Solar Energy pp 95-114

# Mathematical Modelling of Solar Updraft Tower

Chapter
Part of the Energy, Environment, and Sustainability book series (ENENSU)

## Abstract

Solar updraft tower power plant is a way to harness energy from the sun. It is a simple concept which requires low maintenance and utilises land that is already being used for growing plants, and generates power from it. A prototype plant was setup in Manzanares, Spain. Numerical analysis on power generation is performed for a similar plant assuming it is setup in Ropar. By considering losses via convection and radiation through the top surface of the collector, collector efficiency is calculated. Two cases arise here, 1. With 100% collector efficiency and 2. Collector efficiency is obtained after subtracting convection and radiation losses. The influx of solar radiation is highest in June. Hence, the variation of parameters like temperature, velocity, power output, efficiency with time of the day is done by taking averages for the month of June. Next the impact of physical parameters like chimney height, chimney radius and collector radius are studied on 21st June 11:00 to 12:00. How each parameter impacts the output of the plant is studied by creating a mathematical model of the power plant. Methods to improve the power output are discussed.

## Keywords

Solar energy Solar updraft tower Collector Chimney Wind turbine

## Nomenclature

A

Area (m2)

C

Power coefficient for wind turbine, C = 0.45

Cp

Specific heat at constant pressure for air (J/kg K), Cp = 1007 J/kg K

g

Acceleration due to gravity (m/s2), g = 9.81 m/s2

Gsc

Solar constant (W/m2), Gsc = 1367 W/m2

h

Convective heat transfer coefficient (W/m2 K)

H

Height (m)

Io

Hourly incident solar energy on an extra-terrestrial horizontal surface (J/m2)

m

Refractive index

Mass flow rate of air (kg/s)

n

Day of the year

p

Pressure (Pa)

P

Power (kW)

Q

Heat (W)

Q

Hourly average incident heat flux (W/m2)

r

R

Characteristic gas constant (J/kg K), R = 287 J/kg K

T

Temperature (°C)

v

Velocity (m/s)

## Greek symbols

ε

Emissivity

η

Efficiency (%)

ρ

Density (kg/m3)

σ

Stefan-Boltzmann’s constant (W/m2 K4), σ = 5.67 × 10−8 W/m2 K4

τ

Transmissivity

## Subscripts

chim

Chimney

coll

Collector

conv

Convection

i

Inlet of turbine/chimney

o

Ambient

ovr

Overall

turbine

Turbine

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