THE EFFECT OF A NON-UNIFORM SURFACE TEMPERATURE ON LAMINAR NATURAL CONVECTION IN A RECTANGULAR ENCLOSURE

Three dimensional solutions were developed for natural convection in a 2 × 1 × 1 rectangular enclosure by finite-difference calculations. Sawtooth temperature distributions with different amplitudes and orientations were imposed on the lower (2×1) surface to simulate the effect of cooling coils or jackets on the collector plate of a flat-plate solar heater. The shorter dimension of the enclosure was progressively inclined.

The circulation patterns were not changed significantly by the surface temperature distributions. The variation of the Nusselt number with inclination was not changed significantly but the magnitude increased with the amplitude of the surface temperature variations for inclinations of less than 90 degrees.

It is concluded that the collecting plate of a solar collector should be maintained as nearly isothermal as possible to minimize heat losses by natural convection through the air gap.     

Simulation Mathématique de la Circulation de I'Air dans une Enceinte avec Ouvertures et Sources Chaudes Localisées

A mathematical simulation of the air circulation and the temperature inside a rectangular enclosure with multiple openings and with localised rectangular heat sources was made. Finite difference techniques and a simple turbulence model were used to solve the time-averaged partial differential equations for the conservation of mass, momentum and energy. The computations were carried out for a Prandtl number of 0.7, for an Archimedes number of about 34 and for Grashof numbers up to 3 × 10⁹. Comparison of the numerical results to flow visualization and temperature studies in an experimental apparatus indicated good agreement. The combined effect of natural convection from the heat sources and the forced convection through the enclosure creates a complex flow pattern inside the enclosure. These conditions were simulated in an attempt to study the air circulation pattern and the air temperature inside the building of an aluminum reduction plant.     

MATHEMATICAL MODELING OF THERMAL RADIATION EFFECTS ON TRANSIENT GRAVITY-DRIVEN OPTICALLY THICK GRAY CONVECTION FLOW ALONG AN INCLINED PLANE WITH PRESSURE GRADIENT

We study theoretically the unsteady gravity-driven thermal convection flow of a viscous incompressible absorbing-emitting gray gas along an inclined plane in the presence of a pressure gradient and significant thermal radiation effects. The Rosseland diffusion flux model is employed to simulate thermal radiation effects. The momentum and energy conservation equations are nondimensionalized and solved exactly using the Laplace transform technique. Expressions are derived for the frictional shearing stress at the inclined plane surface and also the critical Grashof number. The effects of time (T), Grashof number (Gr), Boltzmann-Rosseland radiation parameter (K₁), and plate inclination (α) on velocity (u) and temperature (θ) distributions are studied. The flow is found to be accelerated with increasing inclination of the plane, increasing free convection effects, and for greater thermal radiation contribution but decelerated with progression of time. Temperature is found to be enhanced with progression of time and with greater thermal radiation contribution. Applications of the model arise in solar energy collector analysis and industrial materials processing.     

Experimental study on the vertical temperature distribution of window ejected fire from an enclosure with adjacent side walls

This paper measured and analyzed the vertical temperature profile of window ejected fire from a cubic enclosure with the effect of adjacent parallel sidewalls. A cubic enclosure size is 0.4 m (height) × 0.4 m (width) × 0.4 m (length). And two side walls were fixed on the both side of the compartment openings, its distance can be changed. K-Type thermocouples (T₁-T₄) were installed in the inside compartment (inner and outer corner), the vertical position along the façade wall and the center of side wall, respectively. It is found that the side wall distance was independent of the temperature distribution inside the enclosure when the opening size changed from 0.2 m to infinity, and the vertical temperature profile along the side wall significantly increased with the decrease of the separation distances of two sidewalls. A dimensionless correlation was proposed to describe the vertical temperature along the facade wall for various side wall separation dimensions. The new findings and the proposed dimensionless correlation provide basic knowledge for describing vertical temperature along the facade wall.     

DESIGN,EXPERIMENTAL AND ECONOMIC EVALUATION OF A COMMERCIAL-TYPE SOLAR DRYER FOR PRODUCTION OF HIGH-QUALITY HAY

Abstract

Design features, development, experimental functional performance and economic evaluation of an energy efficient solar energy dryer for commercial production of high-quality hay and processed forage products are presented. The solar hay dryer consists of an improved solar collector with selective coated aluminum absorber plate and spaced fins, and a drying shed connected to the collector by an insulated duct and having a perforated metal grate floor, swing-away plywood frames and polyethylene curtains for effectively sealing the hay stack, and a crawl space below the floor where a 3-hp in-line centrifugal fan is housed for air circulation by suction. In late August and in early September, 1996, 160 small rectangular bales of alfalfa hay with about 25% bromegrass were successfully dried from 33% initial moisture content to 13%, and from 25% to 11% moisture in 4 and 3 days, respectively, under average weather conditions in Saskatoon, Saskatchewan, Canada. With about 18 m³/min per tonne airflow, 10-15 °C temperature rise above ambit was obtained during peak bright sunshine hours. Relatively high daily average collector Effciency of 76%, high drying effectiveness, drying uniformity, uniform air distribution and tight sealing of the stack were achieved which resulted in an attractive green color of hay, no mold growth on hay, and an overall system drying efficiency of about 79%. Compared to a conventional natural gas drying system or field-drying method, the payback period on extra investment costs recovered through drying cost savings of $3/ t to $6/ t or through over two times higher prices for high-quality hay produced by the solar drying system may be just one or two years, respectively.     

TRANSIENT NATURAL DRYING-INDUCED BOUNDARY LAYERS

ABSTRACT

This work presents a methodology far obtaining heat and mass transfer coefficients for problems involving natural convection along a flat plate. In order to simulate drying conditions, a set of data has been obtained for the temperature range between 20 and 98° C and for various absolute humidities, both of the wall and ambient. It is shown that for drying at temperatures above 80° C, Nusselt and Sherwood numbers change very appreciably with respect to values obtained at smaller temperatures. The simulated results show that even for very low temperature differences, the transient period in natural convection along a flal vertical plate is smaller than 3s.     

基于格子Boltzmann方法的封闭三角腔自然对流的数值模拟

建立了二维不可压缩D2G9格子Boltzmann模型,耦合二维TD2Q5热格子Boltzmann模型,在非平衡态外推的边界条件下,首先对不同Eckert数(Ec)和Prandtl数(Pr)时Couette流的温度场进行数值模拟,计算结果与解析解吻合良好,且在Ec变化很大的条件下,计算结果仍与解析解相符,验证了模型的准确性和稳定性. 然后对封闭三角空腔内不同Rayleigh数(Ra)下的自然对流流场和温度场进行了数值模拟,结果与文献计算值吻合良好,说明格子Boltzmann方法的TD2Q5热模型可用于高Ra时的空腔热流动模拟.     

NATURAL CONVECTION OF A BINARY MIXTURE IN A VERTICAL CLOSED ANNULUS

This article reports an analytical and numerical study of natural convection of a binary mixture within a vertical closed annulus. Neumann boundary conditions for temperature are applied to the vertical walls of the enclosure, while the short walls are insulated. The solutal buoyancy forces are assumed to be induced either by the imposition of constant fluxes of mass on the vertical walls (double-diffusive convection, a = 0) or by temperature gradients (Soret effect, a = 1). The governing parameters for the problem are the thermal Rayleigh number R_T, Prandtl number Pr, Lewis number Le, buoyancy ratio ?, aspect ratio A, constant a, and curvature parameter η. An analytical solution, based on the assumption of parallel flow over a large portion of enclosure, is derived. Numerical confirmation of the analytical results is also presented.     

A New Type of Modular Dryer Combining Solar Energy and Producer Gas

ABSTRACT

The main concept oithis research is to develop a flexible modular dryer that combines two different sources of non-conventional energy. In this study, solar energy and producer gas generated by an up-flow charcoal gasifier were considered.

The drying system was set out by using a 0.6 m3 modular cabinet supporting a solar collector of 2.5 m2 surface area. 16 kg of chatcoal was used in each bateb to feed the gasifier.

The experiment was performed for drying beef that required two different stages of drying temperture: the first. which used producer gas requires approximatly 60°C for four hours and the second used solar energy at 40° for six hours. The energy consumed for drying 16 kg of beef was 7.57 MJ7sol;kg H2o     

SINGLE-LAYER DRYING BEHAVIOR OF MEXICAN TEA LEAVES (CHENOPODIUM AMBROSIOIDES) IN A CONVECTIVE SOLAR DRYER AND MATHEMATICAL MODELING

Single-layer solar drying experiments were conducted for Mexican tea leaves (Chenopodium ambrosioides) grown in Marrakech. An indirect forced convection solar dryer was used in drying the Mexican tea leaves at different conditions such as ambient air temperature (21° to 35°C), drying air temperature (45° to 60°C) with relative humidity (29 to 53%), airflow rate (0.0277 to 0.0556 m ³/s), and solar radiation (150–920 W/m²). The experimental drying curves showed only a falling rate period. In order to select the suitable form of drying curves, 14 mathematical models were applied to the experimental data and compared according to their statistical parameters. The main factor in controlling the drying rate was found to be the temperature. The drying rate equation was determined empirically from the characteristic drying curve. The diffusion coefficient of the Chenopodium ambrosioides leaves was estimated and varied between 1.0209 × 10^?9 and 1.0440 × 10^?8 m ²·s^?1.The activation energy was found to be 89.1486 kJ·mol^?1.     

Numerical model of an inflatable solar collector

The main objective of this paper is to present a mathematical model to simulate the operation of an inflatable solar air heat collector for grain dryers. The solar collector exhibits a semicylindrical shape when air is injected into the confined space between the walls of the two covers. The mathematical model of the collector is obtained by applying the law of conservation of energy on the four main parts of the collector, absorber plate, two covers, and air that flows inside the equipment. To improve the accuracy of the model, the solar collector was divided into N control volumes, with each one containing the four parts, in such a way that one system with 4N differential equations is obtained. The unknown quantities of this system are the temperatures of the absorber plate, air, and walls of both covers in each control volume. The results allow us to conclude that the collector performance strongly depends on several entrance variables of the model (the air flow and air temperature at the collector entrance) and geometric equipment parameters (the collector length, internal radiation at the inner surface of the cover, and space between both covers). Therefore, the model can be used for optimizing the solar collector.     

A GRAPHICAL DESIGN METHOD FOR A PARTIAL SOLAR DRYER FOR CORN

ABSTRACT

This paper presents the application of a design method for a partial solar heating system of polyvalent modular dryers called “GJ-ABAQUE” to the drying of thick layers of grains.

This method is based on the use of charts or polynomial correlations. In the actual case where the drying air is not recycled, we only need one chart which allows one to determine the fraction of the monthly heating load supply by solar energy as a function of two dimensionless parameters. The latter implies the use of monthly average radiation data, the collector surface and estimates of drying loads.

The “GJ-ABAQUE” method was applied for drying 777 kg of corn, corresponding to 1 m³ of fresh product, in a thick layer in each modular dryer.     

THE RELATIVE MAGNITUDE OF RADIATION AND CONVECTION HEATING IN A MUFFLE KILN1

Rates of Heating by Convection and by Radiation in a Muffle Kiln, 38°×18°× 36° high, were each determined for temperatures from 350° to 800°C from measurements with a steady flow water calorimeter whose surface was first gold plated and then covered with a mixture of platinum black and lamp black. Taking the reflecting powers as 91 and 4 per cent, respectively, for the two surfaces, the radiation heating increases approximately according to the Stefan-Boltzmann fourth power law, while the convection heating comes out proportional to the temperature difference between calorimeter and muffle; that is, C=γ(T-t) where γ= 2.34×10⁻⁴ gm. cal./cm.² sec. The ratio of convection to radiation decreases from about .40 at 350° to .10 at 800°C, so that for the higher temperatures the convection heating may be neglected in rough computations of the rate of heating in such a kiln.     

Analysis of Energy and Environmental Parameters during Solar Cabinet Drying of Apple and Carrot

A modular solar cabinet dryer equipped with an air collector including a drying chamber with different tray arrangements was developed to determine moisture changes in different sizes and forms (slices and cubes) of apple and carrot pieces and to carry out serial measurements of temperatures, solar radiation, and air humidity distributions during the drying process. The initial and final moisture contents (w.b.) of fresh products were 88 and 26% for apple and 71 and 13% for carrot with initial weights of 1.56 and 3 kg, respectively. The results revealed that the temperature inside the chamber was strongly negatively correlated with air humidity (R² = 0.91) and that the length of the drying period was influenced by the weather conditions, as the cloudy weather retarded drying of carrots. It was possible to reach an air drying temperature over 41°C with a daily total solar energy incident on the collector's surface of 857.2 kJ/(m² day) for apples and 753.20 kJ/(m² day) for carrots. The analysis of energy requirements to remove moisture from apples and carrots during the total drying period showed values of 3300.19 and 7428.28 kJ/kg, respectively. The amount of air to remove water from the samples was also determined as 126.93 m³ for apples and 928.56 m³ for carrots.     

Simultaneous heat and mass transfer through laminar boundary layers in combined forced and free convection

Heat and mass transfer rates from a vertical plate are reported for combined free and forced convection. Heat transfer coefficients were obtained from temperature gradients at the wall and mass transfer rates from thickness decrease measurements of naphthalene coatings. The free convection data cover a Grashof number range from 100 to 2 × 10⁸ and the combined flow parameters Gr/Re² and Gr'/Re² vary from 0.2 to 100 and 2 × 10^?8 to 3.25, respectively. Predictions from boundary layer solutions are in good agreement with the data. Absorption of ultraviolet light by naphthalene vapor was used to measure free convection concentration profiles. Results prove the versatility of this method.     

Numerical simulation of natural convection in a square enclosure filled with nanofluid using the two-phase Lattice Boltzmann method

Considering interaction forces (gravity and buoyancy force, drag force, interaction potential force, and Brownian force) between nanoparticles and a base fluid, a two-phase Lattice Boltzmann model for natural convection of nanofluid is developed in this work. It is applied to investigate the natural convection in a square enclosure (the left wall is kept at a high constant temperature (T_H), and the top wall is kept at a low constant temperature (T_C)) filled with Al₂O₃/H₂O nanofluid. This model is validated by comparing numerical results with published results, and a satisfactory agreement is shown between them. The effects of different nanoparticle fractions and Rayleigh numbers on natural convection heat transfer of nanofluid are investigated. It is found that the average Nusselt number of the enclosure increases with increasing nanoparticle volume fraction and increases more rapidly at a high Rayleigh number. Also, the effects of forces on nanoparticle volume fraction distribution in the square enclosure are studied in this paper. It is found that the driving force of the temperature difference has the biggest effect on nanoparticle volume fraction distribution. In addition, the effects of interaction forces on flow and heat transfer are investigated. It is found that Brownian force, interaction potential force, and gravity-buoyancy force have positive effects on the enhancement of natural convective heat transfer, while drag force has a negative effect.     

Interactions Between Sodium Oleate and Polyoxyethylene Ether and the Application in the Low-Temperature Flotation of Scheelite at 283 K

The poor collecting performance of fatty acids at low temperatures is a problem in mineral flotation. In this study, the floatability of scheelite at 283 K was studied using sodium oleate and binary mixtures of sodium oleate and lauryl alcohol polyoxyethylene ether (MOA-9) as the collector, and interactions between the two surfactants at 283 K were investigated by the means of surface tension and steady state fluorescence measurements. The flotation experiment results show that the collecting performance of the mixed anonic/nonionic collector is stronger than that of single surfactant, and the best molar ratio of sodium oleate to MOA-9 is 10:1 at pH 10. The surface tension results show that the critical micelle concentration value of sodium oleate, MOA-9 and the binary solution is about 2 × 10^?4, 2.5 × 10^?4, and 1.2 × 10^?4 mol/l, respectively. Compared with single surfactants, the mixture exhibits better surface activities since it is more efficient at decreasing the air–water surface tension. The steady state fluorescence results indicate that the hydrophobic parts of MOA-9 molecules insert into the hydrophobic region of sodium oleate micelles to form larger and less compact mixed micelles. The decrease in zeta potential of scheelite treated with the mixed collector indicates the presence of MOA-9 can enhance the chemical adsorption of sodium oleate on the scheelite surface. Therefore, the mixed anonic/nonionic collector can enhance the flotation behavior of scheelite at 283 K.     

Experimental determination of the discharge flow coefficient at a doorway for fire induced flow in natural and mixed convection

The study is an experimental investigation of the discharge flow coefficient at a doorway‐type opening in the case of a fire in an enclosure open to atmosphere. Natural and mixed convection flows are considered with the use of mechanical ventilation. The discharge coefficient is defined as the ratio between the effective flow rate determined experimentally and a theoretical flow rate based on a Bernoulli approach. The effective mass flow rate is obtained from velocity field measured with stereoscopic particle image velocimetry technique. The theoretical flow rate is calculated from vertical temperature profiles measured from both sides of the doorway. Only inflow rate is considered for the calculation of the discharge coefficient. In natural convection mode, a C_D value of 0.54 ± 0.5 is obtained on a reduced‐scale opening (to be compared with 0.68 at large scale). In a mixed convection case, the discharge coefficient is much lower and reaches 0.26 ± 0.06. This study shows that the discharge coefficient C_D may vary significantly regarding the dimension of the opening and the flow conditions (natural and mixed convection). It illustrates the limits of considering a constant discharge coefficient when dealing with doorway flows in a confined and mechanically ventilated compartment. Copyright © 2014 John Wiley & Sons, Ltd.     

INFLUENCE OF PROCESS CONDITIONS ON THE DRYING RATE OF CASSAVA CHIPS IN A SOLAR SIMULATOR

ABSTRACT

Experiments were carried out in a solar simulator to study the influence of air temperature (25-40°C), air relative humidity (40-80%), air velocity (0.95-2.2 m/s), radiation intensity (0-916 W/m²), and loading density (10-30 kg/m²) on the drying rate of a bed of cassava chips (2×2×2 cm). Well-known thin-layer drying equations were fitted to the experimental data, and the empirical constants were used in a statistical analysis of the influence of process conditions on the drying rate. The air temperature, air velocity, radiation intensity, and loading density influenced the drying rate significantly (p=0.05). The effects of the air temperature and the radiation intensity were attributed to the temperature-dependent diffusion of moisture within the chips, while the effect of the air velocity was ascribed to the resistance to mass transfer at the air-chip interface. Equations were presented to express the empirical constants as functions of the process variables.