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This paper aims to investigate the three-dimensional (3D) numerical simulations, based on the Navier–Stokes equations and the energy equation. Forced convection of a mixture of (60:40) percent ethylene glycol and water, was used as the base fluid and CuO nanoparticles, through a serpentine minichannel.

In this simulation, a serpentine mini-channel heat exchanger was simulated. The fluid studied in this simulation was composed of a mixture of (60:40) per cent ethylene glycol and water, was used as the base fluid and CuO nanoparticles. Four slabs and three serpentines were used in this study. The serpentine section is connected to the slab. Three equidistant circular channels (1 mm in diameter) were implemented inside the slab.

Results show that nanoparticles increase the fluid pressure drop and by changing volume fraction of nanoparticles from 0 to 1 per cent, the pressure drop of nanofluids increases between 42and 47 per cent, for Reynolds numbers from 100 to 500. The existence of serpentine bend in the minichannel heat exchanger causes the heat transfer rate to increase. Increase the volume fraction of nanoparticles reduces the fluid temperature at the outlet of the heat exchanger. The numerical results show that in Re = 500, at the beginning of the last slab in middle channel by changing volume fraction of nanoparticles from 0 to 2 per cent, local Nusselt number 57.40 per cent increase. The existence of the serpentine bend causes the heat transfer rate to increase.

Forced convection of a mixture of (60:40) per cent ethylene glycol and water by using of 3D numerical simulations, based on the Navier–Stokes equations.

The purpose of this paper is to investigate nonlinear vibrations of triple-walled carbon nanotubes buried within Pasternak foundation carrying viscous fluids.

Considering the geometry of nanotubes, the governing equations were initially derived using Timoshenko and modified couple stress theories and by taking into account Von-Karman expressions. Then, by determining boundary conditions, type of fluid motion, Knudsen number and, ultimately, fluid viscosity, the principal equation was solved using differential quadrature method, and linear and nonlinear nanotube frequencies were calculated.

The results indicated that natural frequency is decreased as the fluid velocity and aspect ratio increase. Moreover, as the aspect ratio is increased, the results converge for simple and fixed support boundary conditions, and the ratio of nonlinear to linear frequencies approaches. Natural frequency of vibrations and critical velocity increase as Pasternak coefficient and characteristic length increase. As indicated by the results, by assuming a non-uniform velocity for the fluid and a slip boundary condition at Kn = 0.05, reductions of 10.714 and 28.714% were observed in the critical velocity, respectively. Moreover, the ratio of nonlinear to linear base frequencies decreases as the Winkler and Pasternak coefficients, maximum deflection of the first wall and characteristic length are increased in couple stress theory.

This paper is a numerical investigation of nonlinear vibration analysis for triple-walled carbon nanotubes conveying viscous fluid.

The purpose of this paper is to investigate the mixed convection of a two-phase water–aluminum oxide nanofluid in a cavity under a uniform magnetic field.

The upper wall of the cavity is cold and the lower wall is warm. The effects of different values of Richardson number, Hartmann number, cavitation length and solid nanoparticles concentration on the flow and temperature field and heat transfer rate were evaluated. In this paper, the heat flux was assumed to be constant of 10 (W/m²) and the Reynolds number was assumed to be constant of 300 and the Hartmann number and the volume fraction of solid nanoparticles varied from 0 to 60 and 0 to 0.06, respectively. The Richardson number was considered to be 0.1, 1 and 5. Aspect ratios were 1, 1.5 and 2.

Comparison of the results of this paper with the results of the numerical and experimental studies of other researchers showed a good correlation. The results were presented in the form of velocity and temperature profiles, stream and isotherm lines and Nusselt numbers. The results showed that by increasing the Hartmann number, the heat transfer rate decreases. An increase from 0 to 20 in Hartmann number results in a 20 per cent decrease in Nusselt numbers, and by increasing the Hartmann number from 20 to 40, a 16 per cent decrease is observed in Nusselt number. Accordingly, it is inferred that by increasing the Hartmann number, the reduction in the Nusselt number is decreased. As the Richardson number increased, the heat transfer rate and, consequently, the Nusselt number increased. Therefore, an increase in the Richardson number results in an increase of the Nusselt number, that is, an increase in Richardson number from 0.1 to 1 and from 1 to 5 results in 37 and 47 per cent increase in Nusselt number, respectively.

Even though there have been numerous investigations conducted on convection in cavities under various configurations and boundary conditions, relatively few studies are conducted for the case of nanofluid mixed convection in square lid-driven cavity under the effect of magnetic field using two-phase model.

The purpose of this study is numerical simulation of magnetohydrodynamics (MHD) water–Al₂O₃ nanofluid mixed convection in a grooved channel with internal heat generation in solid cylinders. Simulations were carried out at Reynolds numbers 50 ≤ Re ≤ 100, Hartmann numbers 0 ≤ Ha ≤ 15, Grashof numbers 5,000 ≤ Gr ≤ 10⁻⁴ and volume fraction 0 ≤ φ ≤ 0.04. The effect of Reynolds number and the influence of magnetic field and pressure drop on convective heat transfer coefficient were studied in different volume fractions of nanoparticles at different Reynolds numbers.

The results show that average Nusselt number increases by increasing Reynolds and Hartman numbers. Also, when Hartman number increases, velocity profile becomes asymmetric. Pressure distribution shows that magnetic field applies Lorentz force at opposite direction of the flow, which causes asymmetric distribution of pressure. As a result, pressure in the upper half of the cylinder is higher than the lower half. Finally, velocity and temperature contours along the channel for different Hartmann numbers, volume fraction 3 per cent, Re = 50 and 100 and Gr = 10,000, are presented.

The effect of Reynolds number and the influence of magnetic field and pressure drop on convective heat transfer coefficient were studied in different volume fractions of nanoparticles at different Reynolds numbers.

Effect of MHD on the flow and heat transfer characteristics of Water–Al₂O₃ nanofluid in a grooved channel with internal heat generation in solid cylinders.

The purpose of this study is three-dimensional flow and heat transfer investigation of water/Al₂O₃ nanofluid inside a microchannel with different cross-sections in two-phase mode.

The effect of microchannel walls geometry (trapezoidal, sinusoidal and stepped microchannels) on flow characteristics and also changing circular cross section to trapezoidal cross section in laminar flow at Reynolds numbers of 50, 100, 300 and 600 were investigated. In this study, two-phase water/Al₂O₃ nanofluid is simulated by the mixture model, and the effect of volume fraction of nanoparticles on performance evaluation criterion (PEC) is studied. The accuracy of obtained results was compared with the experimental and numerical results of other similar papers.

Results show that in flow at lower Reynolds numbers, sinusoidal walls create a pressure drop in pure water flow which improves heat transfer to obtain PEC < 1. However, in sinusoidal and stepped microchannel with higher Reynolds numbers, PEC > 1. Results showed that the stepped microchannel had higher pressure drop, better thermal performance and higher PEC than other microchannels.

Review of previous studies showed that existing papers have not compared and investigated nanofluid in a two-phase mode in inhomogeneous circular, stepped and sinusoidal cross and trapezoidal cross-sections by considering the effect of changing channel shape, which is the aim of the present paper.

This study aims to apply the lattice Boltzmann method to investigate the natural convection flows utilizing nanofluids in a semicircular cavity. The fluid in the cavity is a water-based nanofluid containing Al₂O₃ or Cu nanoparticles.

The study has been carried out for the Rayleigh numbers from 104 to 106 and the solid volume fraction from 0 to 0.05. The effective thermal conductivity and viscosity of nanofluid are calculated by the models of Chon and Brinkman, respectively. The effects of solid volume fraction on hydrodynamic and thermal characteristics are investigated and discussed. The averaged and local Nusselt numbers, streamlines, temperature contours for different values of solid volume fraction and Rayleigh number are illustrated.

The results indicate that more solid volume fraction corresponds to more averaged Nusselt number for both types of nanofluids. It is also found that the effects of solid volume fraction of Cu are stronger than those of Al₂O₃.

Numerical study of natural convection of nanofluid in a semi-circular cavity with lattice Boltzmann method in the presence of water-based nanofluid containing Al₂O₃ or Cu nanoparticles.

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.

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 purpose of this study is simulation the flow boiling inside a tube in the turbulent flow regime for investigating the effect of using a porous medium in the boiling procedure.

To ensure the accuracy of the obtained numerical results, the presented results have been compared with the experimental results, and proper coincidence has been achieved. In this study, the phase change phenomenon of boiling has been modeled by using the Eulerian–Eulerian multi-phase Rensselaer Polytechnic Institute (RPI) wall boiling model.

The obtained results indicate using a porous medium in boiling process is very effective in a way that by using a porous medium inside the tub, the location of changing the liquid to the vapor and the creation of bubbles, changes. By increasing the thermal conductivity of porous medium, the onset of phase changing postpones, which causes the enhancement of heat transfer from the wall to the fluid. Generally, it can be said that using a porous medium in boiling flows, especially in flow with high Reynolds numbers, has a positive effect on heat transfer enhancement. Also, the obtained results revealed that by increasing Reynolds number, the created vapor phase along the tube decreases and by increasing Reynolds number, the Nusselt number enhances.

In present research, by using the computational fluid dynamics, the effect of using a porous medium in the forced boiling of water flow inside a tube has been investigated. The fluid boiling inside the tube has been simulated by using the multi-phase Eulerian RPI wall boiling model, and the effect of thermal conductivity of a porous medium and the Reynolds number on the flow properties, heat transfer and boiling procedure have been investigated.

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.