Applying the kriging method to predicting irradiance variability at a potential PV power plant

One-second irradiance data from forty-five sensors spaced over a one-mile square section of land were analyzed to characterize the short-term (1-s to 1-min) variability of the solar resource in Northern Arizona. The geostatistical interpolation model known as kriging was applied to our data set to better understand the method's strengths and weaknesses in accurately predicting the variations in the irradiance over this relatively small section of land. Of particular interest was to investigate the ability of the kriging method to show the variation in solar irradiance over the section of land as compared to that measured by the sensors. When using data from all the sensors as input to the prediction method, kriging performed very well compared to the sensors. However, because it is unlikely to have a large number of sensors to characterize the variability at a prospective solar site, it was also of interest to investigate how many sensors are required as input to the kriging technique in order to generate a reliable prediction. Solar data from four characteristic periods (related to the four seasons) were analyzed, and different sensor configurations, consisting of subsets of the actual sensor array, were employed using the method to demonstrate the number of sensors required to correctly characterize the short-term irradiance variability at the site. Using four measurement stations as input to the kriging method was shown to reasonably represent the variability in the 1-s to 1-min timescales.     

Effects of viscous dissipation on forced convective heat transfer in a channel embedded in a power-law fluid saturated porous medium

The convective heat transfer analysis in a channel embedded in a power-law fluid saturated porous medium subject to uniform heat flux is presented and compared with a Newtonian fluid concerning the effects of viscous dissipation. Governing momentum and energy equations for non-Newtonian fluids which accounts for the viscous dissipation effects are solved numerically. The temperature profiles of the non-Newtonian fluids are found to relate closely to the velocity profiles. When viscous dissipation is taken account of, Nusselt numbers for non-Newtonian fluid are found to deviate more from Newtonian fluid with increasing Brinkman number for a certain range of the Darcy number.     

Errors associated with the spatial interpolation of mean solar irradiances

Spatial interpolation errors at 2816 grid points covering Canada are determined using 10-year averages of the solar irradiances for 130 stations unevenly distributed throughout the same area. Three specific interpolation schemes are evaluated (2 and 3 station inverse distance weighted interpolation and single station extrapolation) though the data set and algorithm (based on kriging) are sufficiently general that other strategies could also be evaluated.In southern Canada relative values of the extrapolation error for ten-year means are typically between 1 and 2% and decrease to less than 1% if values are interpolated using data from three stations. Errors are higher at coastal locations and in the Canadian Arctic due to generally greater interpolation distances and increased spatial variability. Lower actual irradiances also influences the relative errors.There is little advantage to including additional data from stations in adjacent areas of the U.S. since interpolation and extrapolation errors are generally already less than the errors associated with measurement and modelling procedures and with temporal sampling (i.e., the long-term representativeness of a 10-year mean).     

Stagnation point flow of Maxwell nanofluid containing gyrotactic micro‐organism impinging obliquely on a convective surface

A numerical study is performed to discuss the nonaligned stagnation of a rate type fluid over a convective surface. The rheology of the fluid is presented by the constitutive equation of the Maxwell fluid model. Buongiorno's model is used to elaborate on the effects of Brownian motion and thermophoresis and motile microorganisms are introduced for the stability of the nanoparticles. The governing equations were solved by the implicit finite difference method. Graphical illustrations for velocity, temperature, nanoparticle concentration and motile microorganism profiles for various involved parameters are presented for both convective and nonconvective surfaces. It is depicted that the temperature, nanoparticle, and microorganism concentration profiles decease while both axial and tangential velocities increase with the velocity ratio parameter for both Newtonian and Maxwellian fluids. The magnitude of temperature, nanoparticle, and microorganism concentration profiles is large for the nonconvective surface as compared to the convective surface. The Nusselt number, Sherwood number, and motile organism number decrease as we move from Newtonian fluid to non‐Newtonian fluid. Furthermore, the increase in the Brownian motion parameter and thermophoresis parameter decreases the density of the motile organism over the convective as well as nonconvective surface.     

Accurate Solutions of Rayleigh-Bénard Convection in Confined Two-Layer Systems Using the Spectral Domain Decomposition Method

A spectral Navier-Stokes equation solver has been developed for the accurate prediction of two-dimensional buoyancy-driven convection in confined two-layer systems. In particular, the analysis is focussed on fluids with larger density disparity (heavier fluid is at the bottom), wherein the corresponding interfacial deformation can be neglected. The coupled evolution of flow in both fluid layers is handled through a domain decomposition method involving the influence matrix approach to incorporate the interfacial boundary conditions. The flow variables in the individual domains are transiently evaluated by expanding them in terms of Lagrangian interpolation polynomials defined over the Gauss-Lobatto-Chebyshev points. Using these approaches, the occurrence of mechanical (viscous) and thermal coupling modes has been examined at various interfacial heights in the confined two-layer system. The presence of oscillatory switching (standing wave mode) between the thermal and mechanical coupling modes has also been identified when the fluid layers are of nearly equal height, for a chosen combination of fluid properties. Additionally, benchmark results of spectral accuracy are listed for the sake of comparison with the results of future studies on two-layer convection.     

Solar radiation in Jamaica

Average monthly global radiation in Jamaica was calculated for the years between 1978 and 1987 from values measured at 12 stations and from Angstrom-coefficient derived values. From these values daily global radiation was estimated for various periods at grid points separated by approximately 10 km on a square. Three dimensional plots and contour maps for the various periods were produced. The interpolation was based on kriging adopted by Hay (1986). A relationship between global and diffuse radiation based on the Liu and Jordan (1960) relationship was obtained. The errors in the interpolated annual values were less than 10%. The maps were made available to the public with suggested usages of solar energy. Diffuse radiation formed less than 50% of the total radiation.     

Momentum and Heat Transfer from a Semi-Circular Cylinder to Power-Law Fluids in the Vortex Shedding Regime

Flow and heat transfer from a semi-circular cylinder to power-law fluids has been studied in the laminar vortex shedding regime for the range of conditions as follows: Reynolds number, 40 ≤ Re ≤ 140; Prandtl number, 0.7 ≤ Pr ≤ 50; and power-law index, 0.2 ≤ n ≤ 1.8. Extensive results are presented in terms of the streamline, vorticity and isotherm profiles, drag and lift coefficients, Strouhal number, and Nusselt number. The influence of Reynolds number, Prandtl number, and power-law index are seen to be more prominent in shear-thinning fluids (n < 1) than that in shear-thickening (n > 1) fluids. The shear-thinning fluid behavior enhances the rate of heat transfer, whereas shear-thickening fluid behavior impedes it.     

Momentum and heat transfer characteristics of a semi-circular cylinder immersed in power-law fluids in the steady flow regime

The continuity, momentum and energy equations describing the flow and heat transfer of power-law fluids over a semi-circular cylinder have been solved numerically in the two-dimensional steady flow regime. The influence of the Reynolds number (Re), Prandtl number (Pr) and power-law index (n) on the local and global flow and heat characteristics have been studied over wide ranges of conditions as follows: 0.01 ? Re ? 30, 1 ? Pr ? 100 and 0.2 ? n ? 1.8. The variation of drag coefficient and Nusselt number with the Reynolds number, Prandtl number and power-law index is shown over the aforementioned ranges of conditions. In addition, streamline and isotherm profiles along with the recirculation length and distribution of pressure coefficient and Nusselt number over the surface of the semi-circular cylinder are also presented to gain further insights into the nature of the underlying kinematics. The wake size (recirculation length) shows almost linear dependence on the Reynolds number (Re ? 1) for all values of power-law index studied herein. The drag values show the classical inverse variation with the Reynolds number, especially for shear-thinning fluids at low Reynolds numbers. The point of maximum pressure coefficient is found slightly displaced from the front stagnation point for highly shear-thinning fluids, whereas for shear-thickening and Newtonian fluids, it coincides with the front stagnation point. For fixed values of the Prandtl number and Reynolds number, the rate of heat transfer decreases with the gradual increase in power-law index; this effect is particularly striking at high Prandtl numbers due to the thinning of the thermal boundary layer. Conversely, as expected, shear-thinning behavior facilitates heat transfer and shear-thickening impedes it. The effect of power-law index on both momentum and heat-transfer characteristics is seen to be appreciable at low Reynolds numbers and it gradually diminishes with the increasing Reynolds number.     

Uniform lateral mass flux effect on natural convection of non-Newtonian fluids over a cone in porous media

In this paper, we have investigated a boundary layer analysis for uniform lateral mass flux effect on natural convection of non-Newtonian power-law fluids along an isothermal or isoflux vertical cone embedded in a porous medium. Numerical results for the dimensionless temperature profiles as well as the local Nusselt number are presented for the mass flux parameter, viscosity index n and geometry shape parameter λ. The local surface heat transfer increases for the case withdrawal of fluid, the increase of the value of λ. The local Nusselt number is found to be significantly affected by the surface mass flux than the viscosity index.     

Convective heat transfer of Titania nanofluids of different base fluids in cylindrical annulus with discrete heat source

In the current work, the hydrodynamic and thermal characteristics of Titania nanofluids filling a cylindrical annulus are numerically investigated. Ethylene glycol, engine oil, and water are used as base fluids. The Maxwell model for convective heat transfer in nanofluids is followed to account for the effects of nanoparticle volume fraction distribution on the continuity, momentum, and energy equations, in which a developed computer code is used. The latter is based upon the finite volume method coupled with the SIMPLER algorithm. Numerical results for the heat transfer are presented in the form of streamlines and isotherm profiles for a different value of Rayleigh number, base fluid, and nanoparticle volume fraction. The effects of these parameters on the local Nusselt number are analyzed.     

Heat transfer from a rotating cone or disk to fluids of any prandtl number

A new similarity variable is proposed for the analysis of laminar boundary-layer heat transfer from a rotating cone or disk to fluids of any Prandtl number. Very accurate similarity solutions for both the isothermal and uniform-flux cases are obtained over a very wide range of Prandtl number from 0.001 to infinity. Dimensionless temperature profiles in this range of Prandtl number are very similar. A heat transfer correlation equation of high accuracy for all Prandtl numbers is given.     

1960~2013年云南省降水时空变化特征分析

鉴于分析云南省降水时空变化特征对该地区旱涝灾害预警和水文模型研究具有重要意义,基于云南省29个气象站点1960~2013年的逐日降水资料,采用滑动平均、线性倾向估计、Mann Kendall突变检验、滑动t检验和普通克里格插值等方法分析了该地区降水变化特征、降水变化趋势及空间分布情况。结果表明,年际降水量以7.7 mm/10a的幅度逐渐减少,在2008年发生突变;空间分布不均,整体由东北向西南呈带状递增分布,并形成2个孤岛状的降水集中区。夏、秋、冬三季降水量均逐渐减少,春季增加;季突变时间存在差异性;夏、秋两季空间分布情况与年际类似,春季自南向北逐渐减少,冬季自中部分别向东南和西北呈带状递增分布,同时还具有自南向北呈带状递减分布的特征。     

Laminar Flow and Heat Transfer to a Non-Newtonian Fluid in an Entrance Region of a Square Duct with Prescribed Constant Axial Wall Heat Flux

Abstract

Forced-convection heat transfer information as a function of the pertinent nondimensional numbers is obtained numerically for laminar incompressible non-Newtonian fluid flow in the entrance region of a square duct with simultaneously developing temperature and velocity profiles for constant axial wall heat flux with uniform peripheral wall temperature. The power-law model characterizes the non-Newtonian behavior.

Finite-difference representations are developed for the equations of the mathematical model, and numerical solutions are obtained assuming uniform inlet velocity and temperature distributions. Results are presented for local and mean Nusselt numbers as functions of the Graetz number and the Prandtl number in the entrance region. Comparisons are made with previous analytical work for Newtonian fluids. The results show a strong effect of the Prandtl number on the Nusselt numbers with fully developed and uniform velocity profiles representing the lower and upper limits, respectively. The results provide a new insight into the true three-dimensional character of the pseudoplastlc fluid flow in the entrance region of a square duct and are accurate.     

Heat Transfer of Power-Law Fluids in Plane Couette–Poiseuille Flows with Viscous Dissipation

Abstract

Analytical expressions for the velocity and temperature profiles, bulk temperature and Nusselt numbers, in a fully-developed laminar Couette–Poiseuille flow between parallel plates of a power-law fluid with constant, and distinct, wall heat fluxes, in the presence of viscous dissipation are deduced and presented. Both favorable and adverse pressure gradient cases were analyzed. The walls’ shear stresses ratio, which arises naturally when the dimensionless hydrodynamic solution is obtained, together with the fluid power-law index Brinkman number and the walls’ heat fluxes ratio are the independent variables in the heat transfer solutions. With the exception of Newtonian fluids, there are in general two distinct analytical solutions, one for positive and another for negative values of the walls’ shear stresses ratio. The existence of singular points are also observed, where for a given value of the power-law index, there are values of the walls’ shear stresses ratio for which the Nusselt number becomes independent of the Brinkman number. It was also found that in a Couette–Poiseuille flow, for each value of the power-law index there exists a certain negative value of the walls’ shear stresses ratio that makes the Nusselt numbers at both walls identically zero.     

插值算法在内燃机瞬时转速测量中的应用研究

提出了采样信号的插值计算公式 ;考虑到测量信号中调制现象的影响 ,提出了插值法在瞬时转速计算中的误差公式 ;并针对 6 - 135 G柴油机最高转速对两点插值和三点插值的精度进行了计算 ;最后用实测数据进行了验证。结果表明这是提高瞬时转速测量精度的一种有效方法 ,在 5 0 k Hz的低采样率下即可得到较平滑的瞬时转速波形。     

Effects of dissipation and temperature-dependent viscosity on the performance of plate heat exchangers

The fluid temperature profiles in a multi-passage plate heat exchanger and its effectiveness were calculated with a model which includes dissipation, temperature-dependent viscosity and appropriate correlations for the Nusselt number and the friction coefficient. When the viscosity of the two fluids is low (e.g. water) the results are identical to the classic ε–NTU relations which are obtained by neglecting dissipation and by assuming that fluid properties and heat transfer coefficients are constant. But, when one of the fluids is very viscous (e.g. glycerol) the temperatures of both fluids are significantly higher while the effectiveness can be higher or lower than the value predicted by the classic relations. In particular, for cases with a very viscous hot fluid, the effectiveness may be even higher than unity.     

Forced convective heat transfer between assemblages of spherical particles and power‐law non‐Newtonian liquids with velocity slip at the interface

Heat transfer from spheres can be influenced by a varying degree of slip at the fluid‐particle interface along with the rheology of the surrounding continuous liquid and adjacent spheres. Thus in this study, the effects of dimensionless velocity slip parameter (λ) along with power‐law fluid rheology and other pertinent kinematic flow and heat transfer parameters on isotherm contours, local and average Nusselt numbers of assemblages of spherical slip particles are presented. This is done by adopting a segregated approach where dimensionless momentum and energy equations are solved by SMAC algorithm formulated in spherical coordinates within the finite difference formulation. Before obtaining new results, grid independence studies for either extreme values of power‐law consistency index of non‐Newtonian fluids are carried out. Finally, the major contribution of this study is the development of a correlative equation for the average Nusselt number of assemblages of spherical slip particles in power‐law fluids based on the present results (5880 data points) as a function of pertinent dimensionless parameters.     

Thermal radiation and diffusion effects in MHD Williamson and Casson fluid flows past a slendering stretching surface

The article is presented to analyze the magnetohydrodynamic Casson and Williamson fluids flow over a stretched surface of variable thickness by including the conditions of thermal radiation, velocity slip, temperature, and concentration slip. The equations governing the flow characteristics are transformed to ordinary differential equations by applying similarity transformations. The solution of the simplified equations is obtained by the numerical bvp5c Matlab package. The behavior for Williamson and Casson fluid cases is explored and discussed with the impact of sundry parameters on the flowing fluid, thermal, and diffusion fields. The profiles under the impact of parameters are depicted through graphs. Also, we evaluated the performance of local Nusselt and Sherwood numbers along with the friction of the wall and are displayed through tables. We found that the temperature and mass transfer distribution is low in Williamson fluid when compared to Casson fluid flow. The computed results indicate that the flow, thermal and concentration boundary layer characteristics of Williamson and Casson fluids are not unique.     

Free convection boundary layer flow over a horizontal cylinder of elliptic cross section in porous media saturated by a nanofluid

This work studies the free convection boundary layer flow over a horizontal cylinder of elliptic cross section in porous media saturated by a nanofluid with constant wall temperature and constant wall nanoparticle volume fraction. The effects of Brownian motion and thermophoresis are incorporated into the model for nanofluids. A coordinate transformation is performed, and the obtained nonsimilar governing equations are then solved by the cubic spline collocation method. The effects of the Brownian motion parameter and thermophoresis parameter on the profiles of the temperature, nanoparticle volume fraction and velocity profiles are presented. The local Nusselt number is presented as a function of the thermophoresis parameter, Brownian parameter, Lewis number and the aspect ratio when the major axis of the elliptical cylinder is vertical (slender orientation) and horizontal (blunt orientation). Results show that the local Nusselt number is increased as the thermophoresis parameter or the Brownian parameter is decreased. The local Nusselt number increases as the buoyancy ratio or the Lewis number is decreased. Moreover, the local Nusselt number of the elliptical cylinder with slender orientation is higher than those of the elliptical cylinder with blunt orientation over the lower half cylinder.     

Forced Convection Heat Transfer in Power-Law Fluids Around a Semicircular Cylinder at Incidence

Two-dimensional steady flow and convective heat transfer of power-law fluids past a semicircular cylinder are investigated in the reported work. The heated semicircular cylinder is placed in an unconfined domain at different angles facing the incoming free-stream flow of power-law fluids having a generalized Prandtl number (Pr) = 100. Particular emphasis is given to studying the effect of angle of incidence (0 ≤ α ≤ 180°) on fluid dynamics and thermal transport around the semicircular object for varying Reynolds number (10 ≤ Re ≤ 40) and power-law index (0.4 ≤ n ≤ 1.8). A finite volume-based method is adopted for the numerical computation. The flow and heat transfer phenomena are visualized through the streamline and isotherm profiles at various operating conditions. Also, the pressure coefficient, drag coefficient, and Nusselt number on the surface of the object are presented and discussed.