MESHLESS EFG METHOD IN THREE-DIMENSIONAL HEAT TRANSFER PROBLEMS: A NUMERICAL COMPARISON,COST AND ERROR ANALYSIS

The present analysis deals with the numerical solution of three-dimensional heat transfer problems using a meshless element-free Galerkin (EFG) method. The EFG method utilizes the moving least-square (MLS) approximation to approximate the unknown function of temperature T(x) with T ^h (x). The approximants are constructed by using a weight function, a monomial basis, and a set of coefficients that depends on position. A variational method is used to obtain the discrete equations. The essential boundary conditions are enforced using the Lagrange multiplier method. MATLAB codes have been developed to obtain the numerical results for a model problem of three-dimensional heat transfer in orthotropic materials using different EFG weight functions. Three new weight functions, exponential, elliptical, and cosine, are proposed. A numerical comparison is made among the results obtained using proposed (exponential, elliptical, and cosine) and existing (quadratic) weight functions for a model problem. L₂ error is calculated for the proposed and existing EFG weight functions using 125 nodes. FORTRAN software has also been developed and executed on a PARAM 10000 supercomputing machine to obtain the computational cost of the EFG method. The computational cost of the EFG method is obtained for different orders of Gaussian quadrature and for different values of scaling parameter. The effect of scaling parameter on EFG results (temperature values) is also discussed in detail. The effectiveness of EFG method is shown by comparing the EFG results with those obtained by the finite-element method.     

Numerical simulation and optimization of turbulent fluids in a three-dimensional angled ribbed channel

ABSTRACT

In this study, numerical simulations of turbulent steam forced convection in a three-dimensional angled ribbed channel with constant heat flux are investigated. The elliptical, coupled, steady-state, and three-dimensional governing partial differential equations for turbulent forced convection are solved numerically using the finite volume approach. The standard k?? turbulence model is applied to solve the turbulent governing equations. Numerical results are first validated using reference’s data reported in the literature and the maximum discrepancy between them is 3%. The effects of Reynolds number, angled rib height ratio, angled rib pitch ratio, and rib angle on the friction factor ratio and averaged Nusselt number are investigated. Numerical results show that the increase in heat transfer is accompanied by an increase in the friction factor ratio of the steam, the minimum friction factor ratio occurs at θ = 30^○ and the maximum friction factor ratio is found at θ = 60^○. In addition, after the validation of the numerical results, the numerical optimization of this problem is also presented by using the response surface methodology coupled with computational fluid dynamic method.     

GDQ Method for Natural Convection in a Cubic Cavity Using Velocity–Vorticity Formulation

ABSTRACT

Natural convection in a differentially heated cubic enclosure is studied by solving the velocity–vorticity form of the Navier–Stokes equations by a generalized differential quadrature (GDQ) method. The governing equations in the form of velocity Poisson equations, vorticity transport equations, and energy equation are solved using a coupled numerical scheme via a single global matrix for velocities, vorticities, and temperature. Vorticity and velocity coupling at the solid boundaries is enforced through a higher-order approximation by the GDQ method, thus assuring accurate satisfaction of the continuity equation. Nusselt numbers computed for Ra = 10³, 10⁴, 10⁵, and 10⁶ show good agreement with the benchmark results. A mesh independence study indicates that the present numerical procedure requires much coarse mesh compared to other numerical schemes to produce the benchmark solutions of the flow and heat transfer problems.     

GDQ METHOD FOR NATURAL CONVECTION IN A SQUARE CAVITY USING VELOCITY–VORTICITY FORMULATION

ABSTRACT

This article describes a compact numerical algorithm based on the generalized differential quadrature (GDQ) method for the numerical analysis of natural convection in a differentially heated square cavity. The velocity–vorticity form of the Navier–Stokes equations and energy equation are used to represent the mass, momentum, and energy conservations of the fluid medium in the cavity. The GDQ form of the governing equations and the vorticity definition at the boundaries are solved by a coupled solution algorithm using a global matrix scheme for all the field variables. The vorticity values at the boundary are correctly imposed using the GDQ method, which approximates a given space derivative with higher-order accuracy compared to the existing schemes based on Taylor's series expansion. This has assured a divergence-free solution for the flow field by satisfying the continuity constraint, though the pressure term is not used directly in the present formulation. The proposed algorithm is validated for a lid-driven cavity flow for Reynolds number Re = 100, 400, and 1,000, and the predicted velocity profiles are in excellent agreement with the benchmark solutions. The algorithm is then used to compute the average Nusselt number and flow parameters for natural convection in a square cavity for Rayleigh number Ra = 10³, 10⁴, 10⁵, and 10⁶. These results are in better agreement with the benchmark solutions than the results obtained by other numerical schemes, which used much finer grids compared to the present scheme.     

Numerical simulation and sensitivity analysis of effective parameters on natural convection and entropy generation in a wavy surface cavity filled with a nanofluid using RSM

ABSTRACT

In this work, a 2-D numerical investigation and a sensitivity analysis have been done on the natural convection heat transfer in a wavy surface cavity filled with a nanofluid. For this purpose, the effects of three parameters, the Rayleigh number (10³?≤Ra?≤?10⁵), nanoparticles volume fraction (0.00 ≤??≤?0.04), and the shape of the nanoparticles (spherical, blade, and cylindrical), are studied. Discretization of the governing equations is performed using a finite volume method (FVM) and solved with the SIMPLE algorithm. The effective parameters analysis is processed utilizing the Response Surface Methodology (RSM). Comparison with previously published work is performed and the results are found to be in good agreement. The results showed that increasing the Rayleigh number and ? increases the mean Nusselt number and the total entropy generation. Also, the nanofluids with spherical- and cylindrical-shaped nanoparticles have the highest and lowest Nusselt numbers and entropy generations, respectively. The sensitivity of the mean Nusselt number and entropy generation ratio to Ra and ? is found to be positive, whereas it is predicted to be negative to nanoparticles shape.     

SIMULATION OF NATURAL CONVECTION IN ECCENTRIC ANNULI BETWEEN A SQUARE OUTER CYLINDER AND A CIRCULAR INNER CYLINDER USING LOCAL MQ-DQ METHOD

ABSTRACT

A numerical study of the free convective flow in a horizontal eccentric annulus between a square outer cylinder and a heated circular inner cylinder is undertaken by using a local multiquadrics-based differential quadrature (MQ-DQ) method. The method combines the advantages of the conventional differential quadrature (DQ) method for derivative approximation and the mesh-free nature of the multiquadrics (MQ) method. It is capable of simulating practical problems with much larger discretization systems compared to the traditional global MQ method. In this article, it is shown the local MQ-DQ method can accurately simulate the natural-convection problem at large Rayleigh number (10⁶). Numerical simulations are also carried out to study the effect of geometric parameters, such as eccentricities and angular positions, on the mean and local heat transfer rates.     

Point defect diagrams for pure and doped titanium (IV) oxide TiO2−δ in temperature range of 1073–1573 K

Abstract

The point defect diagrams in non-stoichiometric titanium (IV) oxide TiO_2?δ, pure and doped with M³⁺ and M⁵⁺ metal ions, are presented in this work. A new method was used for the calculations of the diagrams. This method is based on derived relations between standard Gibbs energy of formation of oxygen vacancies and interstitial cations, intrinsic ionic and electronic defects and oxygen pressure at which the oxide has stoichiometric composition, and it uses experimental values of deviation from the stoichiometry. The calculations were performed using the results of studies obtained by many authors in the temperature range of 1073–1573 K.     

HYPERBOLIC STEFAN PROBLEM WITH APPLIED SURFACE HEAT FLUX AND TEMPERATURE-DEPENDENT THERMAL CONDUCTIVITY

Abstract

The hyperbolic Stefan problem with an applied surface heat flux and temperature-dependent thermal conductivity is solved numerically for a semi-infinite slab using Mac-Cormack's predictor-corrector method. Solutions are presented for cases where the melt temperature is both below and above the instantaneous jump in surface temperature at time t = O⁺. The interface condition, surface temperature, and internal temperatures are presented for different Stefan numbers and melt temperatures, as well as thermal conductivity both increasing and decreasing with temperature. The results obtained from the hyperbolic solution are compared with those obtained from the parabolic solution.     

DEFECT CORRECTION WITH A FULLY COUPLED INEXACT NEWTON METHOD

Abstract

We examine the characteristics of a fully coupled inexact Newton method using defect correction to obtain high-order solutions for two problems: natural convection in a square cavity and mixed-convection flow over a backward step. Newton's method produces a linearized system with a Jacobian matrix and a residual vector, each of which can be formed using different discrete operators. Solution accuracy depends on the discretization used for the residuals. Defect correction employs low-order operators for the Jacobian but high-order operators for the residuals. We employ an O(h³) convection operator in the residual vector and upwinding in the Jacobian. We find that defect correction is an efficient and effective way to achieve high-order solutions.     

Double-Diffusive Natural Convection in a Mixture-Filled Cavity with Walls' Opposite Temperatures and Concentrations

ABSTRACT

This paper deals with natural convection flows evolving inside an ended and differentially heated cavity, which is filled either with an air or an air–CO₂ mixture. The investigation was conducted through the laminar regime to analyze buoyancy ratio changes' effect on heat and mass transfers both in aiding and opposing flows. The thermal Rayleigh number was varied from 10³ to 10⁷. Streamlines, isotherms, iso-concentrations, and local and average Nusselt and Sherwood numbers are provided to demonstrate the convective flow induced. The governing equations are solved by finite volume method using SIMPLEC algorithm to handle the pressure–velocity coupling. The buoyancy ratio effect on dynamic, thermal, and mass fields is noteworthy, exhibiting both the competition between thermosolutal forces and fields' stratification. From the results, it turned out that, in general, when the buoyancy ratio is: (1) positive, thermosolutal buoyancy forces are cooperative, (2) nil, solutal buoyancy forces are weak and the flow is merely thermoconvective, (3) negative and greater than ?1, buoyancy effects are competing and thermal convection dominates, (4) ?1, buoyancy effects are canceled and heat and mass transfers are driven only by diffusion, and (5) less than ?1, buoyancy forces compete with a dominant solutal convection.     

Optimization of substrates for Bioelectricity production by Ochrobactrum pseudintermedium KF026284 in a single chambered microbial fuel cell

A new strain of bacterium Ochrobactrum pseudintermedium KF026284 was isolated from a single chambered microbial fuel cell operated with rumen fluid. The bacterium produced maximum power density of 114 mW/m² (0.7 V, 0.6 mA) when nutrient broth was used as the growth medium. The optimization of electricity generation by O. pseudintermedium KF026284 was carried out using various substrates like cellulose, cellobiose, starch, sucrose, and glucose. The bacterium when fed with cellobiose showed an appreciable and sustainable electricity generation with a power density of 150 mW/m² from the 5th day and a maximum power density of 247 mW/m² on the 11th day.     

Numerical investigation of unsteady natural convection heat transfer and entropy generation from a pair of cylinders in a porous enclosure

Abstract

The present study analyses numerically the unsteady heat transfer and entropy generation characteristics in a two-dimensional porous enclosure embedded with two heated circular cylinders at different positions at the vertical mid-plane. The heat transfer is primarily due to conduction for lower values of Darcy number (10^?4), while heat transfer by convection becomes significant for higher values of Darcy number (10^?3, 10^?2). Contrasting features are observed in the variation of time-average Nusselt number with interspacing distance. The major contributor of irreversibility is the entropy generation due to heat transfer for lower values of Darcy number, while for larger values of Darcy number, it varies with Rayleigh number.     

CZTS based thin film solar cells: a status review

Abstract

Today’s thin film photovoltaic technologies comprising CuInS₂ (CIS), CuInGaSe₂ (CIGS) and CdTe rely on elements that are costly and rare in the earth’s crust (e.g. In, Ga, Te) and are toxic (e.g. Cd). Hence, in future cost reduction and increased production, using abundantly available non-toxic elements, seem to be the main issues. Cu₂ZnSnS₄ (CZTS), having the kesterite structure, is one of the most promising absorber layer candidates for low cost thin film solar cells, because of its suitable direct band gap between 1·4 and 1·5 eV and large absorption coefficient, over 10⁴ cm^?1. Also it is composed of earth abundant and non-toxic elements, promising price reductions in future. Recently, research in this area has gained momentum due to the desirability of producing Ga, In and Cd free absorber layers and the potential to obtain new insights. Hence, a review of recent literature is urgently warranted. The CZTS progress and present status of CZTS thin film solar cells has been reviewed, with the hope of identifying new paths for productive research.     

Homogeneous precipitation synthesis and thermoelectric properties of Ca2Co2O5 ceramics

Abstract

Homogeneous precipitation method was applied to synthesise Ca₂Co₂O₅ powders using calcium nitrate, cobalt nitrate and urea as raw materials. Uniform plate-like Ca₂Co₂O₅ powders with an average grain size of 1 μm can be obtained by calcining the precursor for 8 h at 1073 K in the air. The Ca₂Co₂O₅ ceramics were gained after sintering for 4 h at 1083 K using uniaxial pressure moulding and then sintering technique. The thermoelectric properties of ceramic samples were measured from 303 to 973 K, and the result shows that the electrical conductivity, Seebeck coefficient, thermal conductivity and figure of merit of the sample are 2236·85 S m^?1, 175·95 μV K^?1, 1·01 W m^?1 K^?1 and 0·69 at 973 K respectively.     

Controlled synthesis of MnO2/CNT nanocomposites for supercapacitor applications

Abstract

In this work, manganese oxide (MnO₂)/carbon nanotube (CNT) nanocomposites have been prepared as electrode materials for supercapacitor applications. The materials were synthesised using a traditional and facile chemical deposition method. Effects from CNT amounts, synthesis time, pH value and CNT treatment using nitric acid have been thoroughly investigated. It was found that the sample synthesised for 3 h at pH 5 had achieved the best performance with a specific capacitance of 115 F g^?1 at a discharge rate of 0·5 A g^?1. A capacitance retention of 95% after 1000 cycles has been observed for the sample synthesised in the neutral environment. We believe that findings from this work will pave a road for nanostructured MnO₂/CNT composites with better performance in energy storage applications.     

Free convection enhancement in an annulus between horizontal confocal elliptical cylinders using hybrid nanofluids

ABSTRACT

In the present paper, natural convection in an annulus between two confocal elliptic cylinders filled with a Cu-Al₂O₃/water hybrid nanofluid is investigated numerically. The inner cylinder is heated at a constant surface temperature while the outer wall is isothermally cooled. The basic equations are formulated in elliptic coordinates and developed in terms of the vorticity-stream function formulation using the dimensionless form for 2D, laminar and incompressible flow under steady-state condition. The governing equations are discretized using the finite volume method and solved by an in-house FORTRAN code. Numerical simulations are performed for various volume fractions of nanoparticles (0?≤???≤?0.12) and Rayleigh numbers (10³?≤?Ra?≤?3?×?10⁵). The eccentricity of the inner and outer ellipses and the angle of orientation are fixed at e₁?=?0.9, e₂?=?0.6 and γ?=?0° respectively. It is found that employing a Cu-Al₂O₃/water hybrid nanofluid is more efficient in heat transfer rate compared to the similar Al₂O₃/water nanofluid.     

Numerical Study of Effects of Inclination on Buoyancy-Induced Flow Oscillation in a Lid-Driven Arc-Shaped Cavity

ABSTRACT

Numerical predictions of the inclination effects on the buoyancy-induced oscillatory flow in a lid-driven arc-shaped cavity are presented in this report. Governing equations in terms of the stream function–vorticity formulation expressing the laws of conservation in mass, momentum, and energy are solved by the finite-volume method in curvilinear coordinates. Computations have been performed for various combinations of physical parameters. The inclination angle of the cavity (θ) is varied from 0° to 15°, the Reynolds number (Re) is assigned to be 100, 200, and 500, and the Grashof number (Gr) ranges from 3 × 10⁵ to 1 × 10⁷, while the Prandtl number is fixed at 0.71 for air. In these above ranges of the parameters, two kinds of oscillatory flow pattern have been observed, namely, the traversing-periodic and the half-periodic patterns. Attention has been focused on the effects of the inclination effects on the occurrence of these two different oscillatory flow patterns. Meanwhile, periodic variation in the mixed-convection heat transfer accompanying the oscillatory flow field has also been studied, and the results for the local and the overall Nusselt numbers are presented.     

Measurement of a Heated Surface Temperature Using a High-Speed Infrared Camera During Critical Heat Flux Enhancement by a Honeycomb Porous Plate in a Saturated Pool Boiling of a Nanofluid

Abstract

This article presents an experimental study to investigate the critical heat flux (CHF) enhancement mechanism using honeycomb porous plate (HPP). The CHF enhanced significantly with combination of the HPP and nanofluid, up to 3.2?MW/m² at maximum compared to a plain surface, 1.0?MW/m². The mechanism by which the CHF is improved in this system was elucidated by measuring the temperature of the heated surface using an indium tin oxide (ITO) heater and a high-speed infrared camera. The pool boiling experiment of water and nanofluid is performed under saturated temperature and atmospheric pressure conditions. The CHF values obtained using ITO heater is in good agreement with a conventional CHF pool boiling experiment with HPP attachment. High-speed infrared camera is analyzed to understand the behavior of local temperature at various locations over time. It is observed at the burnout condition, the highest average temperature is occurred at the intersection of HPP wall. Moreover, the reversible dry spots were initiated in the cell part of the HPP, and small dry spots coalesced into a growth of large irreversible dryout that leads to burnout. Further CHF enhancement could be realized if the initiation of the dryout region could be suppressed.     

Synthesis and Properties of a Novel Fluorescent Surfactant

Abstract

A novel kind of fluorescent surfactant by having a hydroxyl coumarin group and a sulfonate group attached to the same alkyl chain has been synthesized. The determined critical micelle concentration (CMC) values and surface tensions (γ_cmc) at CMC for the fluorescent surfactant are in good agreement with the conventional surfactants. Ultraviolet absorption and fluorescence parameters of the product against the variation of the pH values are studied. The results indicate that the absorption and fluorescence intensity attribute to the interaction between the product and OH^?. These properties make them very promising for applications of determining the interface properties.     

Estimation of Groundwater Aquifer Formation-strength Parameters from Geophysical Well Logs: The Southwestern Coastal Area of Yun-Lin,Taiwan

Abstract

The purpose of this study is to estimate groundwater aquifer formation-strength parameters including shear modulus, bulk modulus, Poisson's ratio, and Young's modulus by using geophysical well logs. A new dispersed-shale index equation was developed by using the natural gamma-ray log and the compensated formation density log to solve a confusing problem of the compaction factor setting in the calculation of sonic porosity for an unconsolidated groundwater aquifer. A useful Poisson's ratio estimation method was employed to estimate groundwater aquifer formation-strength parameters when shear-wave transit time data is lacking in groundwater wells. Hydrogeologic parameters are characterized in estimating formation-strength parameters. Five wells in the southwestern coastal area of Yun-Lin, Taiwan, were logged, and four shallow aquifers were identified from log-derived hydrogeologic characteristics less than 200 m in depth. The formation-strength parameters for aquifers between 310 and 500 m in depth were calculated in two wells because complete formation density and compressional-wave transit time data were available. The results of the aquifer's formation-strength parameters demonstrate that both shear modulus, ranging from 0.15 to 0.42 * 10⁶ psi, and Young's modulus, ranging from 0.40 to 1.07 * 10⁶ psi, increase with depth, whereas bulk compressibility, ranging from 1.2 to 2.6 * 10^?6 psi^?1, decreases with increasing depth.