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The light is one of the important factors for the microalgae growth in the biofuel technology. As biofuel project is large and expensive thus before setting a microalgae based biofuel project in any geographical location, it is important to investigate the suitability of all important parameters involving with the system. This paper aims to investigate the sunlight availability and the microalgae growth for a photobioreactor at Chittagong University of Engineering and Technology (CUET). A computational growth model related to the average irradiance is proposed to calculate the growth of microalgae. We observed that average irradiance is the highest in June and is the lowest in December. From our simulation it is found that the growth of microalgae varies with the average irradiance in a year.

Continued use of petroleum based fuels is now recognized as unsustainable because of depleting energy source and these categories of fuels have unconstructive environmental affect by increasing Green House Gases (GHG). A major cause of global warming: increased concentrations of GHG. Renewable, carbon neutral, transport fuels are necessary for environmental and cost efficient sustainability [_{2} into the algal biomass [_{2}, temperature and pH [

The tubular photo-bioreactors consist of solar collectors, where microalgae collect energy from the sun. This is usually made of plastic or glass. The solar collector tubes are generally 0.1 m or less in diameter. Tube diameter is limited because light does not penetrate deeply. In outdoor cultivation, the ultimate source of light is the sun, which cannot be controlled. The solar collector must maximize capture of sunlight for photosynthesis [

For understanding the mathematical model, it is necessary to define some parameters of the solar system [

The latitude is the angular distance of the point on the earth measured north (or south) of the equator. It is the

angle between a line from the point on the earth’s surface to the center of the earth and the projection of that line on the equatorial plane. North latitudes are positive and south latitudes are negative. The range of latitudes is given by

The declination angle is the angular distance of the sun north (or south) of the celestial equator. It is the angle between a line extending from the center of the sun to the center of the earth and the projection of this line upon the earth’s equatorial plane. The declination is positive when the sun is north of the equator and negative when the sun is south of the equator. The declination varies from −23.45 degrees to 23.45 degrees. Around December 21, the northern hemisphere of the earth is tilted 23.45 degrees away from the sun, which is the winter solstice for the northern hemisphere and the summer solstice for the southern hemisphere. Around June 22nd, the southern hemisphere is tilted 23.45 degrees away from the sun, which is the summer solstice for the southern hemisphere. On March 22nd and September 23rd are the fall and spring equinoxes when the sunpassing directly over the equator. At the equinoxes, declination is zero. According to Cooper, The declination is calculated with the following formula:

where N is the day of the year. The value of N for any day of the month can be obtained with the help of following

The hour angle is the angle measured in the earth’s equatorial plane between the projection of a line from the point on the earth’s surface to the center of the earth and the projection of a line from the center of the sun to the center of the earth. It expresses the time of the day with respect to the solar noon. At solar noon, it is zero. One hour of time is represented by

Month | Date | The Declination |
---|---|---|

January February March April May June July August September October November December | 10 17 14 11 15 13 19 16 16 14 15 13 | −22.0 −12.6 −3.2 7.9 18.8 23.2 20.8 13.5 1.8 −9.2 −19.1 −23.2 |

where sh is the solar hour to be determined.

The zenith angle is the angle between the sun’s rays and local vertical, i.e. a line perpendicular to the horizontal plane through the point. It is denoted by

It is the angle between the plane of the surface of the object and the horizontal. The range of slope is given by

It is the angle between south and horizontal projection of the surface normal. The sign convention is used for

The angle of incidence is the angle between the solar rays and the surface normal. It is denoted by

Algal suspension in the tubular reactor is considered to be an incompressible viscous single-phase Newtonian fluid. The equations set for the incompressible fluid dynamics is used for current flow behavior i.e., 1) Continuity equation, and 2) The Navier-Stokes equation

where, r represents the density and g denotes the gravity.

The viscosity

where is

When cell proliferation occurs, it induces the change of algal concentration and subsequently the change of viscosity of the algal suspension. In this study, a microalgae cell is considered to be a small sphere [

where

where

where

The equation of average irradiance:

where

The cosine of angle of incidence can be expressed by:

For flat surface [

where

The first step to calculate the microalgae growth is to calculate the Average Irradiance on a horizontal surface of a photobioreactor and to calculate the cosine of angle of incidence using Equation (12). The Average Irradiance is shown in

In ^{3}. There are almost similar scenario is depicted in ^{3}. Therefore, a very slow increase of concentration is observed. From these results we can deduce that the growth related to concentration of microalgae is not constant but the microalgae growth varies with average irradiance of the daylight.

In this paper, the average irradiance for microalgae growth at Chittagong University of Engineering & Technology (CUET), Bangladesh is calculated throughout a year. The concentration of microalgae cell related to the growth rate is simulated by using COMSOL Multiphysics 4.2a. The declination is considered to a relation with the day of

Symbol | Quantity | Values |
---|---|---|

Maximum growth rate | 0.0000175∙s^{−1} | |

Constant | 114.67 µmol∙m^{−2}∙s^{−1} | |

Incident Irradiance | 1630 µmol∙m^{−2}∙s^{−1 } | |

C_{0 } | Initial Concentration | 0.55 kg∙m^{−3} |

a | Constant | 1 |

b | Constant | 200 |

Extinction coefficient | 36.9 m^{2}∙kg^{−1} | |

Tube diameter | 0.05 m | |

Latitude (CUET, Bangladesh ) | 22.4621^{0}^{ } | |

g | Gravity | 9.8 m∙s^{−1} |

a year. From our calculated data it was found that average irradiance is the highest in June and is the lowest in December for an entire year at CUET. It was also observed that the growth of microalgae varies with the average irradiance. It is a kind of feasible analysis for practical implementation of biofuel project at CUET. It is observed that one can take initiative to set a biofuel project from microalgae at CUET in the present available solar energy.

The authors are gratefully acknowledged for the technical supports to the Centre of Excellence in Mathematics, Mahidol University, Rama-6 Road, Bangkok, Thailand.

Ismot Ara Khanam,Ujjwal Kumar Deb, (2016) Calculation of the Average Irradiance and the Microalgae Growth for a Year at CUET, Bangladesh. American Journal of Computational Mathematics,06,237-244. doi: 10.4236/ajcm.2016.63024