A Coupled Pressure-Based Co-Located Finite-Volume Solution Method for Natural-Convection Flows

A pressure-based coupled solution method based on a finite-volume discretization is presented. The method uses a cell-centered co-located variable arrangement on a nonorthogonal two-dimensional structured grid. The coupled algebraic analogs of the mass, momentum, and energy conservation equations for incompressible flow are solved. In addition to coupling the mass and momentum equations, the energy equation is coupled to the velocities via a Newton-Raphson linearization of the energy advection terms. The momentum equations are coupled to the energy equation via an implicit temperature in the Boussinesq approximation. The convergence behavior of the new method is demonstrated on the solution of steady, laminar natural convection in an annulus for Prandtl numbers of 0.707 and 13,050 at a Rayleigh number of 1 × 10⁶. A significant reduction in the number of iterations to convergence is obtained with the new method compared to a method with only velocity-to-temperature coupling and a method with energy and momentum decoupled. An improvement to the new method was obtained by using an approach that uses a delayed time-step increase and a modified face temperature value estimation.     

Simulated energy and exergy analyses of the charging of an oil-pebble bed thermal energy storage system for a solar cooker

Energy balance equations are used to model the solar energy capture (SEC) system and the thermal energy storage (TES) system of a proposed indirect solar cooker. An oil-pebble bed is used as the TES material. Energy and exergy analyses are carried out using two different charging methods to predict the performance of the TES system. The first method charges the TES system at a constant flowrate. In the second method, the flowrate is made variable to maintain a constant charging temperature. A Simulink block model is developed to solve the energy balance equations and to perform energy and exergy analyses. Simulation results using the two methods indicate a greater degree of thermal stratification and energy stored when using constant-temperature charging than when using constant-flowrate charging. There are greater initial energy and exergy rates for the constant-flowrate method when the solar radiation is low. Energy efficiencies using both methods are comparable whilst the constant-temperature method results in greater exergy efficiency at higher levels of the solar radiation. Parametric results showing the effect of each charging method on the energy and exergy efficiencies are also presented.     

A Novel Method of Evaluating Performance Characteristics of a Self-Excited Induction Generator

Self-excited induction generators (SEIG) are increasingly being used in isolated areas to generate electrical energy from both conventional and nonconventional energy sources. This paper proposes a novel method of evaluating the steady-state performance characteristics of a SEIG under various operating conditions. The criteria for the constant terminal voltage and the constant-stator-current operations are also derived and embedded into the system of equations. Unlike the previous methods of analysis, the problem is formulated in a simple and straightforward way without going through lengthy and tedious derivation for the coefficients of a set of nonlinear equations. The formulated problem is then solved using a numerical-based routine “fsolve” given in MATLAB. The effectiveness of the proposed method is then evaluated on a 220-V, 1.5-kW induction generator for various operating conditions. Some of the simulation results obtained by the proposed method are also compared with the corresponding experimental values and are found to be in very good agreement.      

Dynamic analysis of cracks under thermal shock considering thermoelasticity without energy dissipation

This article reports a study of a cracked finite isotropic medium under nonclassic thermal shock based on thermoelasticity without energy dissipation. The time history of stress intensity factors as well as the temperature distribution around the crack tip is analyzed thoroughly. The fully coupled governing equations are discretized in the space by employing the extended finite-element method. The Newmark method is used as the time integration scheme to solve discretized equations. The stress intensity factors, which are extracted using the interaction integral method, are compared with other theories of thermoelasticity. The results of a cracked plate under temperature shock demonstrate that the stress intensity factors based on thermoelasticity without energy dissipation are significantly greater than those based on classic and Lord–Shulman models, whereas the peaks of stress intensity factors under heat flux shock are nearly equal for various theories of thermoelasticity. Furthermore, a mobile cold region is created along slanted crack in the temperature distribution, in which the temperature is less than the applied thermal boundary condition.     

Heat transfer in a conical cylinder with porous medium

In this paper, numerical study of heat transfer in a conical annular cylinder fixed with saturated porous medium is presented. The heat transfer is assumed to take place by natural convection and radiation. The inner surface of conical cylinder is maintained at uniform wall temperature. The governing partial differential equations are non-dimensionalised using suitable non-dimensional parameters and then solved by using finite element method. The porous medium is divided using triangular elements with uneven element size. A computer software is used to solve the coupled momentum and energy equations in an iterative manner. The results are discussed for various values of geometric and physical parameters of porous medium with emphasis on cone angle of the cylinder. It is seen that the cone angle plays a vital role in heat transfer from the hot surface to porous medium.     

Performance Model for a Radiation Recuperator

A procedure has been developed to predict axial temperature distributions for the combustion gas. air, and walls of an annular radiation recuperator. It is based on using the zone method to treat radiation exchange between the combustion gas and its boundaries and on solving a system of nonlinear energy balance equations for the temperature distributions. The procedure may be used for a wide range of design and operating conditions, and parametric calculations have been performed to determine the effect of these conditions on recuperator performance.     

Analysis of combined mode heat transfer in a porous medium using the lattice Boltzmann method

ABSTRACT

Application of the lattice Boltzmann method (LBM) in solving a combined mode conduction, convection, and radiation heat transfer problem in a porous medium is extended. Consideration is given to a 1-D planar porous medium with a localized volumetric heat generation zone. Three particle distribution functions, one each for the solid temperature, the gas temperature, and the intensity of radiation, are simultaneously used to solve the gas- and the solid-phase energy equations. The volumetric radiation source term appears in the solid-phase energy equation, and it is also computed using the LBM. To check the accuracy of the LBM results, the same problem is also solved using the finite volume method (FVM). Effects of convective coupling, flow enthalpy, solid-phase conductivity, scattering albedo porosity, and emissivity on axial temperature distribution are studied and compared with the FVM results. Effects of flow enthalpy, solid-phase conductivity, and emissivity are also studied on radiative output. LBM results are in excellent agreement with those of the FVM.     

STREAMLINE UPWIND PERTOV-GALERKIN FINITE ELEMENT ANALYSIS OF THERMAL EFFECTS ON LOAD CARRYING CAPACITY IN SLIDER BEARINGS

Oil extraction using hot and cold water injection is studied numerically. The flow is mathematically modeled using two pressure equations for the oil and water phases and the energy equation. The resulting system of equations is strongly coupled and nonlinear. The energy equation is of the advection-diffusion type, and temperature propagates as a front through the porous region. The energy equation has been solved using an operator-splitting method. The suitability of this method for oil recovery problems has been independently studied. Results are presented for the amount of oil removed as a function of time. An increase in temperature is seen to improve oil recovery in general. However, for large temperature differences between the oil and the water phases, oil production is seen to fall over the time period considered in the present work.     

NATURAL CONVECTION AND RADIATION IN A SQUARE ENCLOSURE

Natural convection of a radiating fluid in a square enclosure is studied numerically. The coupled momentum, energy, and radiative transfer equations are solved by an iterative procedure. The solutions to the equation of radiative transfer are obtained by the discrete ordinates method using S4 and S8 quadratures. The method is based on control volume formulation and is fully compatible with the SIMPLER algorithm used to solve the momentum and energy equations. The effects of optical thickness and scattering on the flow and temperature fields and heat transfer rates are analyzed. The changes in the buoyant flow patterns and temperature distributions due to the presence of radiation in inclined or heat generating enclosures are also studied. Comparative results obtained by the P-I differential approximation are presented.     

Simultaneous estimation of four parameters in a combined-mode heat transfer in a 2D porous matrix with heat generation

This article reports a study on simultaneous estimation of four parameters for combined-mode conduction and radiation heat transfer in a 2D rectangular porous matrix with a localized volumetric heat generation source. Air flows at uniform velocity through the conducting and radiating porous matrix. In the heat generation zone, and its downstream, the gas temperature is higher than that of the solid, and in the upstream the reverse situation occurs. This temperature difference between gas and the solid results in heat transfer by convection between the two phases, and the analysis thus requires consideration of separate energy equations for the two phases. The solid being involved radiatively, the volumetric radiative source term, in the form of the divergence of radiative heat flux, appears only in the solid-phase energy equation. The two equations are coupled through the convective heat transfer term. Four parameters—scattering albedo, emissivity, solid conductivity, and heat transfer coefficient—are simultaneously estimated based on the solid and gas temperature distributions, and convective and radiative heat fluxes at the outer surface of the porous matrix. In both direct and inverse approaches, the energy equations are solved using the finite volume method. For a test case, determining the genetic algorithm is much more time-consuming than the global search algorithm; in other cases, parameter estimations are done using the global search algorithm. Parameters are found to be estimated accurately.     

Combined Mode Conduction and Radiation Heat Transfer in a Porous Medium and Estimation of the Optical Properties of the Porous Matrix

This article deals with the analysis of combined mode conduction and radiation heat transfer in a porous medium, and simultaneous estimation of the optical properties of the porous matrix. Simultaneous solution of the gas- and solid-phase energy equations encompasses local thermal nonequilibrium, while the convective heat exchange term couples the gas- and the solid-phase energy equations. A localized uniform volumetric heat generation zone is the source of heat transfer in the porous matrix. With volumetric radiative information needed in the solid-phase energy equation computed using the discrete transfer method, the solid- and gas-phase energy equations are simultaneously solved using the finite difference method. For a given set of boundary conditions and operating parameters, the computed temperature distribution serves as the exact temperature profile necessary in the estimation of parameters. In the estimation of parameters using inverse analysis, the objective function is minimized using the genetic algorithm. Effects of measurement error, number of generations, population size, crossover probability, and mutation probability are studied in regard to the accuracy of results and the computational time required. Reasonably accurate estimations of extinction coefficient, scattering albedo, and emissivity of the porous matrix are obtained.     

The boundary element method applied to forced convection heat problems

An integral equation formulation for steady flow of a viscous fluid is presented based on the boundary element method. The continuity, Navier–Stokes and energy equations are used for calculation of the flow and temperature fields. The governing differential equations, in terms of primitive variables, are derived using velocity–pressure–temperature parameters. The calculation of fundamental solutions and solutions tensor is shown. Applications to simple flow cases, such as driven cavity, forward facing step, deep cavity and channel are presented. Convergence difficulties are indicated, which have limited the applications to flows of low Reynolds numbers.     

An analysis of a packed bed latent heat thermal energy storage system using PCM capsules: Numerical investigation

This paper is aimed at analyzing the behavior of a packed bed latent heat thermal energy storage system. The packed bed is composed of spherical capsules filled with paraffin wax as PCM usable with a solar water heating system. The model developed in this study uses the fundamental equations similar to those of Schumann, except that the phase change phenomena of PCM inside the capsules are analyzed by using enthalpy method. The equations are numerically solved, and the results obtained are used for the thermal performance analysis of both charging and discharging processes. The effects of the inlet heat transfer fluid temperature (Stefan number), mass flow rate and phase change temperature range on the thermal performance of the capsules of various radii have been investigated. The results indicate that for the proper modeling of performance of the system the phase change temperature range of the PCM must be accurately known, and should be taken into account.     

Heat transfer in a twin-screw multiphase pump: Thermal modeling and one application in the petroleum industry

This paper presents a model of the heat transfer processes in the casing and rotors of a twin-screw multiphase pump. The model was developed to study the influence of temperature rise in the subsea multiphase pumping system-500 (SMPS), being developed by Petrobras, that operates with a twin-screw multiphase pump. The model is divided in three parts: heat transfer in the casing, in the rotor and energy balance of fluid. For the rotor, a helicoidal coordinate system is used to calculate the heat transfer. Axial symmetry is considered so it is possible to construct a two-dimensional model. The casing is modeled using an eccentric cylindrical coordinate system. In this case, the temperature gradient in axial direction is neglected and a two-dimensional calculation is carried out. The finite volume method is used to solve the transformed partial differential equations. With the two heat transfer models implemented, the fluid temperature is calculated using a simple energy balance that takes into account electric power, transferred heat and fluid internal energy. The implemented model was used to simulate thermal behavior of casing and rotors during loss of prime events faced by SMPS-500. Experimental data collected in pump trials are used as initial input parameters and the model calculates temperature evolution during the loss of prime events.     

Coupled Turbulent Flow,Heat, and Solute Transport in Continuous Casting Processes with an Electromagnetic Brake

ABSTRACT

This study describes the numerical modeling of coupled turbulent fluid flow, heat, and solute transport in a continuous slab caster with an electromagnetic brake (EMBr). Transport equations of total mass, momentum, energy, and species for a binary iron–carbon alloy system are solved using a continuum model. The turbulent effects are taken into account using the standard k–? equations, where coefficients are appropriately modified for phase change. The electromagnetic field is described by Maxwell equations. A finite-volume method is employed to solve the conservation equations associated with appropriate boundary conditions. The process variables considered are the casting speed, magnetic flux density, and carbon segregation. The effects of these process variables on the velocity, temperature, and solute distributions are reported and discussed.     

Bioconvection in a squeezing flow of a micropolar fluid in a horizontal channel

The bioconvection flow of an incompressible micropolar fluid containing microorganisms between two infinite stretchable parallel plates is considered. A mathematical model, with a fully coupled nonlinear system of equations describing the total mass, momentum, thermal energy, mass diffusion, and microorganisms is presented. The governing equations are reduced to a set of nonlinear ordinary differential equations with the help of suitable transformations. The resulting nonlinear ordinary differential equations are linearized using successive linearization method, and the resulting system of linear equations is solved using the Chebyshev collocation method. The detailed analysis illustrating the influences of various physical parameters, such as the micropolar coupling number, squeezing parameter, the bioconvection Schmidt number, Prandtl numbers, Lewis number, and bioconvection Peclet number on the velocity, microrotation, temperature, concentration and motile microorganism distributions, skin friction coefficient, Nusselt number, Sherwood number, and density number of motile microorganism, is examined. The influence of the squeezing parameter is to increase the dimensionless velocities and temperature and to decrease the local Nusselt number and local Sherwood number. The density number of motile microorganism is decreasing with squeezing parameter, bioconvection Lewis number, bioconvection Peclet number, and bioconvection Schmidt number.     

Frost deposition in a parallel plate channel under laminar flow conditions

The subject of this paper is a theoretical and experimental study of frost formation on cooled parallel plates in laminar forced convection. In the experiments time variation of the frost layer thickness was measured at several locations downstream along the test section which was positioned in an open-loop wind tunnel. The parameters varied were air velocity (Reynolds number), air temperature, air humidity ratio, and plate temperature. The process was simulated numerically using a two-dimensional transient model based on the conservation equations of mass, momentum, energy, and species. The physical domain of interest was divided into two subdomains, one for the moist air stream between the plates (gaseous phase), and one for the frost layer (solid phase). The two sets of governing equations were coupled by boundary conditions at the moving interface which required an iterative solution strategy. With this approach, the local distribution of temperature and porosity in the frost layer, which is nearly impossible to obtain in the experiments, could be predicted at any time. The results of the total heat and mass transfer rates as well as the development of the local and average frost thicknesses were compared with the experimental findings.     

Numerical investigation of thermo-bioconvection in a suspension of gravitactic microorganisms

This paper investigates the effect of heating or cooling from below on the development of gravitactic bioconvection in a square enclosure with stress free sidewalls. The governing equations are the Navier–Stokes equations with the Boussinesq approximation, the diffusion equation for the motile microorganism and the energy equation for the temperature. The control volume method is used to solve numerically the complete set of governing equations. It was found that the suspension is destabilized by heating from below and stabilized by cooling from below. A transition from a subcritical bifurcation to a supercritical bifurcation was observed in the case of heating from below when the thermal Rayleigh number was increased.     

Chebyshev Spectral Collocation Method for Unsteady Mhd Flow and Heat Transfer of a Dusty Fluid Between Parallel Plates

The unsteady magnetohydrodynamic flow of a dusty fluid and heat transfer between parallel plates in which the electrically conducting fluid has temperature-dependent viscosity is studied. Both the fluid and the dust particles are governed by the coupled set of momentum and energy equations. The Chebyshev spectral method in space and implicit backward difference in time procedure is presented, introducing physically Navier-slip conditions for both the fluid and dust particle velocities. The Hartmann number, viscosity parameter, and Navier-slip parameter influences on the flow and temperature are simulated.     

Simultaneous Estimation of Properties in a Combined Mode Conduction–Radiation Heat Transfer in a Porous Medium

Simultaneous estimation of thermophysical and optical properties such as the thermal conductivity, the scattering albedo, and the emissivity of a 1‐D planar porous matrix involving combined mode conduction and radiation heat transfer with heat generation is reported. Coupled energy equations for the gas and solid phase account for the nonlocal thermal equilibrium between the two phases. Performances of the genetic algorithm (GA) and the global search algorithm (GSA) in simultaneous estimation of three properties are analyzed. Both the GA and the GSA utilize a priori knowledge of the axial gas temperature distribution, and the magnitudes of the convective and the radiative heat fluxes at the outer surface of the porous matrix. With volumetric radiative information needed in the solid‐phase energy equation computed using the discrete transfer method, the two energy equations are simultaneously solved using the finite volume method. GSA provides better estimation, and computationally, it is much faster than the GA.