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Evaporation
Published in Stephen A. Thompson, Hydrology for Water Management, 2017
Equations (5.1)–(5.4) all describe energy flux. Flux describes the flow of a quantity per unit area per unit time. Energy flux is the flow of energy per unit area per unit time. Units for radiant energy flux are calories per square centimeter per day (cal cm−2 d−1) or watts per square meter (W m−2). (One watt is equal to one joule per second, and one calorie is equal to 4.186 joules.) The solar constantI0 is the flux of insolation measured at the outer edge of the Earth’s atmosphere, perpendicular to the Sun’s rays, at the mean distance between the Earth and the Sun. The current estimated value for the solar constant is 1.97 cal cm−2 min−1 (1372 W m−2). The term solar constant is misleading as the flux varies by as much as 0.5% around this value. Averaged over the entire Earth, only about 50% of the solar constant reaches the Earth’s surface. The remainder is scattered, absorbed or reflected by the atmosphere and the surface (Fig. 5.1). Table 5.2 gives average values for Io in cal cm−2 d−1 for various latitudes. The values in Table 5.2 are based on an earlier (lower) estimate of the solar constant and should be increased by 2% (Frohlich 1977), but only if such precision is warranted.
Liquid crystal technology for vergence-accommodation conflicts in augmented reality and virtual reality systems: a review
Published in Liquid Crystals Reviews, 2021
Another special LC optical component for designing a varifocal AR system is an electrically tunable LC plane-parallel plate [25]. In general, a plane-parallel plate causes a longitudinal shift of a convergent wave, which effectively changes the length of the optical path, as shown in Figure 17(a). The longitudinal shift increases when the refraction angle in the plane-parallel plate decrease, and the refraction angle is determined using Snell’s law when the plate is optical isotropic. As for LC plane-parallel plates, nematic LCs can be adopted. The refraction angle of an LC plane-parallel plate is dependent on the direction of the optic axes of LCs (i.e. the long axes of the LC molecules) and the polarization of the incident light. When the optic axis rotates, the amount of longitudinal shift changes accordingly. Therefore, we can place an LC plane-parallel plate in front of a lens in order to change the object distance. The Poynting vector (direction energy flux), not the wave vector, should be used for the analysis of beam propagation [25].
Paraxial propagation of the first-order chirped Airy vortex beams propagating in a quadratic index media
Published in Journal of Modern Optics, 2020
Lixun Wu, Yaohui Chen, Xinxiang Lai, Zhixiong Mo, Dongmei Deng
To analyze the propagation properties of electromagnetic fields, we investigate the Poynting vector and the angular momentum of the FCAiV beams through the quadratic index media. As we know, the Poynting vector is the vector of the energy flux density in the electromagnetic field, which is usually used to indicate the direction of the energy flow. The Poynting vector can be defined as [33], where is the light velocity in a vacuum, and are the electric and magnetic fields respectively. Considering an -polarized vector potential , where is the unit vector along the x-direction, the time-averaged Poynting vector can be described as [34] Here and are the unit vectors along the and directions, respectively, and denotes the complex conjugate, is the angular frequency.
Convective Heat Transport in a Heat Generating Porous Layer Saturated by a Non-Newtonian Nanofluid
Published in Heat Transfer Engineering, 2019
The energy equation with internal heat generation is where Q is the strength of internal heat generation, (ρc) is the heat capacity of non-Newtonian nanofluid, is the energy flux relative to non-Newtonian nanofluid velocity, and is the addition flow work due to the Brownian motion and the thermophoresis of nanoparticles relative to the flow velocities, here hp is the enthalpy of nanoparticles. The energy flux can be written as the sum of the conduction heat flux and the heat flux due to nanoparticle diffusion as where km is the effective thermal conductivity and hp is the specific enthalpy. Eq. (7) gives where ∇*hp is equal to cp∇*T* and cp is the specific heat of the material constituting the nanoparticles.