By Basant Agrawal
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Creation to Nonimaging Optics covers the theoretical foundations and layout tools of nonimaging optics, in addition to key strategies from similar fields. This totally up-to-date, revised, and multiplied moment version: incorporates a new and intuitive advent with a uncomplicated description of the benefits of nonimaging opticsAdds new chapters on wavefronts for a prescribed output (irradiance or intensity), infinitesimal étendue optics (generalization of the aplanatic optics), and Köhler optics and colour mixingIncorporates new fabric at the simultaneous a number of floor (SMS) layout technique in 3-D, int.
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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 Â 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 Â Gr1=3 Þ4=3 ð1:65Þ where Gz ¼ Re Â 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 Â 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.