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This paper aims to analyze the accuracy of the single and two-phase numerical methods for calculation of ferrofluid convective heat transfer in the presence of a magnetic field. The findings of current study are compared with previous single-phase numerical results and experimental data. Accordingly, the effect of various parameters including nanoparticles concentration, Reynolds number and magnetic field strength on the performance of the single and two-phase models are evaluated.

A two-phase mixture numerical study is carried out to investigate the influence of four U-shaped electromagnets on the hydrodynamic and thermal characteristics of Fe₃O₄/Water ferrofluid flowing inside a heated channel.

It is observed that the applied external magnetic field signifies the convective heat transfer from the channel surface, despite local reduction at a few locations. The maximum heat transfer enhancement is predicted as 23% and 25% using single and two-phase models, respectively. The difference between the results of the two models is mainly attributed to the slip velocity effect which is accounted for in the two-phase model. The magnetic field gradient leads to a significant increase in the slip velocity which in turn causes a slight difference in velocity and temperature profiles obtained by the single and two-phase models in the magnetic field region. According to percentage error calculation, the two-phase method is generally more accurate than the single-phase method. However, the percentage error of both models improves by decreasing either magnetic field intensity or Reynolds number.

For the first time in the literature, to the best of the authors’ knowledge, the current work analyzes the accuracy of the single and two phase numerical methods for calculation of ferrofluid convective heat transfer in the presence of a magnetic field.

The purpose of this paper is to investigate the two-phase flow problems involving gas–liquid mixture.

The governed equations consist of a range of conservation laws modeling a classification of two-phase flow phenomena subjected to a velocity nonequilibrium for the gas–liquid mixture. Effects of the relative velocity are accounted for in the present model by a kinetic constitutive relation coupled to a collection of specific equations governing mass and volume fractions for the gas phase. Unlike many two-phase models, the considered system is fully hyperbolic and fully conservative. The suggested relaxation approach switches a nonlinear hyperbolic system into a semilinear model that includes a source relaxation term and characteristic linear properties. Notably, this model can be solved numerically without the use of Riemann solvers or linear iterations. For accurate time integration, a high-resolution spatial reconstruction and a Runge–Kutta scheme with decreasing total variation are used to discretize the relaxation system.

The method is used in addressing various nonequilibrium two-phase flow problems, accompanied by a comparative study of different reconstructions. The numerical results demonstrate the suggested relaxation method’s high-resolution capabilities, affirming its proficiency in delivering accurate simulations for flow regimes characterized by strong shocks.

While relaxation methods exhibit notable performance and competitive features, as far as we are aware, there has been no endeavor to address nonequilibrium two-phase flow problems using these methods.

In this work, a new two-phase version of the finite element-based Artificial Compressibility (AC) Characteristic-Based Split (CBS) algorithm is developed and applied for the first time to heat and mass transfer phenomena in porous media with associated phase change. The purpose of this study is to provide an alternative for the theoretical analysis and numerical simulation of multiphase transport phenomena in porous media. Traditionally, the more complex Separate Flow Model was used in which the vapour and liquid phases were considered as distinct fluids and mathematically described by the conservation laws for each phase separately, resulting in a large number of governing equations.

Even though the adopted mathematical model presents analogies with the conventional multicomponent mixture flow model, it is characterized by a considerable reduction in the number of the differential equations for the primary variables. The fixed-grid numerical formulation can be applied to the resolution of general problems that may simultaneously include a superheated vapour region, a two-phase zone and a sub-cooled liquid region in a single physical domain with irregular and moving phase interfaces in between. The local thermal non-equilibrium model is introduced to consider the heat exchange between fluid and solid within the porous matrix.

The numerical model is verified considering the transport phenomena in a homogenous and isotropic porous medium in which water is injected from one side and heated from the other side, where it leaves the computational domain in a superheated vapour state. Dominant forces are represented by capillary interactions and two-phase heat conduction. The obtained results have been compared with the numerical data available in the scientific literature.

The present algorithm provides a powerful routine tool for the numerical modelling of complex two-phase transport processes in porous media.

For the first time, the stabilized AC-CBS scheme is applied to the resolution of compressible viscous flow transport in porous materials with associated phase change. A properly stabilized matrix inversion-free procedure employs an adaptive local time step that allows acceleration of the solution process even in the presence of large source terms and low diffusion coefficients values (near the phase change point).

The purpose of this work is to present the implementation of weighted essentially non-oscillatory (WENO) wavelet methods for solving multiphase flow problems. The particular interest is gas–liquid two-phase mixture with velocity non-equilibrium. Numerical simulations are carried out on different scenarios of one-dimensional Riemann problems for gas–liquid flows. Results are validated and qualitatively compared with solutions provided by other standard numerical methods.

This paper extends the framework of WENO wavelet adaptive method to a fully hyperbolic two-phase flow model in a conservative form. The grid adaptivity in each time step is provided by the application of a thresholded interpolating wavelet transform. This facilitates the construction of a small yet effective sparse point representation of the solution. The method of Lax–Friedrich flux splitting is used to resolve the spatial operator in which the flux derivatives are approximated by the WENO scheme.

Hyperbolic models of two-phase flow in conservative form are efficiently solved, as shocks and rarefaction waves are precisely captured by the chosen methodology. Substantial computational gains are obtained through the grid reduction feature while maintaining the quality of the solutions. The results indicate that WENO wavelet methods are robust and sufficient to accurately simulate gas–liquid mixtures.

Resolution of two-phase flows is rarely studied using WENO wavelet methods. It is the first time such a study on the relative velocity is reported in two-phase flows using such methods.

This paper aims to present a novel numerical technique for solving the incompressible multiphase mixture model.

The multiphase mixture model contains a set of momentum and continuity equations for the mixture phase, a second phase continuity equation and the algebraic equation for the relative velocity. For solving continuity equation for the second phase and advection term of momentum, an improved approach fine grid advection-multiphase mixture flow (FGA-MMF) is developed. In the FGA-MMF method, the continuity equation for the second phase is solved with higher-order schemes in a two times finer grid. To solve the advection term of the momentum equation, the advection fluxes of the volume fraction in the continuity equation for the second phase are used.

This approach has been used in various tests to simulate unsteady flow problems. Comparison between numerical results and experimental data demonstrates a satisfactory performance. Numerical examples show that this approach increases the accuracy and stability of the solution and decreases non-monotonic results.

The solver for the multi-phase mixture model can only be adopted to solve the incompressible fluid flow.

The paper developed an innovative solution (FGA-MMF) to find multi-phase flow field value in the multi-phase mixture model. Advantages of the FGA-MMF technique are the ability to accurately determine the phases interpenetrating, decreasing the numerical diffusion of the interface and preventing instability and non-monotonicity in solution of large density variation problems.

This is a 3D numerical study of convective heat transfer through a micro concentric annulus governing non-uniform heat flux boundary conditions employing water-Al₂O₃ nanofluid. The nanofluid is modeled using two-phase mixture model, as it has a good agreement to experimental results.

Half of the inner pipe surface area of the annulus section of a double pipe heat exchanger is exposed to a constant heat flux which two models are considered to divide the exposing surface area to smaller ones considering the fact that in all cases half of the inner pipe surface area has to be exposed to the heat flux: in model (A), the exposing surface area is divided radially to two parts (A1), four parts (A2) and eight parts (A3) by covering the whole length of the annulus and in model (B) the exposing surface area is divided axially to two parts (B1), four parts (B2) and eight parts (B3) by covering half of the annulus radially.

The results reveal that model (B) leads to higher Nusselt numbers compared to model (A); however, at Reynolds number 10, model (A3) exceeds model (B3). The average Nusselt number is increased up to 142 and 83 per cent at models (A3) with Reynolds number 10 and model (B3) with Reynolds number 1000, respectively.

This paper is a two-phase investigation of water-Al₂O₃ nanofluid in a micro concentric annulus under non-uniform heat flux boundary conditions.

The presence of air in the water flow over the hydrofoil is investigated. The examined hydrofoil is ClarkY 11.7% with an angle of attack of 8 deg. The flow simulations are performed with the assumption of different models. The Singhal cavitation model and the models which resolve the non-condensable gas including 2phases and 3phases are implemented in the numerical model. The calculations are performed with the uRANS model with assumption of the constant temperature of the mixture. The two-phase flow is simulated with a mixture model. The dynamics and structures of cavities are compared with literature data and experimental results.

The cavitation regime can be observed in some working conditions of turbomachines. The phase transition, which appears on the blades, is the source of high dynamic forces, noise and also can lead to the intensive erosion of the blade surfaces. The need to control this process and to prevent or reduce the undesirable effects can be fulfilled by the application of non-condensable gases to the liquid.

The results show that the Singhal cavitation model predicts the cavity structure and related characteristics differently with 2phases and 3phases models at low cavitation number where the cavitating flow is highly dynamic. On the other hand, the impact of dissolved air on the cloud structure and dynamic characteristic of cavitating flow is gently observable.

The originality of this paper is the evaluation of different numerical cavitation models for the prediction of dynamic characteristics of cavitating flow in the presence of air.

The purpose of this study is two phase modeling of Water/Cu nanofluid forced convection in different arrangements of elliptical tube banks in a two-dimensional space.

The arrangements of tube banks have been regarded as equal spacing triangle (ES), equilateral triangle (ET) and the rotated square (RS). The obtained results indicate that, among the investigated arrangements, the RS arrangement has the maximum value of heat transfer with cooling fluid. Also, the changes of Nusselt number and the local friction factor are under the influence of three main factors including volume fraction of slid nanoparticles, the changes of fluid velocity parameters on the curved surface of tube and flow separation after crossing from a specified angle of fluid rotation.

In Reynolds number of 250 and in all arrangements of the tube banks, the behavior of Nusselt number is almost the same and the separation of flow happens in almost 155-165 degrees from fluid rotation on surface. In RS arrangement, due to the strength of vortexes after fluid separation, better mixture is created and because of this reason, after the separation zone, the level of local Nusselt number graph enhances significantly.

In this research, the laminar and two-phase flow of Water/Cu nanofluid in tube banks with elliptical cross section has been numerically investigated in a two-dimensional space with different longitudinal arrangements. In this study, the effects of using nanofluid, different arrangements of tube banks and the elliptical cross section on heat transfer and cooling fluid flow among the tube banks of heat exchanger have been numerically simulated by using finite volume method.

Increasing heat transfer rate in spiral heat exchangers is possible by using conventional methods such as increasing number of fluid passes and counter flowing. In addition, newer ideas such as using pillows as baffles in the path of cold and hot fluids and using nanofluids can increase heat transfer rate. The purpose of this study is to simulate turbulent flow and heat transfer of two-phase water-silver nanofluid with 0-6 Vol.% nanoparticle concentration in a 180° path of spiral heat exchanger with elliptic pillows.

In this simulation, the finite volume method and two-phase mixture model are used. The walls are subjected to constant heat flux of q″ = 150,000 Wm⁻². The inlet fluid enters curves path of spiral heat exchanger with uniform temperature T_in = 300 K. After flowing past the pillows and traversing the curved route, the working fluid exchanges heat with hot walls and then exits from the section. In this study, the effect of radiation is disregarded because of low temperature range. Also, temperature jump and velocity slipping are disregarded. The effects of thermophoresis and turbulent diffusion on nanofluid heat transfer are disregarded. By using finite volume method and two-phase mixture model, simulations are performed.

The results show that the flow and heat transfer characteristics are dependent on the height of pillows, nanoparticle concentration and Reynolds number. Increasing Reynolds number, nanoparticle concentration and pillow height causes an increase in Nusselt number, pressure drop and pumping power.

Turbulent flow and heat transfer of two-phase water-silver nanofluid of 0-6 per cent volume fraction in a 180° path of spiral heat exchanger with elliptic pillows is simulated.

The purpose of this paper is to examine the initial mixing of wastewater discharged from submerged outfall diffusers and the influence of port configurations on wastewater distribution based on computational results.

Marine wastewater discharges from multiport diffusers are investigated by numerically solving three-dimensional and uncompressible two-phase flow fields. A mixture model simulates this flow and the standard k-e model to resolve flow turbulence; inter-phase interactions were described in terms of relative slip velocity between phases. Computations were performed for two values of the port spacings s/H with different current Froude numbers F.

Computational results compared well with previous laboratory measurements. Numerical results reveal that for both the closely spaced (s/H=0.21) and widely spaced (s/H=3.0) ports, the normalized dilution Sn becomes independent of F; further, the length of the near field xn and the spreading layer thickness hn are functions of F. For the closely spaced ports, the wastewater discharge behaves like a line plume, the Coanda effect is obvious, quasi-bifurcation is present, horseshoe structures of the jets in the planes are rapidly produced and then squashed and elongated, and the jet trajectories based on maximum velocity precede those based on maximum concentration. For the widely spaced ports, the wastewater discharge behaves like a point plume, the Coanda effect is not obvious, bifurcation is present, horseshoe structures of the jets in the planes are gradually produced and become ellipses, and the jet trajectories based on maximum velocity are similar to those based on maximum concentration.

Semi-empirical equations are presented to predict major near field characteristics. These provide guidance for designing multiport diffusers and assessing environmental impact.