Building Integrated Photovoltaic Thermal Systems : For by Basant Agrawal

By Basant Agrawal

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5. The Rayleigh number is defined as the product of the Grashof number and the Prandtl number. Mathematically: Ra ¼ Gr  Pr ¼ gbr2 L3 Cp DT mK ð1:55Þ Hence the Rayleigh number may also be viewed as the ratio of buoyancy forces and (the product of) thermal and momentum diffusivities. When the Rayleigh number is below the critical value for that fluid, heat transfer is primarily in the form of conduction; when it exceeds the critical value, heat transfer is primarily in the form of convection. Appendix A4 gives the thermophysical properties of air and saturated water such as density, specific heat, kinematic viscosity, dynamic viscosity, thermal 41 Solar Radiation and its Availability on Earth conductivity, expansion coefficient and Prandtl’s number at various temperatures, which can be used to determine the various non-dimensional parameters for a flow.

The circumstances arise when a fluid is forced over a heated surface at a rather low velocity. Coupled with the forced flow velocity is a convective velocity, which is generated by the buoyant forces resulting from a reduction in fluid density near the heated surface. A large Reynolds number implies a large forced-flow velocity and hence less influence of free convection currents. The larger the value of the Grashof–Prandtl product, the more one would expect free convection effects to prevail. Brown and Gauvin1,2 developed a correlation for the mixed convection, laminar flow region of flow through horizontal tubes as follows:  Nu ¼ 1:75 mb mw 0:14 h i1=3 Gz þ 0:012 ðGz  Gr1=3 Þ4=3 ð1:65Þ where Gz ¼ Re  Pr Ld is the Graetz number, mb is the fluid viscosity at the bulk temperature and mw is the fluid viscosity at the wall temperature.

It has been found that average free-convection heat transfer coefficients from the horizontal and vertical surfaces can be represented in a functional form for a variety of configurations as follows: Nu ¼ CðGr  PrÞn ¼ CRan ð1:56Þ The characteristic dimension to be used in the Nusselt and Grashof numbers depends on the geometry. For a horizontal plate it is the average of the length and breadth of the plate; for a vertical plate it is the height of the plate; and for a horizontal cylinder it is the diameter.

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