Correlations for estimating solar radiation using sunshine hours and temperature measurement in Osogbo,Osun State,Nigeria

In this study, the global solar radiation on horizontal surface in Osogbo, Osun state, Nigeria was analyzed using 11-year data (1997–2007). Correlations using linear and quadratic expressions were developed to relate the global solar radiation on horizontal surface based on relative sunshine hours and temperature measurements for evaluating the monthly average daily global solar radiation. The calculated monthly clearness index values indicate that the prevailing weather condition in Osogbo is heavily overcast. All the developed quadratic correlations gave better correlation coefficients (0.834, 0.872 and 0.823 respectively) than the linear models. However, the Hargreaves and Samani related based quadratic model gave the best among the three developed quadratic expressions and is therefore suggested for estimating the monthly global radiation in this site and its surroundings.     

Influence of multiple internal reflection of transmitted solar radiation between interfaces on temperature regime of transparent flat solar collector casing covers

Analytical expressions are proposed to calculate the temperature regime of the transparent covers of flat solar collector casings. These expressions account for the influence of multiple internal reflection of transmitted solar radiation between the interfaces of the transparent covers. An example of the calculation of a practical implementation of the results is presented.     

Temperature field and heat flows through transparent covers of flat-plate solar collector housing

Analytical expressions to calculate the temperature field and heat flows through transparent covers of flat-plate solar collector housings are proposed, taking into account the exponential distribution of the power of the internal source through its thickness, which is formed as a result of partial absorption and conversion to heat of the transmitted total (direct and diffuse) solar radiation incident on its front surface and the diffuse solar radiation incident on its back surface and reflected by the light-absorbing surface of the collector heat-exchange panel.     

A thermal model for photovoltaic systems

The energy balance of photovoltaic (PV) cells is modelled based on climate variables. Module temperature change is shown to be in a non-steady state with respect to time. Theoretical expressions model the energy transfer processes involved: short wave radiation, long wave radiation, convection and electrical energy production. The combined model is found to agree well with the response of the measured model temperature to transient changes in irradiance. It is found that the most precise fit to measured data is obtained by fitting the value of the forced convection coefficient for module convection. The fitted values of this coefficient were found to be within the range predicted by previous authors. Though the model is found to be accurate to within 6 K of measured temperature values 95% of the time in cloudy conditions, best accuracy is obtained in clear and overcast conditions when irradiance is subject to less fluctuation.     

Triple diffusive flow of nanofluid with buoyancy forces and nonlinear thermal radiation over a horizontal plate

The present attempt is made to elaborate the features of triple diffusive convective flow of an incompressible nanoliquid induced by horizontal surface under buoyancy forces. The effect of nonlinear thermal radiation is taken into account. Heat flux model of radiation is formulated through Rosseland's approximation. The radiation phenomenon plays a key role in modern solar energy equipment's. The nondimensional variables are introduced to convert the dimensional mathematical expressions into dimensionless single independent variable. Numerical scheme is developed to obtain the solution of mathematical model. The importance of controlling constraints on flow quantities are characterized through plots. The quantities of engineering importance are computed and elaborated graphically. It is noticed that the presence of salts and nanoparticles enhance the thermal performance of base liquid. The liquid temperature and its relevant thickness of thermal layer improved significantly with an increment in the values of radiative parameter. The larger values of parameters of Brownian motion and thermophoretic correspond to higher temperature profiles.     

Thermal restoration of a wall after the interruption of solar radiation flux

The transient phenomenon of the thermal restoration of an opaque wall of a room after the interruption of solar radiation flux was analysed. The wall, was initially, in thermal equilibrium under solar radiation. When the solar radiation flux was interrupted, the temperature distribution on the wall cross-section went through a transient state until it reached a final equilibrium state. During the thermal restoration of the wall, a thermal gain is maintained for the room as a result of the exploitation of a part of the thermal energy stored in the wall. Analytical expressions have been obtained for the duration of the thermal restoration, for the thermal gain of the room during this transient state and for the coefficients of storage and exploitation of the solar radiation by the wall.     

Energy requirements for a swimming pool through a water-atmosphere energy balance

The methodology displayed here is to calculate the energy requirements for heating a swimming pool to a desired temperature. This methodology consists of an energy balance between water-atmosphere as is used in the temperature evaluation of cooling ponds in power plants. Different mathematical expressions are given to calculate such a balance. It is necessary to know the month of the year, the ambient temperature, relative humidity, wind velocity, and solar radiation. With these parameters it is possible to know the natural temperature of the water, natural evaporation, energy needed to reach a determined swimming pool temperature and the evaporation of the heated pool.     

A model of the thermal restoration transient state of an opaque wall after the interruption of solar radiation

The temperature distribution of an outer wall of a room subjected to solar radiation goes through a transient state until it reaches a thermal equilibrium state. After an interruption of solar radiation, the temperature profile on the wall cross-section, starting from the latter thermal equilibrium state, returns through a transient state to the initial thermal equilibrium state. The transient state between the above two equilibrium states is called the thermal restoration transient state of the wall. The duration of the thermal restoration transient state depends on the structural characteristics of the wall and on the thermal parameters of the room–environment system. The influence of the thermal restoration transient state on the evaluation of the ability of an opaque wall to store and exploit solar radiation and on the computation of the resulting thermal gain of the room during the thermal restoration of the wall is important, because it acts as a flywheel. In the present work analytical expressions yielding the temperature profiles and the duration of the transient state as a function of thermal and structural characteristics have been developed. An analytical model for the thermal gain of the room during the thermal restoration of the wall also was developed. An experimental verification of the duration of the transient state of the thermal restoration was made.     

Zero‐mass flux and Cattaneo–Christov heat flux through a Prandtl non‐Newtonian nanofluid in Darcy–Forchheimer porous space

The Darcy–Forchheimer Prandtl fluid flow due to moving sheet is described here. The familiar energy transfer model, namely, the Cattaneo–Christov model of heat transportation, is adopted under thermal radiation phenomenon. The Prandtl non‐Newtonian nanofluid is accounted as a functioning fluid. The functioning fluid flows in Darcy–Forchheimer porosity space. The boundary‐layer and similarity variables are executed to reframe the mathematical expressions into simplified and single independent variable. Numerical solutions of nonlinear dimensionless expressions are calculated. The variations of distinct constraints on important quantities are demonstrated through tabular and pictorial forms. It is visualized that the velocity of non‐Newtonian nanofluid is enhanced significantly by incrementing the elastic parameter. Improving the thermophoretic and Brownian movement parametric values leads to higher profile of Prandtl nanofluid temperature.     

Salt gradient stabilized solar pond collector

This paper presents a theoretical analysis of a salt gradient solar pond as a steady state flat plate solar energy collector. We explicitly take into account the convective heat and mass flux through the pond surface and evaluate the temperature and heat fluxes at various levels in the pond by solving the Fourier heat conduction equation with internal heat generation resulting from the absorption of solar radiation as it passes through the pond water. These evaluations, in combination with energy balance considerations, enable the derivation of the expressions for solar pond efficiency of heat collection as well as the efficiency of heat removal. The efficiency expressions are Hottel-Whillier-Bliss type, prevalent for flat plate collectors. Numerical computations are made to investigate the optimization of geometrical and operational parameters of the solar pond. For given atmospheric air temperature, solar insolation and heat collection temperature, there is an optimum thickness of nonconvective zone for which the heat collection efficiency is maximum. The heat removal factor is also similar to that of a flat plate collector and the maximum efficiency of heat removal depends on both the flow rate and the temperature in the nonconvective zone.     

Heat engineering calculation of a parabolo-cylindrical solar concentrator with tubular reactor for crude oil preparation for refining in the oil fields

A technique is proposed for the heat engineering calculation of a parabolo-cylindrical concentrator with tubular solar reactor, and the expressions are presented to calculate, for the specified flux density of the direct solar radiation in the particular region located at latitude 42 N (Baku and other Azerbaijan regions), the temperature of the solar reactor surface and the fluid.     

Modeling thermal behavior and work flux in finite-rate systems with radiation

We apply thermodynamic analysis in modeling, simulation and optimization of radiation engines as non-linear energy converters. We also perform critical analysis of available data for photon flux and photon density that leads to exact numerical value of photon flux constant. Basic thermodynamic principles lead to expressions for converter’s efficiency and generated work in terms of driving energy flux in the system. Steady and dynamical processes are investigated. In the latter, associated with an exhaust of radiation resource measured in terms of its temperature decrease, real work is a cumulative effect obtained in a system composed of a radiation fluid, sequence of engines, and an infinite bath. Variational calculus is applied in trajectory optimization of relaxing radiation described by a pseudo-Newtonian model. The principal performance function that expresses optimal work depends on thermal coordinates and a dissipation index, h, in fact a Hamiltonian of the optimization problem for extremum power or minimum entropy production. As an example of work limit in the radiation system under pseudo-Newtonian approximation the generalized exergy of radiation fluid is estimated in terms of finite rates quantified by Hamiltonian h. The primary results are dynamical equations of state for radiation temperature and work output in terms of process control variables. In the second part of this paper these equations and their discrete counterparts will serve to derive efficient algorithms for work optimization in the form of Hamilton–Jacobi–Bellman equations and dynamic programming equations. Significance of non-linear analyses in dynamic optimization of radiation systems is underlined.     

On the heat flow into the ground

Two expressions have been developed to predict the periodic variation of the ground temperature with depth. They are based on the energy balance equation at the ground surface and the assumption that the temperature variation at the ground surface is in the form of a sine-wave or a Fourier series. The energy balance equation involves the periodic variation of solar radiation, atmospheric temperature and the latent heat flux due to evaporation. The heat flux into the ground has been derived and the damping depth and the corresponding ground temperature have been calculated. A parametric study showed that the ground temperature and the amplitude of the heat flux into the ground increase with the increasing in the air relative humidity and the ground absorptivity. Conversely, they decrease with the increasing in the evaporation fraction and wind speed. The values of the damping depth is almost the same while the corresponding ground temperature is influenced by the various parameters significantly.     

Calculation of the proportion of sky seen by windows with finite horizontal and vertical projections

This paper presents convenient analytical expressions for the proportion of sky seen by windows shaded by horizontal or vertical projections of any width and of finite or infinite length. The projections may be offset from the window edge, and horizontal projections may be placed asymmetrically over the window. These expressions can be used to calculate the diffuse radiation incident on the shaded window, assuming that the radiation is isotropically distributed. Comparisons with other less general or less convenient methods show excellent agreement. The errors involved in using the simpler expressions for infinite-width projections to describe finite-width projections are quantified, and are found to be small in practical cases.     

On the oscillating plate-temperature flow of a polar fluid past a vertical porous plate in the presence of couple stresses and radiation

The paper studies the two-dimensional oscillatory flow of a polar electrically conducting viscous incompressible Bossinesq fluid past an infinite vertical plate whose temperature varied periodically about a mean constant non-zero value with time. The governing equations of this class of polar fluids are known to exhibit a boundary layer phenomenon. Employing a standard perturbative series method, expressions are obtained for the flow variables—velocity, temperature and plate surface skin friction, highlighting the effect of viscous dissipation heating. The numerical results obtained agree with and compliment results of earlier studies and are discussed quantitatively with the aid of graphs outlining the effects of radiation on the velocity field.     

Experimental and theoretical investigation of global and diffuse solar radiation in the United Arab Emirates

In the present study, the global, direct and diffuse components of solar radiation as well as temperature, relative humidity and wind speed have been continuously monitored and analysed on an hourly, daily and monthly basis. The monthly average daily total solar radiation varies from 2700 W h/m² in December to 8000 W h/m² in June with an average clearness index of 0.65. Experimental data are compared to the predictions of different theoretical models as functions of declination and hour angles. Correlations are obtained describing the variation of hourly, daily and monthly averages of total and diffuse solar radiation using polynomial expressions. Empirical correlations describing the dependence of the daily average diffuse to total radiation ratio on the clearness index are also obtained. Data for the daily diffuse to total radiation ratio are compared to correlations obtained by other investigators. The comparison shows a reasonable agreement with some scatter due to the seasonal dependence of the correlation. Comparison of calculations with experimental measurements under clear sky conditions show excellent agreement with a maximum error of 8%.     

Simulation of fourth-grade magnetized fluid flow due to motile cilia in a heated curved channel

This research aims to investigate the main features of the ciliary flow of fourth-grade fluid in a curved channel. The fluid is considered electrically conducting with a radial magnetic field effect. The constitutive relation for energy is formulated with the addition of viscous dissipation and thermal radiation. The governing system of coupled partial differential equations with extremely nonlinear expressions is simplified using the long wavelength and low Reynolds number approximations. The numerical outcomes of simplified normalized equations are obtained using the finite difference method incorporating the relaxation algorithm. The numerical outcomes regarding the influences of several physical parameters on the temperature, velocity, pumping characteristics, and stream function are examined through graphs. The outcomes reveal that fluid velocity diminishes by enhancing the magnetic parameter. Also, the temperature is enhanced by enhancing the values of the Brickman number. The current model has been used in bioengineering processes, microfluidics, and drug delivery systems.     

PREDICTING THE BROADBAND AEROSOL TRANSMITTANCE FOR SOLAR RADIATION MODELS

Based on a detailed spectral aerosol model (1), the total scattering and absorption broadband aerosol transmission functions are estimated. Using parameterization techniques, analytical expressions for the broadband aerosol transmission functions are obtained. The accuracy of the proposed expressions are verified with various tests. The proposed broadband aerosol transmission functions can be combined directly with the solar radiation models to predict accurately the direct beam, the diffuse and the total solar radiation at a given place.     

A non-linear flat-plate collector model

The analysis of a non-linear flat-plate collector is presented in which the overall loss coefficient is assumed to be a linear function of the temperature difference between the fluid in the collector and the environment. The instantaneous performance of collectors calculated using linear and non-linear models is presented in terms of three dimensionless numbers. For an assumed parabolic solar radiation profile, the average daily performance for a constant fluid inlet temperature can be presented in terms of three further dimensionless numbers. The resulting expressions for both instantaneous and daily performance are shown graphically. A method of calculating linear collector performance characteristics from non-linear curve fitting to experimental results is shown so that the predicted daily performance from non-linear and linear curve fits can be compared. In most circumstances, a linear fit is adequate.