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The purpose of this paper is to improve the 2D incompressible smoothed particle hydrodynamics (ISPH) method by working on the wall boundary conditions in ISPH method. Here, two different wall boundary conditions in ISPH method including dummy wall particles and analytical kernel renormalization wall boundary conditions have been discussed in details.

The ISPH algorithm based on the projection method with a divergence velocity condition with improved boundary conditions has been adapted.

The authors tested the current ISPH method with the improved boundary conditions by a lid-driven cavity for different Reynolds number 100 ≤ Re ≤ 1,000. The results are well validated with the benchmark problems.

In the case of dummy wall boundary particles, the homogeneous Newman boundary condition was applied in solving the linear systems of pressure Poisson equation. In the case of renormalization wall boundary conditions, the authors analytically computed the renormalization factor and its gradient based on a quintic kernel function.

The purpose of this study is to simulate the natural convection of a heated square shape embedded in a circular enclosure filled with nanofluid using an incompressible smoothed particle hydrodynamics (ISPH) method.

In the ISPH method, the evaluated pressure was stabilized by using a modified source term in solving the pressure Poisson equation. The divergence of the velocity was corrected, and the dummy particles were used to treat the rigid boundary. Dummy wall particles were initially settled in outer layers of the circular enclosure for preventing particle penetration and reducing the error of truncated kernel. The circular enclosure was partially filled with a porous medium near to the outer region. The single-phase model was used for the nanofluid, and the Brinkman–Forchheimer-extended Darcy model was used for the porous medium. Dummy wall particles were initially settled in outer layers of circular enclosure for preventing particle penetration and reducing error from the truncated kernel on the boundary.

The length of the inner square shape plays an important role in enhancing the heat transfer and reducing the fluid flow inside a circular enclosure. The porous layer represents a resistance force for the fluid flow and heat transfer, and, consequently, the velocity field and temperature distributions are reduced at the outer region of the circular cylinder. Then, the radius of the inner square shape, Darcy parameter and radius of the porous layer were considered the main factors for controlling the fluid flow and heat transfer inside a circular enclosure. The average Nusselt number decreases as the inner square length, radius of the porous layer and solid volume fraction increase.

The stabilized ISPH method is corrected for simulating the natural convection from an inner hot square inside a nanofluid-filled circular enclosure saturated with a partial layer of a porous medium.

This study aims to focus on the numerical simulation of natural convection from heated novel fin shapes in a cavity filled with nanofluid and saturated with a partial layer of porous medium using improved incompressible smoothed particle hydrodynamics (ISPH) method.

The dimensionless of Lagrangian description for the governing equations were numerically solved using improved ISPH method. The current ISPH method was improved in term of wall boundary treatment by using renormalization kernel function. The effects of different novel heated (Tree, T, H, V, and Z) fin shapes, Rayleigh number Ra(10³ – 10⁶ ), porous height H_p (0.2-0.6), Darcy parameter Da(10⁻⁵ − 10⁻¹ ) and solid volume fraction ϕ(0.0-0.05) on the heat transfer of nanofluid have been investigated.

The results showed that the variation on the heated novel fin shapes gives a suitable choice for enhancement heat transfer inside multi-layer porous cavity. Among all fin shapes, the H-fin shape causes the maximum stream function and Z-fin shape causes the highest value of average Nusselt number. The concentrations of the fluid flows in the nanofluid region depend on the Rayleigh and Darcy parameters. In addition, the penetrations of the fluid flows through porous layers are affected by porous heights and Darcy parameter.

Natural convection from novel heated fins in a cavity filled with nanofluid and saturated with a partial layer of porous medium have been investigated numerically using improved ISPH method.

The purpose of this study is to simulate the thermo-solutal convection resulting from a circular cylinder hanging in a rod inside a ∧-shaped cavity.

The two dimensional ∧-shaped cavity is filled by Al₂O₃-water nanofluid and saturated by three different levels of heterogeneous porous media. An incompressible smoothed particle hydrodynamics (ISPH) method is adopted to solve the governing equations of the present problem. The present simulations have been performed for the alteration of buoyancy ratio (−2≤N≤2), radius of a circular cylinder (0.05≤Rc≤0.3), a height of a rod (0.1≤Lh≤0.4), Darcy parameter (10−3≤Da≤10−5), Lewis number (1≤Le≤40), solid volume fraction (0≤ϕ≤0.06), porous levels (0≤η1=η2≤1.5)and various boundary-wall conditions.

The performed numerical simulations indicated the importance of embedded shapes on the distributions of temperature, concentration and velocity fields inside ∧-shaped cavity. Increasing buoyancy ratio parameter enhances thermo-solutal convection and nanofluid velocity. Adiabatic conditions of the vertical-walls of ∧-shaped cavity augment the distributions of the temperature and concentration. Regardless the Darcy parameter, a homogeneous porous medium gives the lowest values of a nanofluid velocity.

ISPH method is used to simulate thermo-solutal convection of a nanofluid inside a novel ∧-shaped cavity containing a novel embedded shape and heterogeneous porous media.

In various kinds of materials processes, heat and mass transfer control in nuclear phenomena, constructing buildings, turbines and electronic circuits, etc., there are numerous problems that cannot be enlightened by uniform wall temperature. To explore such physical phenomena researchers incorporate non-uniform or ramped temperature conditions at the boundary, the purpose of this paper is to achieve the closed-form solution of a time-dependent magnetohydrodynamic (MHD) boundary layer flow with heat and mass transfer of an electrically conducting non-Newtonian Casson fluid toward an infinite vertical plate subject to the ramped temperature and concentration (RTC). The consequences of chemical reaction in the mass equation and thermal radiation in the energy equation are encompassed in this analysis. The flow regime manifests with pertinent physical impacts of the magnetic field, thermal radiation, chemical reaction and heat generation/absorption. A first-order chemical reaction that is proportional to the concentration itself directly is assumed. The Rosseland approximation is adopted to describe the radiative heat flux in the energy equation.

The problem is formulated in terms of partial differential equations with the appropriate physical initial and boundary conditions. To make the governing equations dimensionless, some suitable non-dimensional variables are introduced. The resulting non-dimensional equations are solved analytically by applying the Laplace transform method. The mathematical expressions for skin friction, Nusselt number and Sherwood number are calculated and expressed in closed form. Impacts of various associated physical parameters on the pertinent flow quantities, namely, velocity, temperature and concentration profiles, skin friction, Nusselt number and Sherwood number, are demonstrated and analyzed via graphs and tables.

Graphical analysis reveals that the boundary layer flow and heat and mass transfer attributes are significantly varied for the embedded physical parameters in the case of constant temperature and concentration (CTC) as compared to RTC. It is worthy to note that the fluid velocity is high with CTC and lower for RTC. Also, the fluid velocity declines with the augmentation of the magnetic parameter. Moreover, growth in thermal radiation leads to a declination in the temperature profile.

The proposed model has relevance in numerous engineering and technical procedures including industries related to polymers, area of chemical productions, nuclear energy, electronics and aerodynamics. Encouraged by such applications, the present work is undertaken.

Literature review unveils that sundry studies have been carried out in the presence of uniform wall temperature. Few studies have been conducted by considering non-uniform or ramped wall temperature and concentration. The authors are focused on an analytical investigation of an unsteady MHD boundary layer flow with heat and mass transfer of non-Newtonian Casson fluid past a moving plate subject to the RTC at the plate. Based on the authors’ knowledge, the present study has, so far, not appeared in scientific communications. Obtained analytical solutions are verified by considering particular cases of the published works.

Obtaining the maximum possible flow rates that can be induced by free convection in open‐ended vertical eccentric annuli under fundamental thermal boundary conditions of the fourth kind (heating or cooling one of the annulus walls with a uniform heat flux while keeping the other wall at ambient temperature). Obtaining the maximum possible flow rates that can be induced by free convection in open‐ended vertical eccentric annuli under fundamental thermal boundary conditions of the fourth kind (heating or cooling one of the annulus walls with a uniform heat flux while keeping the other wall at ambient temperature).

The fully‐developed laminar free convection momentum equation has been solved numerically using an analytical solution of the governing energy equation.

Results are presented to show the effect of the annulus radius ratio and the dimensionless eccentricity on the induced flow rate, the total heat absorbed by the fluid, and the fully developed Nusselt numbers on the two boundaries of the annulus for a fluid of Prandtl number 0.7.

Applications of the obtained results can be of value in the heat‐exchanger industry, in cooling of underground electric cables, and in cooling small vertical electric motors and generators.

The paper presents a solution that is not available in the literature for the problem of fully developed free convection in open‐ended vertical eccentric annular channels under thermal boundary conditions of the fourth kind. Also presents the maximum possible induced flow rates, the total heat absorbed by the fluid, and the Nusselt numbers on the two boundaries of the annulus. The effects of N and E (the radius ratio and eccentricity, respectively) on these results are presented. Such results are very much needed for design purposes of heat transfer equipment.

Turbomachinery, including pumps, are mainly designed to extract/produce energy from/to the flow. A major challenge in the numerical simulation of turbomachinery is the inlet flow rate, which is routinely treated as a known boundary condition for simulation purposes but is properly a dependent output of the solution. As a consequence, the results from numerical simulations may be erroneous due to the incorrect specification of the discharge flow rate. Moreover, the transient behavior of the pumps in their initial states of startup and final states of shutoff phases has not been studied numerically. This paper aims to develop a coupled procedure for calculating the transient inlet flow rate as a part of the solution via application of the control volume method for linear momentum. Large eddy simulation of a four-blade axial hydraulic pump is carried out to calculate the forces at every time step. The sharp interface immersed boundary method is used to resolve the flow around the complex geometry of the propeller, stator and the pipe casing. The effect of the spurious pressure fluctuations, inherent in the sharp interface immersed boundary method, is damped by local time-averaging of the forces. The developed code is validated by comparing the steady-state volumetric flow rate with the experimental data provided by the pump manufacturer. The instantaneous and time-averaged flow fields are also studied to reveal the flow pattern and turbulence characteristics in the pump flow field.

The authors use control volume analysis for linear momentum to simulate the discharge rate as part of the solution in a large eddy simulation of an axial hydraulic pump. The linear momentum balance equation is used to update the inlet flow rate. The sharp interface immersed boundary method with dynamic Smagorinsky sub-grid stress model and a proper wall model is used.

The steady-state volumetric flow rate has been computed and validated by comparing to the flow rate specified by the manufacturer at the simulation conditions, which shows a promising result. The instantaneous and time averaged flow fields are also studied to reveal the flow pattern and turbulence characteristics in the pump flow field.

An approach is proposed for computing the volumetric flow rate as a coupled part of the flow solution, enabling the simulation of turbomachinery at all phases, including the startup/shutdown phase. To the best of the authors’ knowledge, this is the first large eddy simulation of a hydraulic pump to calculate the transient inlet flow rate as a part of the solution rather than specifying it as a fixed boundary condition. The method serves as a numerical framework for simulating problems incorporating complex shapes with moving/stationary parts at all regimes including the transient start-up and shut-down phases.

A few earlier studies presented infeasible heatline trajectories for natural convection within annular domains involving an inner circular cylinder and outer square/circular enclosure. The purpose of this paper is to revisit and illustrate the correct heatline trajectories for various test cases.

Galerkin finite element based methodology and space adaptive grid have been used to simulate natural convective flows within the annular domains. The prediction of heatlines involves derivatives at the nodes, which are evaluated based on finite element basis functions and contributions from neighboring elements.

The heatlines in the earlier work indicate infeasible heat flow paths such as heat flow from one portion to the other of isothermal hot walls and heat flow across the adiabatic walls. Current results illustrate physically consistent heat flow paths involving perpendicularly emerging heatlines from hot to cold walls for conductive transport, long heat flow paths around the closed-loop heatline cells for convective transport and parallel layout of heatlines to the adiabatic walls. Results also demonstrate complex heatlines involving multiple flow vortices and complex flow structures.

Current work translates heatfunctions from energy flux vectors, which are determined by using basis sets. This work demonstrates the expected heatline trajectories for various scenarios involving conductive and convective heat transport within enclosures with an inner hot object as a first attempt, and the results are precursors for the understanding of energy flow estimates.

A finite element method for the analysis of combined radiative and conductive heat transport in a finite axisymmetric configuration is presented. The appropriate integro‐differential governing equations for a grey and non‐scattering medium with grey and diffuse walls are developed and solved for several model problems. We consider axisymmetric, cylindrical geometries with top and bottom boundaries of arbitrary convex shape. The method is accurate for media of any optical thickness and is capable of handling a wide array of axisymmetric geometries and boundary conditions. Several techniques are presented to reduce computational overhead, such as employing a Swartz‐Wendroff approximation and cut‐off criteria for evaluating radiation integrals. The method is successfully tested against several cases from the literature and is applied to some additional example problems to demonstrate its versatility. Solution of a free‐boundary, combined‐mode heat transfer problem representing the solidification of a semitransparent material, the Bridgman growth of an yttrium aluminium garnet (YAG) crystal, demonstrates the utility of this method for analysis of a complex materials processing system. The method is suitable for application to other research areas, such as the study of glass processing and the design of combustion furnace systems.

A numerical method is developed which can simulate the interaction between a finite compliant panel and an unsteady potential flow. A boundary‐element technique yields the flow solution whilst finite‐differences are used to solve the wall dynamics; these are then coupled to generate a fully interactive wall/flow system. Thus, the evolution of any wall disturbance can be followed. Parallel computing is appropriately employed and a stability investigation of a realistic compliant panel is carried out. Three‐dimensional flexural waves are found below a critical flow speed whilst beyond this threshold, essentially two‐dimensional unstable divergence waves are found. The form of divergence shows good agreement with that seen in experimental studies. The versatility of this new method will permit the investigation of a wide variety of single‐ and multi‐panel configurations subject to different forms of excitation.