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Solar chimney's are extensively used, but this design has not been prototyped.

A solar or thermal chimney is a form of passive ventilation that can be applied to a structure. It uses the principles of heat transfer and fluid mechanics to naturally ventilate a structure without the need of an outside source of electricity. This makes the solar chimney a promising alternative to forced air in both the developed and the developing world.

Indoor air quality is a health issue that plagues the developing world. In many regions, the ambient temperature of a household can far exceed a comfortable living temperature. In others, families prepare their food and water indoors and the living space is laden with smoke.[1] Implementing a solar chimney in an appropriate climate can help increase the indoor air quality of a home and subsequently improve the health and living conditions of residents.

## Principles

A solar chimney takes advantage of the fact that as the temperature of air changes, the density of air changes as well. The chimney is heated during daylight hours due to sunlight exposure. This, in turn, heats the air inside the chimney, creating a temperature difference between the air in the chimney and the air in the dwelling. Since air density varies with temperature, there will be a density difference between the air within the dwelling and the air within the solar chimney. The difference in density creates a pressure difference and drives the air inside the dwelling into the solar chimney and the air in the solar chimney to the exterior. This process exchanges the air inside the dwelling, providing air exchange and a breeze for occupants. This increases indoor air quality and comfort.

### Pressure Difference

The pressure difference created by a difference in density can be modeled using equation 1 below.[2] Please note that inside refers to the interior of the dwelling and that outside refers to the chimney's interior at the specified height.

(1)

${\displaystyle dp=g\cdot (\rho _{inside}-\rho _{outside})\cdot h}$

where

${\displaystyle dp}$ = pressure difference between chimney air and inside air (Pa)
${\displaystyle g}$ = gravitational constant (N/kg)
${\displaystyle \rho _{inside}}$ = density of the inside air (kg/m^3)
${\displaystyle \rho _{outside}}$ = density of the outside air (kg/m^3)
${\displaystyle h}$ = height of chimney (m)

### Air Velocity

To determine the effect of the solar chimney on ventilation, we must find the velocity. The equation for velocity due to the density difference is shown below.

(2)

${\displaystyle V={\sqrt {{2\cdot g\cdot (\rho _{inside}-\rho _{outside})\cdot h} \over (({{f\cdot l\cdot \rho _{outside}}/{d_{h}}})+\sum {k\cdot \rho _{outside}})}}}$

where

${\displaystyle V}$ = air velocity (m/s)
${\displaystyle f}$ = friction coefficient (no units)
${\displaystyle l}$ = length of chimney considered (m)
${\displaystyle d_{h}}$ = hydraulic diameter of chimney (m)
${\displaystyle k}$ = minor losses (no units)

### Air Volumetric Flow Rate

Once the velocity is determined, the volumetric flow rate of the air can be found using equation 3 below.

(3)

${\displaystyle q=V\cdot (\pi \cdot d_{h}^{2}/4)}$

where

q = volumetric flow rate (m^3/s)

## Finite Element Analysis

A finite element analysis was performed using THERM 6.2 software.[3] THERM is a software that is mainly used as a modelling program for glazing systems in buildings. THERM is the benchmarking program used by the NFRC (National Fenestration Rating Council) to model energy and solar properties of fenestration assemblies and was created by Lawrence Berkeley National Laboratory. The software is used by many leading glazing manufacturers in order to test their glazing system performance. The software is freeware and as such can be used by anyone without purchasing a license.

With knowledge of the software, it is possible to use the features of therm to estimate the thermal profile of a system by assigning appropriate boundary conditions and defining material properties. A model of the solar chimney described in the construction section was created using THERM. The exterior temperature was assumed to be 33 degrees celsius, the interior temperature was assumed to be 24 degrees celsius, and the ground temperature was assumed to be 25 degrees celsius. The wood used was assumed to be douglas fir. The results of the analysis as well as the thermal profile of the chimney are shown below. The findings from the therm program are used in the performance results section and the theory described in the principles section to estimate the velocity and volumetric flow rate of the air leaving the home.

## Solar Chimney Performance Results

Using the model, at a height of 3 metres the temperature inside the solar chimney was determined to be 32 degrees celsius. Although the final legend value shown is 31.1 degrees celsius, the THERM software can display the temperature at any point in the analysis, and 32 degrees celsius was the returned value at the 3 metre location. Using a minor loss factor of 0.5 due to the corner in the flow and a friction coefficient of 0.2 the air velocity was determined to be 2 metres per second. As a result, the volumetric flow rate of air leaving the dwelling to the inside of the solar chimney was determined to be 0.25 metres cubed per second. At this rate, the air exchange per hour of air was calculated to be 889 metres cubed per hour. The solar chimney would be most efficient at the hottest time of the day and gradually reduce in efficiency until the cooler hours of the day, due to the reduced temperature difference between the temperature in the dwelling and the temperature in the solar chimney.

## Construction

The construction of the solar chimney was designed with simple building principles in mind.[4] The maximum height of the solar chimney was determined by using the maximum unloaded 2 x 4 stud wall height, 3.6m, as described by the Ontario Building Code 2006[5] in Division B Part 9 table 9.23.10.1.

The larger studs were spaced at 16" on centre as also described by table 9.23.10.1.. This ensures that the structure is designed with the safety of its users in mind. The solar chimney is a simple stud wall design with an extrusion at its base that connects the solar chimney to the dwelling it serves. Since the primary goal of the project was to perform the finite element analysis and to assess the feasibility of the solar chimney on a theoretical basis, rough google sketch drawings were drawn based on Canadian Building Principles in order to visualize the implementation of the concept. Further work will have to be done to adjust the conceptual design to be implemented in different areas of the world, where the same construction materials and methods may not be appropriate or be available.

The solar chimney would be constructed mainly of 2 x 4s. The sections were modelled after a generic stud wall for simplicity. The sections can all be nailed together so no specialized equipment would be required. The framing as shown needs to be covered by either sheathing or a plywood in order to shield the inside of the dwelling from the outside, and for the solar chimney to function. The exterior finishing should match the existing finishing of the dwelling and be integrated as part of the building envelope in order to ensure that the dwelling is shielded from the elements to its original standard.

Sheathing and matched roofing materials should be added to the top of the chimney in order to prevent water from seeping inside. Depending on the location, it may also be wise to add mosquito netting around the chimney flue. All wood in contact with grade should be pressure treated or measures should be taken to counteract moisture buildup in the wood in order to prevent rotting. Please see below for a description of how to build the concept solar chimney.

1

Construct as shown by first nailing two 2" x 4" x 12' pieces of lumber to a 2" x 4" x 16" bottom plate. Nail the 2" x 4" x 16" top plate to the top of the 2' x 4' x 12'. For stability, hammer in a 2" x 4" x 13" piece of lumber at around the center of the frame and nail into place. Construct a total of 4.

2

Lay one of the four components assembled in step one flat on the ground. Place another of the components made in step 1 on top of the component on the ground at 90 degrees and flush with its side. Nail in place. Place the third component on the other side of the component on the ground, at 90 degrees and flush with the side and bottom. Nail in place.
Take the last component from step one and place flat on the ground. Flip the component made in step two over and place it on top of the last component from step 1. Ensure that the sides and bottom are flush. Nail into place. Please see pictures from step 6 to preserve space.

3

Nail four pieces of 2" x 4" x 3.5" to the top of the assembly created in step 3.

4

Construct a small stud wall section using two 2" x 4" x 12" and two 2" x 4" x 10" pieces. Construct two.

5

Secure one of the sections completed in step 4 to the bottom of the stud wall section completed in step 3. Nail two 2" x 4" x 10" pieces of wood on either side of the small section flush against the side of the stud wall. Secure the second stud wall from step 4 above the two pieces.

6

Cover the exterior of the stud wall with sheathing and match the exterior cladding and roof finish of the dwelling.

## Conclusion

Using the finite element analysis model and the described equations in the principles section, the total volumetric flow rate of air leaving the dwelling per second was determined to be 0.25 metres cubed per second. This represents an improvement in air exchange from the dwelling. Installing the solar chimney would increase the air quality in the dwelling, improving living condition for its inhabitants. The solar chimney has the potential to have its performance increased by using materials such as glass that enhance gains due to solar radiation. This would increase the effectiveness of the unit, but would also make the construction of the unit more complex and costly. To be implemented as an appropriate technology, the cost must be kept to a minimum. Further research into construction methods of a specific region would allow for a specific prototype to be designed taking into account the area's building practices.