Double-Diffusive Natural Convection with Cross-Diffusion Effects in an Anisotropic Porous Enclosure Using ISPH Method

A study on heat and mass transfer behaviour on an anisotropic porous medium embedded in square cavity/annulus is conducted using Incompressibe Smoothed Particle Hydrodynamics (ISPH) method. In the case of square cavity, the left wall has hot temperature Th and mass Ch and the right wall has cool temperature Tc and mass Cc and both of the top and bottom walls are adiabatic. While in the case of square annulus, the inner surface wall is considered to have a cool temperature Tc and mass Cc while the outer surface is exposed to a hot temperature Th and mass Ch. The governing partial differential equations are transformed to non-dimensional governing equations and are solved using ISPH method. The results present the influences of the Dufour and Soret effects on the heat and mass transfer. The effects of various physical parameters such as Darcy parameter, permeability ratio, inclination angle of permeability and Rayleigh numbers on the temperature and concentration profiles together with the local Nusselt and Sherwood numbers are presented graphically. The results from the current ISPH method are well validated and have favorable comparisons with previously published results and solutions by the finite volume method

A Stabilized Incompressible SPH Method by Relaxing the Density Invariance Condition

A stabilized Incompressible Smoothed Particle Hydrodynamics (ISPH) is proposed to simulate free surface flow problems. In the ISPH, pressure is evaluated by solving pressure Poisson equation using a semi-implicit algorithm based on the projection method. Even if the pressure is evaluated implicitly, the unrealistic pressure fluctuations cannot be eliminated. In order to overcome this problem, there are several improvements. One is small compressibility approach, and the other is introduction of two kinds of pressure Poisson equation related to velocity divergence-free and density invariance conditions, respectively. In this paper, a stabilized formulation, which was originally proposed in the framework of Moving Particle Semi-implicit (MPS) method, is applied to ISPH in order to relax the density invariance condition. This formulation leads to a new pressure Poisson equation with a relaxation coefficient, which can be estimated by a preanalysis calculation. The efficiency of the proposed formulation is tested by a couple of numerical examples of dam-breaking problem, and its effects are discussed by using several resolution models with different particle initial distances. Also, the effect of eddy viscosity is briefly discussed in this paper

Heat and mass transport of nano-encapsulated phase change materials in a complex cavity: An artificial neural network coupled with incompressible smoothed particle hydrodynamics simulations

This work simulates thermo-diffusion and diffusion-thermo on heat, mass transfer, and fluid flow of nano-encapsulated phase change materials (NEPCM) within a complex cavity. It is a novel study in handling the heat/mass transfer inside a highly complicated shape saturated by a partial layer porous medium. In addition, an artificial neural network (ANN) model is used in conjunction with the incompressible smoothed particle hydrodynamics (ISPH) simulation to forecast the mean Nusselt and Sherwood numbers ($\stackrel{-}{Nu}$ and $\stackrel{-}{Sh}$). Heat and mass transfer, as well as thermo-diffusion effects, are useful in a variety of applications, including chemical engineering, material processing, and multifunctional heat exchangers. The ISPH method is used to solve the system of governing equations for the heat and mass transfer inside a complex cavity. The scales of pertinent parameters are fusion temperature ${\theta }_{f} = 0.05-0.95$, Rayleigh number $Ra = {10}^{3}-{10}^{6}$, buoyancy ratio parameter $N = -2-1$, Darcy number $Da = {10}^{-2}-{10}^{-5}$, Lewis number $Le = 1-20$, Dufour number $Du = 0-0.25$, and Soret number $Sr = 0-0.8$. Alterations of Rayleigh number are effective in enhancing the intensity of heat and mass transfer and velocity field of NEPCM within a complex cavity. The high complexity of a closed domain reduced the influences of Soret-Dufour numbers on heat and mass transfer especially at the steady state. The fusion temperature works well in adjusting the intensity and location of a heat capacity ratio inside a complex cavity. The presence of a porous layer in a cavity's center decreases the velocity field within a complex cavity at a reduction in Darcy number. The goal values of $\stackrel{-}{Nu}$ and $\stackrel{-}{Sh}$ for each data point are compared to those estimated by the ANN model. It is discovered that the ANN model's $\stackrel{-}{Nu}$ and $\stackrel{-}{Sh}$ values correspond completely with the target values. The exact harmony of the ANN model prediction values with the target values demonstrates that the developed ANN model can forecast the $\stackrel{-}{Nu}$ and $\stackrel{-}{Sh}$ values precisely

Thermal radiation impacts on natural convection of NEPCM in a porous annulus between two horizontal wavy cavities

In this work, the simulations of fractional-time derivative systems of natural convection in a porous annulus suspended by NEPCM under the magnetic field and thermal radiation influences are conducted by the ISPH method. The annulus is constructed amongst the exterior horizontal wavy cavity and interior horizontal wavy blockage. Here, the novelty is appearing in simulating the powers of a magnetic field on natural convection in a novel shape of an annulus between two horizontal wavy shapes. The outer vertical sides are kept at Th and the flat sides are adiabatic. The inner wavy blockage is kept at Tc with zero velocities. The fractional time-derivative, nanoparticle parameter, dimensionless time parameter, Darcy parameter, Hartmann number, thermal radiation parameter, Rayleigh number effects on the heat transfer within an annulus are examined. The outcomes revealed that the contributions of the time-fractional derivative are appearing well at the initial time step. Increasing nanoparticle concentration to 5% shrinks the nanofluid flow. The heat capacity is affected by the differences in the thermal radiation parameter. The thermal radiation parameter is enhancing the mean Nusselt number and diminishes the nanofluid flow in an annulus. The extra Rayleigh number boosts the temperature strength and nanofluid velocity within an annulus

Double-diffusive natural convection in an enclosure filled with nanofluid using ISPH method

The double-diffusive natural convection in an enclosure filled with nanofluid is studied using ISPH method. The model used for the nanofluid incorporates the effects of Brownian motion and thermophoresis. In addition the thermal energy equations include regular diffusion and cross-diffusion terms. In ISPH algorithm, a semi implicit velocity correction procedure is utilized and the pressure is implicitly evaluated by solving pressure Poisson equation. The results are presented with flow configurations, isotherms, concentration and nanoparticle volume fraction contours and average Nusselt and Sherwood numbers for different cases. The results from this investigation are well validated and have favorable comparisons with previously published results. It is found that, among all cases, a good natural convection can be obtained by considering the double diffusive case. An increase in Soret number accompanied by a decrease in Dufour number results in an increase in average Nusselt number and a decrease in average Sherwood number

ISPH analysis of thermosolutal convection from an embedded I-Shaped inside an inclined infinite-shaped enclosure suspended by NEPCM

The present work introduces numerical simulations based on an incompressible scheme of smoothed particle hydrodynamics (ISPH) method for the thermosolutal convection from an inner I-shaped inside an infinite-shaped cavity embedded by nano-encapsulated phase change materials (NEPCMs). An infinite-shaped enclosure is occupied by a nanofluid and a porous medium. In this work, the heat capacity of a core and shell is used for the overall heat capacity of encapsulated nanoparticles. An inner I-shaped is embedded inside a center of an enclosure and it carries Th and Ch. The simulations are performed for different values of a length of an inner I-shaped L2(0.4≤L2≤1.5), a Stefan parameter Ste(0.2≤Ste≤0.9), a fusion temperature θf(0.05≤θf≤0.95), Darcy parameter Da(10−2≤Da≤10−5), an inclination angle γ (0≤γ≤π/2) and Rayleigh number Ra(103≤Ra≤106). The numerical simulations showed that a fusion temperature θf adjust the situations of a melting solidification zone. Further, the intensity of a melting solidification zone is adjusted by a Stefan parameter. Augmentations of an inner I-shaped length and Rayleigh number are powering buoyancy forces and thus the flow speed, and heat & mass transport are enhanced inside an infinite-shaped cavity. Mean Nusselt and Sherwood numbers are enhanced as I-shaped length and Rayleigh number are powered