Performance Analysis of Solar Chimney Power Plant from Geothermal Waste Heat Source a Case of Aluto-Langano, Ethiopia.

In this paper, the transient thermal simulation on working fluid of solar updraft power plant using waste water was investigated to characterize the enhancement by numerical and theoretical method. Numerical solution technique used to solve a differential equation form of governing equations using finite difference discretization scheme. Most of the researches done on geometrical parameters to perform the mathematical modeling. This paper combines some of the above improvements on the performance of plant and combines them with new idea of heat source as waste heat in Aluto Langano geothermal power plant. Moreover, this study using dimensions of plant constructed in Manzanares, Spain height of chimney =194.6 m, diameter of collector=244 m, diameter of chimney=10.16 m. The obtained result, the collector temperature increases by 7 °C, the pressure potential is found 182.82 Pa, the pressure drop on the turbine was 121.88 Pa, the pressure loss was 60.94 Pa and the power output 123.59 kW. As a result, the collector efficiency increases to 43.58% and the overall efficiency of plant to 0.242%.


Modeling of the Collector Roof, chimney and turbine
Correspondingly, the following assumptions are taken to avoid complexity of mathematical model: • Temperature rises in the solar collector is along radial direction [1] • The collector roof and ground temperature has no variation along collector radius and thickness [2] • Insignificant variation of velocity and temperature along chimney cross-section.
• The flow is one-dimensional, unsteady and inside parallel plate flow.
• Boussinesq assumption is valid for the airflow inside the tower [3] • No heat loss throughout the chimney.
• The temperature at some depth below the ground surface is constant.
• There is no radial conduction in the ground surface Energy equation

Energy Balance and Discretization of Collector Roof
For roof: For air For geothermal pipe pipe p + , + , + 2 For the ground storage

Available Pressure Capacity due to Slanted Roof and Tower
The tower converts the temperature difference to the velocity of air. The rising of temperature creates the density difference in the collector that works as the driving force for fluid air. By taking the air as a working fluid, the whole pressure capacity converts to the moving pressure of airflow. In variable density assumptions, air is an ideal gas, and insignificant loss throughout the chimney wall. A mathematical equation developed to investigate the efficiency of the plant under conservation of energy and momentum principle.
The frictionless momentum equation express as; The increased pressure capacity to drive flow of air from the roof inlet to chimney outlet written as: After integration of Eq. (1.9) can written as; The integral part of the Eq. (1.11) eliminated by inserting the average density of working fluid inside the roof into Eq. (1.10) can rewritten as: In addition, the expression Eq. (1.12) of the slanted collector pressure capacity ∆ppoten can write as; At an arbitrary position, the height of collector described by radius and the inclination angle β: 14) The effective tower height Heff for the Plant defined as the sum height of collector, Hcoll, and the chimney height, Hchimney.
The frictionless adiabatic flow of the dry air experience no entropy changes in the process and defined as: The gas constant of dry air is = 287 / . . Temperature varies with altitude equal to 0.00975 / .
The relation between ambient air static temperature and height is described as: Where, ∞0 is the atmospheric air temperature at sea level .
The variation of pressure due to gravity is given by: After substitution of Eq. (1.18) into Eq. (1.21) we get And the static pressure ∞4 of dry atmosphere given by: The pressure potential converted to dynamic pressure calculated as: The thermal efficiency of the plant defined as the ratio of the fluid power of the air flow at the tower inlet to incoming solar radiation to air flow obtained from the slanted collector. It can also define as thermal energy to kinetic energy, which mainly determined by atmospheric temperature To at sea level and chimney hight Hch [3,4].
The efficiency of collector roof is the ratio of useful energy transferred to the fluid air to the incoming solar radiation intercepted by the roof and the heat generation from the geothermal power plant waste heat.

Result and Discussion
The initial condition of the plant on Aluto Langano weather condition are tabulated in Table 3.1 by using this initial conditions numerical solutions are solved. The simulation result of the Figure  3.7 is tabulated in Table 3.2.         respectively, have the same effect with the pressure and velocity graphs [5].      The change in temperature is 27 °C, which is 7 °C increment with Manzanares proto type as shown in Table 3.3. The maximum velocity achieved at the outlet of collector is 15.8 m/s and 182.8 Pa potential pressures observed at the chimney inlet. The total pressure drop at the turbine is 120.4 Pa and 62.3 Pa pressure loss occurred due to inlet pressure loss to collector and turbine. The amount of power output increases from 50 kW to 123 kW and efficiency of the collector increases from 32% to 43.58%. Hence, the total efficiency of the plant increased from 0.176% to 0.242%. Table 3.

Comparisons of this Work and Previous Works on Reference Plant
The result of the study shows, the solar chimney power plant improved by combining waste heat from another power plant. The model results of this study validated with the previous works and good result has been get with improved efficiency and greater power output.