Saturated solar ponds: 1. Simulation procedure

The mass and energy balances on the upper convective zone, nonconvective zone, and lower convective zone of a saturated solar pond are written to yield a set of nonlinear partial differential equations. These are solved numerically to predict the thermal performance of the pond over a long period of time for various initial and boundary conditions. This model considers external parameters such as hourly variation of incident solar radiation, ambient temperature, air velocity, and relative humidity. Temperature and concentration dependence of density, thermal conductivity, specific heat, and mass diffusivity are taken into account. Heat transfer modes considered between the upper convective zone and the ambient are convection, evaporation, and radiation. Ground heat losses from the lower convective zone are also considered. This model is used to study the development of temperature and concentration profiles inside a saturated solar pond. This model can also be used to predict the long-term performance of a saturated solar pond for various heat extraction temperatures and rates.     

Transient performance of a two-dimensional salt gradient solar pond—A numerical study

Solar ponds have recently become an important source of energy that is used in many different applications. The technology of the solar pond is based on storing solar energy in salt-gradient stratified zones. Many experimental and numerical investigations concerning the optimum operational conditions and economical feasibility of solar ponds have been published in the last few decades. In the present study, a novel two-dimensional mathematical model that uses derived variables is developed and presented. This model utilizes vorticity, dilatation, density, temperature and concentration as dependent variables. The resulting governing partial differential equations are solved numerically in order to predict the transient performance of a solar pond in the two-dimensional domain. The boundary conditions are based on measured ambient and ground temperatures at Kuwait city. Based on the present formulation, a computer code has been developed to solve the problem at different operating conditions. The results are compared with the available experimental data and one-dimensional numerical results. Two-dimensionality effects are found to depend mainly on the aspect ratio of the pond. A parametric study is conducted to determine the optimum pond dimensions and operating conditions.     

Experimental inward solidification of initially superheated water in a cylinder

The subject of this investigation was the freezing of initially superheated pure water, at small Stefan numbers, contained in a horizontal cylinder. Three experiments were conducted and were compared to an analytical model based upon the heat balance integral method which considered one-dimensional (radial) conductive heat transfer with either zero or a finite amount of initial superheat contained in the water. The equations are solved numerically, employing the Runge-Kutta method for solving the first order governing differential equations. The solution yielded the radius of the phase change boundary as a function of time and the time for the liquid to reach the phase change temperature (0°C) when there is initial superheat. The analytical and experimental solidification time results obtained in this investigation compare very well. As in previous studies, the solidification time was found to be a linear function of Stefan number for zero initial superheat. The analytical results obtained for no initial superheat, though, differ somewhat from the results of some other investigations. Free convection affects appeared to be negligible.     

Performance of trombe walls and roof pond systems

This paper describes an analysis of the periodic heat transfer through thermal storage walls and roof pond systems subjected to periodic solar radiation and atmospheric air on one side and in contact with room air at constant temperature (corresponding to air-conditioned rooms) on the other. A one-dimensional heat conduction equation for temperature distribution in the walls and roof has been solved using the appropriate boundary conditions at the surfaces; explicit expressions for the periodic heat flux through storage walls and the roof have been derived. Numerical calculations for the periodic heat flux into the room have been made in order to assess the relative thermal performance of storage walls and roof pond systems in both winter and summer. It is found that a thermal storage mass wall is preferable for longer heat storage times while a water wall is suitable for rapid heat dissipation into the living space. For New Delhi, a roof pond system comprised of water-concrete-insulation, in ascending order of thickness, in the summer and in descending order of thickness in the winter, is found to be most desirable, whereas a combination with an ascending order of thickness is more appropriate for a typical cold climate like that of Boulder, Colorado, USA.     

Estimating heat losses in solar high-temperature heat accumulators based on a nonstationary three-layer model

A model and program for numerical research on the temperature and heat losses in solar high-temperature heat accumulators (HTHAs) are developed. The model is a one-dimensional three-layer system (insulation-accumulator-insulation) constructed on the basis of a one-dimensional nonstationary model of heat exchange with asymmetric boundary conditions and includes heat losses by radiation. The model can be also used for three-layer contacting bodies. It is shown that with respect to low-temperature heat accumulators in HTHAs, the materials best suited for heat accumulation are those with high volumetric heat capacities. A one-dimensional model with an accuracy of up to 10% can be used to estimate the characteristics of real volumetric 24-h high-temperature heat accumulators, and with an error of up to 30% for 48- to 72-h HTHAs.     

A RECTANGULAR SOLAR POND MODEL INCORPORATING EMPIRICAL FUNCTIONS FOR AIR AND SOIL TEMPERATURES

A novel theoretical model, capable of giving the temporal temperature variation at any point inside or outside a non-insulated rectangular solar pond at any time, is presented. Incorporating the finite difference approach, the model makes use of one- and two-dimensional heat balances written on discrete regions in the brine and in the soil adjacent to the pond. These simultaneous equations are solved for the local temperatures, using a computer program. Values of hourly averaged air temperature and daily averaged soil temperature for the site were used as input parameters, and empirical functions for the time-dependence of these variables were incorporated into the theoretical model. It was found necessary to use this level of detail of the meteorological data for reliable predictions on the solar ponds. The model results are compared with measured results on an actual solar pond built in Cukurova, Turkey. The modelled and experimental temperature profiles are found to be in a very good agreement. The results indicate that the thickness of the salt gradient region of a solar pond should not be less than 1.3 m. Heat losses form the pond side-walls was found not to effect the performance of solar ponds when the surface area is greater than 100 m².     

Transient analysis of energy storage in a thermally stratified water tank

A one-dimensional transient heat conduction model to describe the decay of the thermocline in a stratified water tank is presented. The problem is formulated as an initial boundary value problem and the resulting governing equations in the fluid and in the storage wall are solved numerically to obtain the temperature profiles in the wall and the fluid. The formulation considers the axial conduction of heat, both in the fluid and in the solid wall. The mixing parameters introduced in the boundary conditions at the top and bottom of the tank in the fluid region account for mixing due to inlet and outlet streams with the stored fluid. The model is applicable to the storage of both hot and chilled water. The model is validated with experimental data from the literature. The parameters that influence the operation of a stratified thermal energy storage for both heat and cool storage are examined. © 1998 John Wiley & Sons, Ltd.     

Transient two-dimensional model of frost formation on a fin-and-tube heat exchanger

In the paper, numerical and experimental analyses of heat and mass transfer during frost formation on a fin-and-tube heat exchanger have been presented. Modelling of the frost formation on cold surfaces placed in a humid air stream, requires a complex mathematical approach. A transient two-dimensional mathematical model of frost formation has been developed. The applied mathematical model has been defined using governing equations for the boundary layer that include air and frost sub-domains as well as a boundary condition on the air–frost interface. The mathematical model with initial and boundary conditions has been discretised according to the finite volume method and solved numerically using the SIMPLER algorithm for the velocity–pressure coupling. Results have shown that the frost layer formation significantly influences the heat transfer between air and fins. As a result of numerical calculations, time-wise frost thickness variations for different air humidities, temperatures and velocities have been presented. Using the developed mathematical model, the algorithm and the computer code, which have been experimentally validated, it is possible to predict a decrease of exchanged heat flux in the heat exchanger under frost growth conditions.     

Prediction of Coupled Heat and Moisture Transfer in Early-Age Massive Concrete Structures

The issues connected with the determination of thermal and moisture fields in early-age massive concrete are discussed here. The coupled equations, which govern the heat and mass transfer in early-age mass concrete as well as the initial and boundary conditions are presented. Next, the discretization in the space was made using the finite element method; the finite difference method was introduced for the discretization in time. As a result, the matrix form of the heat and moisture transfer equations was obtained. The proposed model was implemented in the original computer program TEMWIL, which can be applied to spatial massive structures in order to forecast the temperature and moisture distribution. Essential thermodiffusion coefficients for early-age concrete were also discussed. Finally, some computations concerning different curing conditions for the massive foundation slab were presented.     

Application of nonlinear programming methods for calculation of temperature profiles in parallel-flow multi-channel heat exchangers

This paper presents an algorithm combining non-linear programming techniques with methods of solving initial value problems to solve a non-linear boundary value problem describing the temperature field in a parallel-flow multi-channel heat exchanger. The method is illustrated by an example of determining temperature profiles in a four-channel heat exchanger. The calculations are performed with the aid of the computer program Mathcad^® 2000 Professional.     

METHODOLOGY TO GENERATE ACCURATE SOLUTIONS FOR VERIFICATION IN TRANSIENT THREE-DIMENSIONAL HEAT CONDUCTION

This article describes the development of accurate solutions for transient three-dimensional conductive heat transfer in Cartesian coordinates for a parallelepiped which is homogeneous and has constant thermal properties. The intended use of these solutions is for verification of numerical computer programs which are used for solving transient heat conduction problems. Verification is a process to ensure that a computer code is free of errors and accurately solves the mathematical equations. The exact solutions presented in this article can have any combination of boundary conditions of specified temperature, prescribed heat flux, or imposed convection coefficient and ambient temperature on the surfaces of the parallelepiped. Additionally, spatially uniform nonzero initial condition and internal energy generation are treated. The methodology to obtain the analytical solutions and sample calculations are presented.     

Simulation of the control of a salt gradient solar pond in the south of Tunisia

We are interested in the modeling and control of a salt gradient solar pond (SGSP) in the south of Tunisia. We developed a model of a closed cycle salt gradient solar pond (CCSGSP) that ensures successful year round operation. This model was used to study the response of the solar pond (SP) to various control techniques. It takes into account heat and salt diffusion within the pond and simulates the transient behavior of a SGSP. Furthermore, we investigated the dynamic process, which involves internal gradient stability, boundary behavior between the gradient zone and the convective zones. We thus incorporated the double diffusive processes into the SP model by using the one dimensional stability criterion produced by linear theory. The governing differential equations are solved numerically by using a control-volume scheme.The results show that successful operation of a SP requires three things: the maintenance of the storage zone temperature through heat extraction and brine injection, the use of surface washing to control the deepening of the upper mixed layer and a well designed initial salt stratification to prevent the formation of instability within the gradient. Using linear salinity profile as an initial condition, three round year simulations were run using average meteorological data with the result that adequate stability (Rρ2 throughout the gradient and Rρ10 at the interfaces) was maintained. Numerical results show also that 10–30% efficiency could have been reached if heat extraction is performed routinely especially when one considers that the storage temperature is within 40–80 °C. The model is validated against data taken from the operation of the UTEP SP. Close correlation between computed and measured data was obtained.     

Investigation on the dynamic responses of a generalized thermoelastic problem with variable properties and nonlocal effect

To explore the dynamic responses of generalized thermoelastic problems with nonlocal effect in microtemporal scale, a finite length thermoelastic rod subjected to a moving heat source is modeled and investigated in generalized thermoelasticity. The rod is fixed at both ends and its material properties are temperature-dependent. The corresponding governing equations are first given and then reduced into one-dimensional ones with temperature-dependent properties assumed to be functions of reference temperature. Subsequently, the equations after normalization are solved together with the initial conditions and the boundary conditions by means of Laplace transform and its numerical inversion. The distributions of the nondimensional temperature, displacement, and stress are obtained and illustrated graphically. In calculation, the effects of the velocity of the heat source, the temperature-dependent properties and the nonlocal parameter on the distributions of the considered variables are emphatically examined and discussed in detail. The results show that the velocity of the heat source and the variable properties markedly influence the variations of the considered variables, while the nonlocal parameter barely influences the variations of the nondimensional temperature, slightly influences the variations of the peak value of the nondimensional displacement and significantly influences the variations of the peak value of the nondimensional stress.     

Determination of skin temperature distribution and heat flux during simulated fires using Green's functions over finite-length scales

One of the current practices for measuring heat flux during flash fire testing, forest fires, and other industrial cases focuses on the use of semi-infinite models to predict the heat flux during exposure through surface temperature measurements on simulated skin sensors. For short time frames, these models can be shown to have acceptable accuracy. However, when considering longer time exposures at reduced heat fluxes, such as with firefighters in a forest fire, the accuracy of these models could be brought into question. A one-dimensional, finite length scale, transient heat conduction model was developed using a Green's function approach on a rectangular sensor. The model was developed using transient temperature boundary conditions to avoid the use of complicated radiation and convection conditions at each boundary. For comparison, a semi-infinite model utilizing the same boundary condition on the exposed face was solved using both the Laplace transform method and Green's function method. Experimental data was obtained during exposure to a cone calorimeter. All measurements were taken for a minimum duration of 2 min. This temperature data was used to develop appropriate curves for the boundary conditions and validate the analytical models. It was found that the temperature obtained from the one-dimensional transient heat conduction model based on Green's functions agreed well with the experimental results over longer exposure times, and with reduced error when compared with the semi-infinite model. This suggests that modeling the problem on a finite-length scale will produce more accurate or more conservative temperature and heat flux results over extended periods of exposure in high heat load applications.     

Experimental and numerical analysis of sodium-carbonate salt gradient solar-pond performance under simulated solar-radiation

The objective of this study is to investigate experimentally and theoretically whether sodium carbonate (Na₂CO₃) salt is suitable for establishing a salinity gradient in a salt-gradient solar-pond (SGSP). For this purpose, a small-scale prismatic solar-pond was constructed. Experiments were conducted in the laboratory under the incident radiation from two halogen-lamps acting as a solar simulator. Furthermore, a one-dimensional transient mathematical model that describes the heat and mass transfer behaviour of the SGSP was developed. The differential equations obtained were solved numerically using a finite-difference method. It was found from the experiments that the density gradient, achieved using sodium carbonate salt, can suppress convection from the bottom to the surface of the pond.     

Studies on membrane viscosity stabilized solar pond

In this nonsalt type of solar pond, the nonconvecting layer is composed of a viscous polymer solution partitioned by a number of transparent films. An advantage of partitioning is that a thinner polymer solution can be used and that the light transmittance increases. Results of experimental and theoretical investigations on the performance of this solar pond are summarized as follows:

1. 1. Ionized polyacrylamide solution was chosen as the thickener based on tests about solubility, viscosity, light transmittance and stability.

2. 2. The critical temperature difference for the onset of convection in the polymer layer (ΔT/L)_cr [°C/m] was given by the following formula based on the measurements in various thicknesses of the polymer layers (L) [m] and various concentrations (ζ) [%],

(ΔT/l)_cr=(55−185lnL)exp(4.66L^0.505lnζ

3. 3. An outdoor model pond, 200 × 150 cm surface and 100 cm depth, was constructed in Osaka. Four types of model ponds were tested, and the availability of membrane type with partition films was confirmed.

4. 4. The theoretical temperature rise of the pond using a one-dimensional model was calculated by solving the equations of the heat balance in the pond. As a result, the optimum values of thickness of polymer layer and number of films was determined

     

A phase change processor method for solving a one-dimensional phase change problem with convection boundary

A simple yet accurate iterative method for solving a one-dimensional phase change problem with convection boundary is described. The one-dimensional model takes into account the variation in the wall temperature along the direction of the flow as well as the sensible heat during preheating/pre-cooling of the phase change material (PCM). The mathematical derivation of convective boundary conditions has been integrated into a phase change processor (PCP) algorithm that solves the liquid fraction and temperature of the nodes. The algorithm is based on the heat balance at each node as it undergoes heating or cooling which inevitably involves phase change. The paper presents the model and its experimental validation.     

Spectral calculation of the thermal performance of a solar pond and comparison of the results with experiments

This paper deals with a method and the result of the spectroscopic calculation on heat balance of a salt-gradient solar pond under the conditions of spectral solar radiation. Furthermore, reflection of the ray incident upon the surface of the pond water, refraction of the rays within the salt-water layer and diffusion of salt in the pond water are considered. On the other hand, in order to make a clear mechanism of the heat collection and heat storage of the solar pond, we conducted an indoor experiment and a numerical analysis on a small scale model of the salt-gradient solar pond with 2 m² surface area and 1.6 m depth, under the incident rays from a Xe-lamp solar simulator. According to the above experimental analysis, we made a simulation model of thermal performance for a solar pond and carried out the calculation from the heat balance. We found that the simulation calculations correspond well to the experimental results, so that our thermal simulation model and method might be correct. We also did the thermal calculation by changing the incident rays from a Xe-lamp into natural ray (Moon’s spectrum) and Halogen lamp. As a result, it was found that the temperature distributions in the solar pond were notably different due to spectral characteristics of the incident ray. Therefore, the spectroscopic consideration for thermal performance of any solar pond is necessary to obtain a correct solution under the spectral incidence with special wavelength distributions.     

Thermal buckling and postbuckling responses of geometrically imperfect FG porous beams based on physical neutral plane

Abstract

Considering the third-order shear deformation and physical neutral plane theories, thermal postbuckling analysis for functionally graded (FG) porous beam are performed in this research. The cases of shear deformable functionally graded materials (FGM) beams with initial deflection and uniformly distributed porosity are considered. Geometrically imperfect FG porous beams with two different types of immovable boundary conditions as clamped–rolling and clamped–clamped are analyzed. Thermomechanical nonhomogeneous material properties of the FG porous beam are assumed to be temperature and position dependent. FG porous beams are subjected to different types of thermal loads as heat conduction and uniform temperature rise. Heat conduction equation is solved analytically using the polynomial series solution for the one-dimensional condition. The governing equilibrium equations are obtained by applying the virtual displacement principle. Assuming von Kármán type of geometrical nonlinearity, equilibrium equations are nonlinear and are solved using an analytical method. A two-step perturbation technique is used to obtain the thermal buckling and postbuckling responses of FG porous beams. The numerical results are compared with the case of perfect FGM Timoshenko beams without porosity distribution based on the midplane formulation. Parametric studies of the perfect/imperfect FG porous beams for two types of thermal loading and boundary conditions are provided.     

6110A柴油机绝热性能的预测

本文建立了计算直喷式柴油机气缸内热力过程、气缸周壁传热和气缸盖排气道传热的数学模型,并编制了计算机程序。采用解析法处理气缸周壁传热,特别是应用二维解析法建立活塞顶传热,将气缸周璧传热计算与柴油机气缸内热力过程计算相结合,互为边界条件,因此能模拟计算绝热机工作过程。在几种气缸周壁绝热层布置形式下,以6110A柴油机为例进行了非增压、增压和增压带动力涡轮在标定工况下的模拟计算,并分析了绝热对发动机性能,燃烧过程以及热平衡的影响。为研制绝热发动机提供了预测数据。