m3).

The total three-dimensional vapor flow (j) given by

summing the vapor flow (jv) and the liquid flow (jl) can be

described as:

j

rl

DTT; u

@T

@x DuT; u

@u

@x

i

DTT; u@T

@y DuT; u

@u

@yj

DTT; u

@T

@z DuT; u

@u

@z

@Kg

@z

k; (3)

with DT= DTl + DTv and Du = Dul + Duv, where DTl is the

liquid phase transport coefficient associated to a temperature

gradient (m2 /(s K)), DTv, vapor phase transport coefficient

associated to a temperature gradient (m2/(s K)), Dul, liquid

phase transport coefficient associated to a moisture content

gradient (m2/s), Duv, vapor phase transport coefficient asso-

ciated to a moisture content gradient (m2/s), DT, mass

transport coefficient associated to a temperature gradient

(m2/s K) and Du is the mass transport coefficient associated

to a moisture content gradient (m2/s).Fig. 1 shows the physical domain. According to Fig. 1,

the boundary conditions, for the most generic case (three-

dimensional), can be mathematically expressed as:

Surface 1 (in contact with internal air):lfT; u

@T

@y

yH

LTjvyH

hfTint TyH Xmi1

fvefsT4sur T

4yH

LThmfrv;int rv;yH (4)

Surface 2 (in contact with external air):lsT; u

@T

@y

yH

LTjvyH

hsText TyH asqr LThmsrv;ext rv;yH esRlw; (5)

where h(T1

Ty=H) represents the heat exchanged by con-vection with the external air, described by the surface

conductance h, asqr is the absorbed short-wave radiation

and LThmrv;1 rv;yH, the phase-change energy term.The long-wave radiation loss is defined as Rlw (W/m

2) and e

is the surface emissivity. The solar absorptivity is repre-

sented by a and the mass convection coefficient by hm,

which is related to h by the Lewis relation.

Similarly, the mass balance at the upper surface is written

as:DufT; u

@u

@y DTfT; u

@T

@y

yH

hmf

rlrv;int ryH;

(6)

for surface 1 (in contact with internal air), and as:DusT; u

@u

@y DTsT; u

@T

@y

yH

hms

rlrv;ext ryH;

(7)

for surface 2 (in contact with external air).

The other soil domain surfaces were all considered

adiabatic and impermeable.

Eqs. (6) and (7) show a vapor concentration difference,

Drv, on their right-hand side. This difference is between the

porous surface and air and is normally determined by using

the values of previous iterations for temperature and

moisture content, generating additional numerical instabil-

ity. Due to the instability created by this source term, the

solution of the linear set of discretized equations normally

requires the use of very small time steps, which can be

exceedingly time consuming especially in long-term soil

simulations; in some research cases, a time period of several

decades has to be simulated, taking into account the three-


Fig. 1. Physical domain for ground and floor.


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The sensible heat released by the building envelope and

floor is calculated as:

Qst Xmi1

hintAiTxet Tintt (14)

for the sensible conduction load and as:

Qfloort Xnj1

LTyHthmfAj;frv;intt rv;ft (15)

for the latent load from floor.

In Eq. (14) Ai represents the area of the i-th surface (m2),

hint the convection heat transfer coefficients (W/(m2 K)),

Tx=e(t) the temperature at the i-th internal surface of the

building (8C) and Tint(t) the room air temperature (8C). In

Eq. (15), n is the number of control volumes of the floor

surface discretized by using the finite-volume method; L, the

vaporization latent heat (J/kg); hmf, the floor mass

convection coefficient (m/s); Aj,f, the area of j-th control

volumes of the floor surface discretized by using the finite-

volume method (m2); rv,int, internal water vapor density (kg/

m3); rv,fthe water vapor density of each control volume (kg/

m3). The temperature and vapor density are calculated by the

combined heat and moisture transfer model described in

Section 2.1 by using the values of temperature, moisture

content and sorption isotherm.

In terms of water vapor mass balance, different

contributions were considered: ventilation, infiltration,

internal generation, people breath and floor surface. In this

way, the lumped formulation becomes:

minf mventWext Wint mb mger

Xnj1

hDAj;f

Wv;f Wint

! rairVair

dWint

dt; (16)

where mint is the mass flow by infiltration (kg/s); mvent, the

mass flow by ventilation (kg/s); Wext the external humidity

ratio (kg water/kg dry air); Wint, the internal humidity ratio

(kg water/kg dry air); mb, the water vapor flow from the

breath of occupants (kg/s); mger, the internal water-vapor

generation rate (kg/s); hD, the mass transfer coefficient (kg/

m2 s); Aj,f represents the area of j-th control volumes of the

floor surface (m2); Wv,f, the humidity ratio of each control

volume (kg water/kg dry air); rair

, the air density (kg dry air/

m3); Vair is the room volume (m3).

The water-vapor mass flow from the people breath is

calculated as shown in ASHRAE [21], which takes into

account the room air temperature, humidity ratio and

physical activity as well.

Santos and Mendes [22] presented and discussed

different numerical methods used to integrate the differential

governing equations in the air domain (Eqs. (13) and (16)),

showing the results in terms of accuracy and computer run

time. In their analysis, it was shown that the use of explicit

methods such as Euler and Modified Euler requires

imperatively very small time steps, making simulations

extremely time consuming. A third method used was the one

obtained by the Matlab program, which provides analytical

expressions to be solved in a real simultaneous way.

However, these expressions are time consuming due to their

great size, even though they require less iterations due to the

numerical robustness.

In order to avoid limitations such as the requirement ofsmall time steps and high computer run time, it was shown

that the use of a semi-analytical method could be a good

strategy to solve the differential governing equations for the

room air, as it combines robustness and rapidness, which are

important criteria in whole-building simulation programs.

This last method solves analytically each equation (mass and

energy balances), but with numerical coupling between each

other. In this way, for the proposed problem, Eqs. (13) and

(16) can be written as:

A BTint rcVdTint

dt(17)

and

C DWint rVdWint

dt; (18)

which gives

Tint e

BrcVDtA BT0 A

B(19)

and

Wint e

DrVDtC DW0 C

D; (20)

where T0 and W0 are the temperature and the humidity ratiocalculated at the previous time step and

A Xmi1

hAiTi Egs EglWprev;

B Xmi1

hAi;

C minfWext mrespTprev mger Xnj1

hDAj;fWv;f and

D minf mvent

Xm

i1

hDAj;f

;

with Egs as the sensible energy (infiltration + generation)(W),

Egl, the latent energy (infiltration + generation) (W), Ti, the

temperature of each surface of the building envelope (8C).

3. Simulation procedure

A C-code was elaborated for the prediction of the

building hygrothermal performance. For the simulation, a

25-m2 single-zone building with two windows (single glass

layer) and one door, distributed as shown in Fig. 3 was

considered. For the conduction load calculation, 0.19-m



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4. Results

The boundary conditions, the pre-simulation time period

(warm-up), the size of the physical domain, the simulation

time step, the grid refinement, the convergence errors and the

required computer run time are important simulation

parameters, which have to be chosen very carefully in

order to accurately predict temperature and moisture content

profiles in soils under different sort of weather data.

In the sensitivity analysis, the results presented in Figs. 5

10 were obtained by carrying out simulations for the sandy

silt soil only. In Section 4.4, the comparison results shown

in Figs. 1117 were obtained for both sandy silt and sand

soils.

In all cases, sinusoidal functions (Eqs. (21)(23)) have

been considered to represent the weather. In the soil domain

of the building located in the city of Curitiba-Brazil (south

latitude of 25.48), a constant convection heat transfer

coefficient of 10 W/(m2 K), an absorptivity of 0.5 and a

constant long-wave radiation loss of 30 W/m2 were

considered as a boundary condition at the upper surface.


Fig. 5. Temperature profiles of the sandy silt soil for different time steps.

Fig. 6. Moisture content profiles of the sandy silt soil for different time

steps.

Fig. 7. Temperature profiles of the sandy silt soil for different node

numbers.

Fig. 8. Moisture content profiles of the sandy silt soil for different node

numbers.

Fig. 9. Temperature profiles in a soil physical domain with a 5-m depth.

Fig. 10. Moisture content profiles in a soil physical domain with a 5-m

depth.


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The other surfaces were considered adiabatic and imperme-able.

In the analysis of moisture effects on indoor air (Section

4.4), three different boundary conditions were considered

for the external ground upper surface: (i) solar radiation; (ii)

rain with no solar radiation effect; (iii) rain followed by solar

radiation. For the purely conductive model, rain was not

considered.

4.1. Time step sensitivity

For the time step sensitivity analysis, the temperature and

moisture content profiles presented in Figs. 5 and 6 cor-

respond to theone obtainedon December31stat 12:00 p.m. of

the fifth year of simulation period. In this comparison, time

step of 1, 10, 30 and 60 min were considered.

A maximum temperature difference of approximately

0.3 8C on the ground surface was noticed in Fig. 5, by

comparing the different time steps. However, the moisture

content did not present any plausible difference, as it can be


Fig. 11. Variation of the internal temperature after two years of pre-

simulation.

Fig. 12. Internal humidity ratio after two years of pre-simulation period.

Fig. 13. Heat transferrate from floor (25 m2) in thesimulationperiod of one

month.

Fig. 14. Internal temperature after two years of pre-simulation period with

an infiltration rate of 10 L/s.

Fig. 15. Internal temperature considering soil and floor as sand.

Fig. 16. Internal humidity ratio considering soil and floor as sand.


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seen in Fig. 6. The low sensitivity to the time step was due to

the use of a robust numerical method [26].

4.2. Grid size refinement

In a similar way, in the analysis of sensitivity to the grid

size refinement, the values of temperature and moisture

content correspond to the one attained at 12:00 p.m. on

December 31st of the fifth year of simulation period. The

number of nodes (300, 500 and 1000) was varied on the

vertical direction only, since this is the direction where the

temperature and moisture content gradients are predomi-

nant, when no solar shading effect is considered. A time step

of 10 min was used in this case.

Increasing the number of nodes on the gravity direction

axis from 300 to 1000, a maximum temperature difference of1.8 8C (Fig. 7) is noticed. On the other hand, according to the

results presented in Fig. 8, the moisture content profile

showed a highest absolute difference of nearly 0.1 (vol.%) at

the soil top surface.

The simulation performed showed a higher sensitivity to

the grid refinement than to the time step, which has to be

carefully done as the required computer run time is much

more sensitive to the grid size than to the time step.

4.3. Depth sensitivity

Santos and Mendes [27] have presented results compar-

ing soil domains with different depth, showing that a 5-m

depth soil domain could provide reasonable results,

especially near the upper surface. In this way, for the

weather functions presented in Eqs. (21)(23), the tem-

perature and moisture content distributions vary with time

according to the results presented in Figs. 9 and 10, for a 1-h

time step and a grid of 4961 nodes.

It is possible to notice in Figs. 9 and 10 that the

temperature and moisture content values remain constant, in

essence, at the upper surface. A very slow evolution

especially in the moisture content distribution was

remarked. The time evolution differences in the temperature

and moisture content profiles are mainly attributed to the

high thermal and hygric soil capacities.

4.4. Moisture effects on indoor air

A warm-up period of two years was employed for the

analysis of the moisture effects on the heat and mass transfercalculation through the floor and ground. In Figs. 1114, for

the soil a sandy-silt type was considered, which properties

were gathered from Oliveira et al. [25] and for the floor,

properties from mortar [28] were used. Those strongly

moisture-content-dependent properties include specific heat,

density, thermal conductivity and liquid and vapor transport

coefficients associated to temperature and moisture content

gradients.

Three different boundary conditions were considered for

the external ground upper soil surface: (i) solar radiation; (ii)

rain with no solar radiation effect; (iii) rain followed by solar

radiation. For the purely conductive model, rain was not

considered.

Convection heat transfer has been taken into account in

all cases. For all external surfaces, a constant convection

heat transfer coefficient of 12 W/(m2 K) was adopted and,

for all internal surfaces, 3 W/(m2 K) was considered. A

constant long-wave radiation loss of 100 W/m2 was

attributed for the ground and roof as well as an absorptivity

of 0.5 for the ground and 0.3 for other surfaces. In the soil

domain, the laterals and lower surface were considered

adiabatic and impermeable.

In Figs. 1117, a temperature of 20 8C and a volumetric

moisture content of 4% were considered as initial conditions.

Fig. 11 shows the variation of the room air temperature.During the simulation period, it was not verified a significant

variation between the purely conductive model and the

model that takes moisture transport through the ground and

floor into account. The decrease of the internal temperature

in the rain case is mainly due to the absenceof solar radiation

during the 1-month period for the first case and 3 days, for

the second case. Therefore, it can be clearly noticeable that

solar radiation, in this case, is the uppermost thermal load

source considered in the room air energy balance.

A higher difference of approximately 15% on the internal

humidity ratio was verified in Fig. 12, when the purely

conductive model for the ground and floor is considered. It

was also noticed a low daily variation of humidity ratio when

moisture is not neglected, i.e., a lower buffer effect of

humidity in air occurs when moisture buffer capacity

materials are employed.

In the case moisture is disregarded, water vapor is only

exchanged by ex- or infiltration. Nevertheless, when

moisture is considered, the vapor flow exchanged with the

floor can be a significant counterpoise on the room air

moisture balance, providing different results in terms of

room air relative humidity.

In this context, some research [29,30] has also been

conducted to aware about the importance of indoor relative


Fig. 17. Heat transfer rate from floor considering soil and floor as sand in

the simulation period of one month.


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humidity, which significantly affects: (i) thermal and

respiratory comfort; (ii) perception of indoor air quality;

(iii) occupant health; (iv) durability of building materials (v)

energy consumption. For example, there will be twice as

many occupants dissatisfied with the indoor comfort

conditions at 24 8C and 70% relative humidity than at

248

C and 40% [30]. At the same time, the occupants willperceive the indoor air quality (IAQ) to be better at lower

humidity (in fact enthalpy) and recent research results show

that ventilation rates could be decreased notably by

maintaining a moderate enthalpy in spaces. Humidity also

influences the growth of dust mites and fungi and the

occurrence of respiratory infections, with values between 30

and 55% relative humidity recommended [30].

In addition, Salonvaara and Ojanen [31] showed also that

materials with hygroscopic capacity have the ability to

improve the performance of building envelope structures

even to such level that condensation and mold growth

conditions are eliminated.

Furthermore, there is a need to improve the indoor air

relative humidity prediction by incorporating accurate

moisture models in building thermal simulation programs

[32]. The realization of this need led to formation of an

International Research Project, in the framework of the

International Energy agency, which started in late 2003 and

comprising as many as 19 countries [30].

In Fig. 13, the heat exchanged with the floor can be

observed for the same three scenarios presented for the

relative humidity results (Fig. 12). The absence of solar

radiation during the rain period, causes the decrease of the

internal temperature of the building, increasing the heat flux

from the floor. In this case, difference of up to 100% wasobserved in Fig. 13, for the heat flux between the model that

does not consider moisture and the one that considers

moisture with boundary condition of rain.

Fig. 14 shows the evolution of room air temperature when

an infiltration rate of 10 L/s is applied. In this case, a

maximum difference of 0.5 8C was verified between the

peak values, attributed to the increase of vapor concentration

difference between internal air and floor surface, caused by

an increase of the infiltration flow.

In Figs. 1517, a sand floor was considered in order to

observe a higher evaporation rate potential. In this case, the

effect of solar radiation was also ignored and an infiltration

rate of 20 L/s was adopted.

Fig. 15 shows a small difference between the temperature

peaks for the two models.

Fig. 16 illustrates a difference of 10% on the internal

humidity ratio for the two first days of simulation. Although

the values of heat transfer rate does not present a significant

variation on the internal temperature, it is observed, in

Fig. 17, a great difference of up to 110% between the results.

In this way, the heat transfer rate at the floor surface can

be very important on the calculation of sensible heat factor

for the building, depending on the direction of the latent and

sensible heat flux exchanged with the floor.

5. Conclusion

Building simulation codes present some simplifications

on their calculation routines of heat transfer through the

ground. Regarding the ground heat transfer some aspects

should be clarified: the multidimensional phenomenon; the

transient behavior; the great number of involved parameters,mainly when moisture is considered.

A review in the literature showed divergences about

moisture effects on the ground heat transfer. In addition,

most of programs do not consider the three-dimensional

asymmetrical effect in the soil.

In this way, some comparison exercises were carried out

to show how important moisture in soils can be in different

scenarios, taking into account a coupled three-dimensional

heat and moisture transfer model integrated to a single-zone

building model.

Simulations carried out for sensitivity analyses of timestep

and grid size shown the importance of refinement at the upper

surface, which is in contact with air. On the other hand, the

results were not so sensitive to time step, allowing the

adoption of high values of time step with no loss of accuracy

thanksto therobust algorithmand to the linearization of vapor

concentration difference at soil top surface.

We also noticed the importance of a pre-simulation

period of several years for the correct estimation of

temperature and moisture content profiles. As computer

run time plays an important role in long-term soil

simulations, a depth of 5 m was suggested whereas the

main temperature and moisture content gradients are close to

the upper surface, affecting somewhat the thermal behavior

of low-rise buildings.Concerning the moisture effects on indoor air analysis, it

is showed a very slight difference in terms of room air

temperature between the purely conductive model for the

ground and the moisture model, due to the importance of

solar gains compared to ground heat transfer in the room

energy balance and due to the different time scales between

room air and soil. However, a significant difference of 15%

was noticed on the room air humidity ratio, even for the high

infiltration rate case. Therefore, higher energy consumption

could be expected when an air conditioning system is used

due to the augmentation of building latent loads.

Besides the energy related aspects, moisture models shall

be incorporated to building simulation codes due to other

indoor relative humidity effects such as perception of indoor

air quality, occupants health and durability of building

materials.

Regarding the heat flux through building floor, it was

noted a small thermal load contribution in both models.

However, the absence of solar radiation during the rain

period caused a room temperature reduction, occasioning an

increase of ground heat transfer of approximately 100%.

In order to increase the evaporative flux, the floor surface

was considered composed uniquely of sand. In this case, no

significant variations on the room temperature values were



12/12

verified between the two models. However, these results

could be more expressive for the calculation of sensible heat

factor for building zones, depending on the direction of the

latent and sensible heat fluxes at the floor surface.

Although the moisture effect has caused no significant

difference on the room air temperature, a building with a

greater area of contact with the ground or in undergroundzones where the solar radiation effect is not predominant, the

moisture flux through the floor could contribute more

effectively for the room air energy balance.

To conclude, some recommendations are addressed for

further work: (i) Simulation of underground zones and

include the moisture effects on the building envelope as

well; (ii) determination empirical correlations for ground

heat transfer; (iii) improvement of the rain model.

Acknowledgments

The authors thank the Brazilian Research Council

(CNPq) of the Secretary for Science and Technology of

Brazil for support of this work.

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