# Category SOLAR ENERGY 3

## Dimensionless numbers and momentum and heat transfer correlations

Before there were computers we let nature be the computer. This was performed by using dimensionless numbers and developing correlations between them, particularly when designing complicated flow or heat transfer processes. The essence of the procedure was to take the differ­ential equation applicable to the process at hand and make it dimension­less. The variables were all made dimensionless with process parameters such that they were all of order one in dimensionless form. How this allows nature to be the computer will become evident below.

Consider the velocity gradient dvz/dr for pressure driven flow of water in a pipe, see Fig. C.1. The appropriate velocity component of interest is that in the z-direction, vz for cylindrical coordinates. The radial position is given by r...

## Physical properties

Fig. B.1 Various properties of liquid water including: viscosity (д, •), density (p, o), heat capacity (Cp, ■), thermal conductivity (k, □), a group of parameters used in the calculation of the Rayleigh number (Ra = [gxp2Cp/kp]ATL3 = CRaATL3, see the text for the definition of the parameters used to determine CRa, *) and the Prandtl number (Pr, д). The dimensions for each parameter are given in the equation and their magnitude on the graph can be ascertained by putting 0 °C in the equation. All the equations in the graph have the temperature T in °C. Data are from J. R. Welty et al., ‘Fundamentals of momentum, heat and mass transfer,’ Third Edition, John Wiley & Sons (1984).

Fig. B...

## Useful numbers, constants and relations

Table A.1 Numerical prefixes

 Prefix Symbol Value Prefix Symbol Value Yotta Y 1—1 О to Yocto y i—1 О 1 to Zetta Z 1021 Zepto z 10-21 Exa E 1018 Atto a 10-18 Peta* P 1015 Femto f 10-15 Tera T 1012 Pico p 10-12 Giga G 109 Nano n 10-9 Mega M 106 Micro 10-6 Kilo k 103 Milli m 10-3 Hecto h 102 Centi c 10-2 Deca da 101 Deci d 10-1

*The prefix Quadrillion is used in the USA energy industry to represent 1015, such as Quadrillion BTUs or Quads.

Table A.2 Energy and power conversion factors

 6.242 x 1018 eV 4.184 J 1055 J J cal BTU 1015 BTU 1.055 x 1018 J 745.7 W Quad Quad hp
 Table A...

## The effect of an envelope

When a cover was placed on a flat plate solar energy collector it was found that the device became more thermally efficient despite the fact that the cover admitted less insolation. The gauge of the insolation reaching and absorbed by the absorber plate was || or ||, which is a com­plicated calculation requiring detailed knowledge of the cover and ab­sorber material properties. In spite this, consideration of the product was given in Chapter 8; now the analysis becomes more challenging with a curved surface such as the envelope. In addition, the reflection optics, that is the reflection of insolation from the parabolic mirror to the ab­sorber pipe, must also be considered to find an effective jar|...

## The basic process

The basic parabolic trough STEGE process has a large area of parabolic reflectors that concentrate insolation to absorber pipes through which

a heat transfer fluid (typically) flows to receive the energy. The pipes have a selective surface and are surrounded by a clear glass concentric tube to minimize heat transfer to the surroundings, similar to the cover used in a flat plate solar energy collector.

The heat transfer fluid can be a synthetic oil, like Therminol VP-1, whose properties are given in Appendix B, that can withstand the high temperatures required to establish an efficient process. Yet, the devel­opment of new heat transfer fluids is an active area of research and in some cases molten salts are being considered...

## Parabolic reflectors to concentrate insolation

In order to use solar energy to produce steam and hence power a Rankine cycle to generate electricity, one must concentrate the solar radiation. The concentrated insolation is absorbed by a pipe that has the heat transfer fluid flowing through it. It was demonstrated in the previous chapter that a flat plate solar energy collector can heat water fairly effi­ciently to order 50 °C, however, much higher temperatures, approaching 400 °C, are required for electricity generation. Here the use of parabolic reflectors is considered for electricity production.

Previously we found that concentrating the sunlight can produce a large temperature rise over a short length of pipe in a solar concentrator, in Example 3.6...

## The Rankine cycle

The Rankine cycle is the cycle of choice to produce electricity and is shown in Fig. 9.1 in a pressure (P)-enthalpy (H) diagram. Water is the usual working fluid in the cycle. Although there are more details to the cycle than shown, such as a reheat component, this will be ignored here so the reader may understand the basics of the cycle and the concept behind its design. It differs from the basic Carnot cycle in important aspects which will be discussed within the text below.

The four components to the cycle are the pump, boiler, turbine and condenser. We will begin with the pump and work around the cycle explaining how the steps between each component occur and the reason why they are designed that way...