1. Introduction

The beauty of house is characterized by several parameters including the conceptual aspect, the architectural appearance, the aesthetics, and the thermal comfort inside the house (which has appositive or negative impact on the health of occupants but also labor productivity). More conceptual, architectural, aesthetic and climatic parameters, other parameters are taken into account including: orientation of the walls relative to the facades solar trajectory, the materials of the building envelope, the area of the wall panels and frames, the protection of openings, the choice of equipment etc....

Thermal comfort is often defined by the satisfaction expressed about the thermal environment. There is a distinction between the overall thermal discomfort (body as a whole) and local thermal discomfort which corresponds to a cooling or undesired local warming of the body (asymmetric temperature, air flow, etc.).

2. The Phenomena of Heat Exchange of a Man and His Environment inside a House

The exchange of energy of a man with his external environment by four mechanisms: conduction, convection, radiation and evaporation. The conduction, the convection and the radiation are sensible heat exchanges while evaporation is a latent heat exchange. [1]

As shown the Fig.1, the Conduction is the phenomenon of heat exchange between the skin and solid elements with which the skin is in contact. The convection phenomenon is the exchange of heat between the skin and the ambient air. The radiation refers to the phenomenon of emission or transmission of energy in the form of waves or particles. The evaporation is the phenomenon of heat transfer due to the change of state of water.

Figure 1. Illustration of the four mechanisms of heat exchange

3. Equation of Thermal Balance of a Man

The thermal balance of a man can be written in the form of equation (ASHRAE, 1993). [2]

M . W. C. R . Esk . Eres. Cres . Ssk. S c.

The heat flux are calculated per unit of body surface area

Where:

M: metabolism [W /m²];

W: outside work [W /m²];

C: convective heat flux, in watts per square meter of exchange surface area [W /m²];

R: radioactive heat flux [W / m²];

Esk: exchanges heat by evaporation [W / m²];

Eres:evaporative heat exchange during breathing [W / m²];

Cres: convection heat exchange during breathing [W / m²];

Ssk: heat stored in the skin [W /m²];

Sc: heat stored within the body [W / m²];

Note here that the part of metabolism (denoted W) is used by the muscles for external work and therefore does not contribute to the maintenance of thermal equilibrium. It is almost zero if a person sleeps [3].

The Fig.2 shows the values of metabolism which is given by the body activity.

Figure 2. Values of metabolism given by the body activity

4. Some of Negative Effects on Summer Thermal Discomfort

l Deterioration of well-being (living and working);

l Fatigue, drowsiness on the part of employees;

l Drop of their activity and their neuromuscular and cognitive performance;

l Increase response times well as errors or omissions during exposure to high temperatures.

l Deterioration of health (morbidity and mortality) when weather conditions are severe (extreme heat, poor building design)

l In residential housing, the discomfort was degradation welfare of the occupants.

l The consequences are both physical (reduced form, for example) and psychological (eg, aggressiveness).

l Sleep, which has important consequences for the physical and psychological health of individuals, may especially be affected by high temperatures.

5. Example of Mortality due to Thermal Discomfort

The results of the 2003 heat wave are now established approximately22, 080 deaths in Europe (Kovats et al., 2004). Ledrans (2006) conducted a synthesis of studies on heat wave between 2003and 2005. [4]

These studies suggest both that the little self (the elderly, people with a physical disability or mental illness) were more vulnerable to heat and secondly, that if the level photo chemical pollution (ozone) have had a significant impact during the heat wave, the observed mortality remains very much linked to the specific effect of heat.

6. Relationship between Thermal Comfort and Labor Productivity

The effect of indoor air temperature on labor productivity was also determined by Niemelä R at al. They realized that for an interior discomfort due to the higher temperature (32 ^°C for example); the labor productivity may decrease up to 12% as illustrated in the Fig.3 below. [5]

Figure 3. Illustration of relationship between thermal comfort and labor productivity

7. Indoor Calorific Intake

Outdoor intake by insulation

The intensity of solar radiation received by an orientation wall depends on its height and the angle formed by the direction and the plane of the wall. These angular values vary depending on the time of day.

a. On the opaque wall

Solar radiation does not directly through the opaque wall. A portion of the solar radiation flux is absorbed and another is reflected by the wall. as shown in the following figure (Fig.4).

Figure 4. Solar radiation on the opaque wall

There are three types of temperatures with respect to solar radiation on the wall

te = Actual outdoor temperature

tef = Fictitious outdoor temperature

ti = indoor temperature

The amount of heat passing through the wall is given by the following formula:

Qm = α . F . S . Rm [6]

Where:

α = absorption coefficient of the wall receiving the radiation. The values of absorption coefficient for wall (α) are given in the Tab.1below

F = wall surface in m²

S = factor of solar radiation

Rm = solar radiation absorbed on the surface of the wall (W/ m²)

The absorption coefficient "α" depends on the color and nature of the wall

The radiation factor "F" indicates the proportion of heat absorbed by the surface and transmitted through the wall

The value of solar radiation "Rm" on a wall depends on:

The latitude in which the local is;

The orientation of the wall;

Time for which the calculation is performed.

b. On the glazing wall

When solar radiation encounters a glazing wall, the heat flux (F) expressed in W/ m² is partially reflected (fr), absorbed (fa), the rest is transmitted (ft) in the room as shown in the following figure (Fig.5).

Figure 5. Solar radiation on the single glazing

The amount of heat passing through the glazing (Qv):

Qv = α . g . S . Rv [W] [7]

Where: α = absorption coefficient of the glazing. The values of absorption coefficient for glazing (α) are given in the Tab.1 below

g = reduction factor depends on the type of protection window against solar radiation

S = glass surface (m²)

Rv = intensity of solar radiation on windows (W/ m²)

Table 1. Absorbing heat coefficient depending on the color and nature of the wall or glazing [8] Nature of the surface Color absorption heat coefficient (α) Very light surface White stone, white surface, light or cream, light cement. 0.4 Dark surface Fibro, unpainted wood, brown stone, red brick, dark cement. 0.7 Very dark surface Dark slate roof, very dark asphalt cartons 0.9 Glazing Single glazing 1 Double glazing 0.9 Triple glazing 0.8

8. Types of Local Orientation Determine the Time of Maximum Heat Load [9]

The Fig.6 shows the 27 possibilities of wall orientation of a house and the perception of the solar heat on the walls depends on the orientation, the solar trajectory, the duration and the time of exposure. The peak hours for maximum heat load on the walls depend on how the windows are protected as is shown in the Tab.2.

Figure 6. Possible building orientations

Table 2. Peak hours for maximum heat load depending on the walls orientation [10] Possible Walls orientation Number of exposed walls Orientation of exposed walls Peak hours for maximum heat load Protected windows Non-protected windows a b a b 1 1 N - - 2pm 2pm 2 N-E - - 2pm 2pm 3 E 00pm 00pm 9 am 9am 4 S-E 1 pm 1pm 10 am 10am 5 S 2pm 1pm 1pm 1pm 6 S-W 3pm 2pm 4pm 3pm 7 W 3pm 3pm 4pm 4pm 8 N-W 4pm 3pm 5pm 4pm 9 2 N-E, N,E 2pm 2pm 9am 9am 10 N-E, S-E 2pm 1pm 9am 9am 11 S-E, S, E 2pm 1pm 10am 10am 12 S-E, S-W 3pm 2pm 3pm 3pm 13 S-W, S, W 3pm 2pm 3pm 3pm 14 S-W, N-O 3pm 3pm 4pm 4pm 15 W,N 3pm 3pm 4pm 4pm 16 N-W, N-E 4pm 3pm 5pm 5pm 17 3 W,N,E 4pm 3pm 4pm 4pm 18 N-W, N-E, S-E 3pm 3pm 4pm 4pm 19 N, E, S 2pm 2pm 10am 10am 20 N-E, S-E, S-W 3pm 2pm 3pm 3pm 21 E, S, W 3pm 2pm 3pm 3pm 22 S-E, S-W, N-W 3pm 3pm 4pm 4pm 23 S, W, N 3pm 3pm 4pm 4pm 24 S-W, N-W, N-E 4pm 3pm 4pm 4pm 25 4 S,W,N,E 3pm 2pm 3pm 3pm 26 S-W, N-W,N-E, S-E 3pm 2pm 4pm 4pm 27 - - - - 2pm 2pm

9. Case Study

“Study of the amount of solar heat through the walls of a house built in Bujumbura city with different materials and choice of a proper facades orientation for its internal comfort”

The house is built either by Exposed and filled baked brick either by Filled baked brick with ordinary coating with cement mortar either by Tinted glazing.

9.1. House Plans

The Fig.7 is the plane view of the house while the Fig.8 is the main facade in perspective oriented in the west

Figure 7. House plane view

Figure 8. Main facade in perspective oriented in the west

9.2. West Facade Wall Materials

Scenario 1: Exposed and filled baked bricks;

Scenario 2: Filled baked bricks with ordinary coating with cement mortar;

Scenario 3: Tinted glazing

9.3. Dimensions of Walls and Openings

The dimensions and surfaces of walls and openings are given in the Tab.3 and Tab.4.below.

Table 3. Surface of walls Orientation Area (m2) WEST 29.82 EAST 26.09 NORTH 20.10 SOUTH 28.18

Table 4. Dimensions of openings (Doors and windows) Type of openings Width (m) Height (m) Surface (m2) Double glazed door (P1) 1.80 2.10 3.78 Door (P2) 0.90 2.10 1.89 Window (F1) 2.00 1.20 2.40 Window (F2) 2.00 1.20 2.40 Window (F3) 2.00 1.20 2.40 Window (F4) 2.00 1.20 2.40 Window (F5) 0.80 0.40 0.32 Window (F6) 2.00 1.20 2.40 Window (F7) 0.55 0.40 0.22 Window (F8) 1.00 1.20 1.20

9.4. Parameters for Calculating the Contributions of Solar Radiation on the Facade Walls

9.4.1. The Amount of Heat through the Wall

[Qm]: Qm = α . F . S . Rm

Where:

α = absorption coefficient of the wall receiving the radiation

S = wall surfaceinm²

F = factor of solar radiation

Rm = solar radiation absorbed on the surface of the wall (W/m²)

The absorption coefficient "α" depends on the color and nature of the wall

a. Exposed and filled baked bricks: α = 0.7

b. Filled baked bricks with ordinary coating with cement mortar: α = 0.7

c. Tinted glazing: α = 1

9.4.2. Solar Radiation Factor (F)

The solar radiation factor (F) for the walls is given by the heat transfer coefficient (U) whose values are typically ranged between 0 and 2 for the commonly used materials. The table below (Tab.5) gives the values of solar radiation factor (F) for the heat transfer coefficient ranged between 0 and 4.

Table 5. Solar radiation factor [11] Heat transfer coefficient of the wall "U" (W /m2 °C) Solar radiation factor (F) 0 0 1 0.05 2 0.1 3 0.15 4 0.20

9.4.3. Thermal Transmission Coefficient (U) of the Walls

a. Exposed and filled baked bricks: U = 0,9 W/m2°C ; F = 0,045

b. Filled baked brick with ordinary coating with cement mortar: U = 1,15 W/m2°C; F = 0,057

c. Tinted glazing: U = 5,8 W/m2°C

9.4.4. Solar Radiation on Wall "Rm"

The value of solar radiation on the wall "Rm" depends on:

l The latitude in which the local is,

l The orientation of the wall,

l The time for which the calculation is performed.

9.5. Solar Radiation in Burundi

The solar radiation data in Burundi are given in the Tab.6 and are calculated based on the NASA global climatic data posted in RETScreen International software. [12]

Table 6. Solar radiation data in Burundi

9.6. Amount of Heat through the Walls of Facades (Qm)

The amount of heat through the walls of facades (Qm) is calculated based on the formula [6] whose calculation factors are the wall surface in m² (S), the absorption coefficient of the wall receiving the radiation (α), the factor of solar radiation (F) and the solar radiation absorbed on the surface of the wall (Rm) as shown in the Tab.7 and Tab.8 for walls of exposed and filled baked bricks and filled baked brick with ordinary coating with cement mortar.

Table 7. Heat through the wall of exposed and filled baked bricks Facade Orientation Area (m2) α F Rm (W/m²) Qm (W) Time West West 29.82 0.7 0.057 570 678.20 4(pm) Northwest 29.82 0.7 0.057 605 719.80 3(pm) North 29.82 0.7 0.057 295 351 11-12(am) Northeast 29.82 0.7 0.057 605 719.80 9(am) East 29.82 0.7 0.057 570 678.20 8(am) Southeast 29.82 0.7 0.057 230 273.60 8(am) South 29.82 0.7 0.057 295 351 11-12(am) Southwest 29.82 0.7 0.057 230 273.60 4(pm)

Table 8. Heat through the wall of Filled baked brick with ordinary coating with cement mortar Facade Orientation Area (m2) α F Rm (W/m²) Qm (W) Time West West 29.82 0.7 0.09 570 1070.83 4(pm) Northwest 29.82 0.7 0.09 605 1136.59 3(pm) North 29.82 0.7 0.09 295 554.20 11-12(am) Northeast 29.82 0.7 0.09 605 1136.59 9(am) East 29.82 0.7 0.09 570 1070.83 8(am) Southeast 29.82 0.7 0.09 230 432.09 8(am) South 29.82 0.7 0.09 295 554.20 11-12(am) Southwest 29.82 0.7 0.09 230 432.09 4(pm)

Note here that in the heat of calculation, the west facade of the plan (walls and openings) was considered able to occupy all eight possible directions (West, Northwest, North, Northeast, East, and Southeast, South and Southwest)

For readability of the results, a legend of 4 different colors is used:

9.6.1. Heat through the Wall with Different Materials

The tables below (Tab.7 and Tab.8) show the amount of heat for respectively exposed and filled baked bricks and filled baked brick with ordinary coating with cement mortar at different times.

9.6.2. Wall with Tinted Glazing

For the solar heat on tinted glazing, the amount heat passing through is calculated using the same way as the amount heat passing through the walls built in other materials except that instead of using the factor of radiation (F), we use reduction factor (g).

The amount of heat passing through the glazing (Qv): Qv = α . g. S. Rv [W]

Where:

α = The absorption coefficient of the glazing

g = The reduction factor which depends on the type of protection window against solar radiation.

In this case, g = 0.69

S = Glazing area (m²)

Rv = Intensity of solar radiation on glazing (W/m²). It is defined in the same manner as Rm and is given in the table, column "v"

The three following tables (Tab.9, Tab.10 and Tab.11) show the results of the amount of heat passing through the wall of Tinted glazing, the single glazing with unprotected metal frame and the tinted glazing with unprotected metal frame. For easier reading, the curves of Fig.5 illustrate the summary of the amount of heat passing through the openings.

Table 9. Amount of Heat through the wall of Tinted glazing Facade Orientation Area (m2) α g Rv (W/m²) Qv (W) Time West Openings West 29.82 1 0.69 490 10082.14 4(pm) Northwest 29.82 1 0.69 510 10493.65 3(pm) North 29.82 1 0.69 220 4526.67 11(am)-1(pm) Northeast 29.82 1 0.69 510 10493.65 9(am) East 29.82 1 0.69 220 4526.67 8(am) Southeast 29.82 1 0.69 170 3497.88 8(am) South 29.82 1 0.69 220 4526.67 11(am)-1(pm) Southwest 29.82 1 0.69 170 3497.88 4(pm)

Table 10. Amount of Heat through the single glazing with unprotected metal frame Facade Orientation Area (m2) α g Rv (W/m²) Qv (W) Time West Openings West 10.98 1 0.85 490 4573.17 4(pm) Northwest 10.98 1 0.85 510 4753.83 3(pm) North 10.98 1 0.85 220 2053.26 11-1(pm) Northeast 10.98 1 0.85 510 4753.83 9(am) East 10.98 1 0.85 220 2053.26 8(am) Southeast 10.98 1 0.85 170 1586.61 8(am) South 10.98 1 0.85 220 2053.26 11(am)-1(pm) Southwest 10.98 1 0.85 170 1586.61 4(pm)

Table 11. Heat through the tinted glazing with unprotected metal frame Facade Orientation Area (m2) α g Rv (W/m²) Qv (W) Time West Openings West 10.98 1 0.69 490 3712.33 4(pm) Northwest 10.98 1 0.69 510 3863.86 3(pm) North 10.98 1 0.69 220 1666.76 11(am)-1(pm) Northeast 10.98 1 0.69 510 3863.86 9(am) East 10.98 1 0.69 220 1666.76 8(am) Southeast 10.98 1 0.69 170 1287.95 8(am) South 10.98 1 0.69 220 1666.76 11(am)-1(pm) Southwest 10.98 1 0.69 170 1287.95 4(pm)

In the Figures 9 and 10, we find that the walls oriented in N-W and N-E absorb more solar heat respectively at 3 pm and at 9 am while the walls oriented in S-E and S-W absorb less solar heat respectively at 8 am and at 4 pm. We find also that for wall oriented in the North, there is a large reduction of solar heat between 11 am and 1pm especially for tinted glazing wall.

Figure 9. Curves illustrating the summary results Qm (W) for bricks wall

Figure 10. Curves illustrating the summary results Qv (W) for tinted glazing

9.7. Amount of Heat Passing through the Openings

The tables below (Tab.12, Tab.13, Tab.14 and Tab.15) show the amount of heat through the openings (walls and windows) of the west facade at different times. The first case (Tab.12) shows the result of heat for openings of the west facade in glazing transparent white- medium with external protection and metal frame. The second case (Tab.13) shows the result of heat for transparent glazing, white- medium with internal protection and metal frame. The third case (Tab.14) shows the result of transparent glazing, white- medium with internal protection and metal frame and the fourth case (Tab.15) shows the result of transparent glazing, medium Pastel with external protection and metal frame.

Table 12. Heat through the openings of the west facade in glazing transparent white- medium with external protection and metal frame Facade Orientation Area (m2) α F Rv (W/m²) Qv (W) Time West Openings West 10.98 1 0.21 490 1129.84 4 (pm) Northwest 10.98 1 0.21 510 1175.95 3(pm) North 10.98 1 0.21 220 507.27 11 (am)-1(pm) Northeast 10.98 1 0.21 510 1175.95 9 (am) East 10.98 1 0.21 220 507.27 8 (am) Southeast 10.98 1 0.21 170 391.98 8(am) South 10.98 1 0.21 220 507.27 11(am)-1(pm) Southwest 10.98 1 0.21 170 391.98 4(pm)

Table 13. Heat through the openings of the west facade in transparent glazing, white-medium with internal protection and metal frame Facade Orientation Area (m2) α F Rv (W/m²) Qv (W) Time West Openings West 10.98 1 0.38 490 2044.47 4(pm) Northwest 10.98 1 0.38 510 2127.92 3(pm) North 10.98 1 0.38 220 917.92 11(am)-1(pm) Northeast 10.98 1 0.38 510 2127.92 9(am) East 10.98 1 0.38 220 917.92 8(am) Southeast 10.98 1 0.38 170 709.30 8(am) South 10.98 1 0.38 220 917.92 11(am)-1(pm) Southwest 10.98 1 0.38 170 709.30 4(pm)

Table 14. Heat through the openings of the west facade in transparent glazing, medium Pastel with external protection and metal frame Facade Orientation Area (m2) α F Rv (W/m²) Qv (W) Time West Openings West 10.98 1 0.19 490 1022.23 4(pm) Northwest 10.98 1 0.19 510 1063.96 3(pm) North 10.98 1 0.19 220 458.96 11(am)-1(pm) Northeast 10.98 1 0.19 510 1063.96 9(am) East 10.98 1 0.19 220 1022.23 8(am) Southeast 10.98 1 0.19 170 354.65 8(am) South 10.98 1 0.19 220 458.96 11(am)-1(pm) Southwest 10.98 1 0.19 170 354.65 4(pm)

Table 15. Heat through the openings of the west facade in transparent glazing, medium Pastel with internal protection and metal frame Facade Orientation Area (m2) α F Rv (W/m²) Qv (W) Time West Openings West 10.98 1 0.29 490 1560.25 4(pm) Northwest 10.98 1 0.29 510 1623.94 3(pm) North 10.98 1 0.29 220 700.52 11(am)-1(pm) Northeast 10.98 1 0.29 510 1623.94 9(am) East 10.98 1 0.29 220 1560.25 8(am) Southeast 10.98 1 0.29 170 541.31 8(am) South 10.98 1 0.29 220 700.52 11(am)-1(pm) Southwest 10.98 1 0.29 170 541.31 4(pm)

9.8. Summary Heat Results Q v (W) for Openings (door and windows) for West Façade

For openings, the absorption of solar heat depends on several parameters including the nature of the materials that make up these openings, the protection system (external or internal), etc..

The shape of the curves of opening protected externally (Fig.11) is almost identical to those of walls but for openings protected internally, the solar heat still high from 8am to 9am and from 3pm and 4pm.

Figure 11. Summary heat results of solar heat through openings (door and windows)

10. Conclusions

Wall orientation and time of maximum solar charge

In Bujumbura city, for a given wall exposed to the summer sun, the maximum solar absorption depends on its orientation and exposure time.

The best orientation for a minimum solar heat on the walls and openings are South-Est (S-E) and South-West (S-W)

11. Recommendations

1. To each person to put in his mind that:

Ø The heat discomfort in a room has a negative impact on the health of occupants especially during the summer;

Ø The heat discomfort during the summer in an administrative building has a negative impact not only on the health of occupants but also on the performance of work.

Ø The air conditioning system increases the electricity bill.

2. To Builders:

Ø To choose the orientation of the walls while knowing that at Bujumbura city, the Southeast and the and the Southwest are the orientations where the walls or openings absorb less solar heat during the summer while the Northeast and Northwest absorb more solar heat.

Ø To focus on the outdoor sun protection for openings compared to other systems of internal protection;

Ø To choose glazing with low solar factor.

Ø To avoid building of walls with tinted glazing to meet the aesthetic appearance without thought about the external protection of heat solar because in addition to the cost of internal protection, the indoor climate is still required especially during the summer.

ACKOWLEDGMENTS

The author would like to sincerely thank all those who contributed in the preparation of this article from the beginning until its publication