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This study aims to analyze the two-dimensional ferrofluid flow in porous media. The effects of changes in parameters such as permeability parameter, buoyancy parameter, Reynolds and Prandtl numbers, radiation parameter, velocity slip parameter, energy dissipation parameter and viscosity parameter on the velocity and temperature profile are displayed numerically and graphically.

By using simplification, nonlinear differential equations are converted into ordinary nonlinear equations. Modeling is done in the Cartesian coordinate system. The finite element method (FEM) and the Akbari-Ganji method (AGM) are used to solve the present problem. The finite element model determines each parameter’s effect on the fluid’s velocity and temperature.

The results show that if the viscosity parameter increases, the temperature of the fluid increases, but the velocity of the fluid decreases. As can be seen in the figures, by increasing the permeability parameter, a reduction in velocity and an enhancement in fluid temperature are observed. When the Reynolds number increases, an increase in fluid velocity and temperature is observed. If the speed slip parameter increases, the speed decreases, and as the energy dissipation parameter increases, the temperature also increases.

When considering factors like thermal conductivity and variable viscosity in this context, they can significantly impact velocity slippage conditions. The primary objective of the present study is to assess the influence of thermal conductivity parameters and variable viscosity within a porous medium on ferrofluid behavior. This particular flow configuration is chosen due to the essential role of ferrofluids and their extensive use in engineering, industry and medicine.

The current analysis produces the fractional sample of non-Newtonian Casson and Williamson boundary layer flow considering the heat flux and the slip velocity. An extended sheet with a nonuniform thickness causes the steady boundary layer flow’s temperature and velocity fields. Our purpose in this research is to use Akbari Ganji method (AGM) to solve equations and compare the accuracy of this method with the spectral collocation method.

The trial polynomials that will be utilized to carry out the AGM are then used to solve the nonlinear governing system of the PDEs, which has been transformed into a nonlinear collection of linked ODEs.

The profile of temperature and dimensionless velocity for different parameters were displayed graphically. Also, the effect of two different parameters simultaneously on the temperature is displayed in three dimensions. The results demonstrate that the skin-friction coefficient rises with growing magnetic numbers, whereas the Casson and the local Williamson parameters show reverse manners.

Moreover, the usefulness and precision of the presented approach are pleasing, as can be seen by comparing the results with previous research. Also, the calculated solutions utilizing the provided procedure were physically sufficient and precise.

Nanofluid flow which is squeezed between parallel plates is studied using differential transformation method (DTM). The fluid in the enclosure is water containing different types of nanoparticles: Al₂O₃ and CuO. The effective thermal conductivity and viscosity of nanofluid are calculated by Koo–Kleinstreuer–Li (KKL) correlation. The comparison between the results from DTM and numerical method are in well agreement which proofs the capability of this method for solving such problems. Effects of the squeeze number and nanofluid volume fraction on flow and heat transfer are examined. Results indicate that Nusselt number augment with increase of the nanoparticle volume fraction. Also, it can be found that heat transfer enhancement of CuO is higher than Al₂O₃.

The problem of nanofluid flow which is squeezed between parallel plates is investigated analytically using DTM. The fluid in the enclosure is water containing different types of nanoparticles: Al₂O₃ and CuO. The effective thermal conductivity and viscosity of nanofluid are calculated by KKL correlation. In this model, effect of Brownian motion on the effective thermal conductivity is considered. The comparison between the results from DTM and numerical method are in well agreement which proves the capability of this method for solving such problems. The effect of the squeeze number and the nanofluid volume fraction on flow and heat transfer is investigated. The results show that Nusselt number increase with increase of the nanoparticle volume fraction. Also, it can be found that heat transfer enhancement of CuO is higher than Al₂O₃.

The effect of the squeeze number and the nanofluid volume fraction on flow and heat transfer is investigated. The results show that Nusselt number increase with increase of the nanoparticle volume fraction. Also, it can be found that heat transfer enhancement of CuO is higher than Al₂O₃.

This paper is original.

This study aims to explore the idea of solving the problem of squeezing nanofluid flow between two parallel plates using a novel mathematical method.

The unsteady squeezing flow is a coupled fourth-order boundary value problem with flow velocity and temperature as the desired unknowns. In the first step, the conditions that guarantee the existence of a unique solution are obtained. Then following Green’s function-based approach, an iterative method for solving the problem is developed.

The accuracy of the method is examined by comparing the obtained results with existing numerical data, indicating excellent agreement between the two. In addition, the effects of nanoparticle shape and volume fraction on the flow and heat transfer characteristics are addressed. The results reveal that although the nanoparticle shape strongly affects the temperature distribution in the squeezing flow, it only has a slight impact on the velocity field. Furthermore, the highest and lowest Nusselt numbers belong to the platelets and spherical nanoparticles, respectively.

A semi-analytical method with computational support is developed for solving the unsteady squeezing flow problem. Moreover, the existence and uniqueness of the solution are discussed for the first time.

This paper aims to solve the Falkner–Skan problem over an isothermal moving wedge using the combination of the quasilinearization method and the fractional order of rational Chebyshev function (FRC) collocation method on a semi-infinite domain.

The quasilinearization method converts the equation into a sequence of linear equations, and then by using the FRC collocation method, these linear equations are solved. The governing nonlinear partial differential equations are reduced to the nonlinear ordinary differential equation by similarity transformations.

The entropy generation and the effects of the various parameters of the problem are investigated, and various graphs for them are plotted.

Very good approximation solutions to the system of equations in the problem are obtained, and the convergence of numerical results is shown by using plots and tables.

The purpose of this paper is to theoretically investigate the effects of nanoparticle migration on the heat transfer enhancement at film boiling of nanofluids. The modified Buongiorno model is used for modeling the nanofluids to observe the effects of nanoparticle migration.

The governing partial differential equations including continuity, momentum, energy and nanoparticle continuity are transformed to ordinary ones and solved numerically. For nanoparticle distribution, an analytical expression has been found. The results have been obtained for different parameters, including the Brownian motion to thermophoretic diffusion N_BT, saturation nanoparticle volume fraction ϕ_sat and normal temperature difference.

A closed-form expression for nanoparticle distribution is obtained, and it is indicated that nanoparticle migration significantly affects the flow fields and thermophysical properties of nanofluids. It was shown that temperature gradient at heated wall grows as the migration of nanoparticles increases, which has positive effects on the heat transfer rate. However, decrement of thermal conductivity at heated wall because of nanoparticle depletion plays a negative role in heat transfer enhancement. In fact, there is a tradeoff between thermal conductivity reduction and an increment in temperature gradient at the wall, which determines the net enhancement/deterioration of the heat transfer rate.

Flow has been assumed to be laminar, and the vapor temperature is constant such that boiling is the only heat transfer mechanism between the liquid-vapor interface. Also, the shear stress at the liquid-vapor interface is assumed to be negligible. The film thickness is small relative to the plate length to justify the boundary layer assumptions. Inertia forces are neglected relative to shear stress forces.

Outcomes of the present study are suitable for several heat exchange purposes such as evaporation and condensation in heat pipes, immersion, microchannel cooling of microelectronics and crystal growth.

The novelty of this paper has three aspects: modeling the film boiling of nanofluids considering the effects of nanoparticle migration; how it influences the cooling performance; and an analytical expression for the nanoparticle distribution at film boiling of nanofluids.

The purpose of this study is, mixed convection on magnetohydrodynamic (MHD) flow of Eyring–Powell nanofluid over a stretching cylindrical surface in the presence of thermal radiation, chemical reaction, heat generation and Joule heating effect is investigated and analyzed. The Brownian motion and thermophoresis phenomenon are used to model nanoparticles (Buongiorno’s model).

The numerical method is applied to solve the governing equations. Obtained results from the effects of different parameters changes on velocity, temperature and concentration profiles are reported as diagrams.

As a result, velocity profile has been reduced by increasing the Hartman number (magnetic field parameter) because of the existence of Lorentz force and increasing Eyring–Powell fluid parameter. In addition, the nanoparticle concentration profile has been reduced because of increase in chemical reaction parameter. At the end, the effects of different parameters on skin friction coefficient and local Nusselt number are investigated.

Eyring–Powell nanofluid and MHD have significant influence on flow profile.

The purpose of this paper is to investigate natural convection in a porous wavy-walled enclosure that is including a cylinder cavity in the middle of it and filled with a hybrid nanofluid contains 1-Butanol as the base fluid and MoS₂–Fe₃O₄ hybrid nanoparticles.

The domain of interest is bounded by constant temperature horizontal corrugated surfaces and isothermal vertical flat surfaces. The numerical outputs are explained in the type of isotherms, streamline and average Nusselt number with variations of the Rayleigh number, Hartmann number, nanoparticle shape factor and porosity of the porous medium. For solving the governing equations, the finite element method has been used.

The results show that Nuave is proportional to Rayleigh and nanoparticle shape factor directly as well as it has an inverse relation with Hartmann and porosity. The obtained results reveal that the shape factor parameter has a significant effect on the heat transfer performance, which shows a 55.44% contribution on the average Nusselt number.

As a novelty, to maximize the heat transfer performance in a corrugated walls enclosure, the optimal parameters have intended by using the response surface and Taguchi methods. Additionally, an accurate correlation for the average Nusselt number is developed with sensibly great precision.

The purpose of this study is investigating the effect of using multi-phase nanofluids, Rayleigh number and baffle arrangement simultaneously on the heat transfer rate and Predict the optimal arrangement type of baffles in the differentiation of Rayleigh number in a 3D enclosure.

Simulations were performed on the base of the L25 Taguchi orthogonal array, and each test was conducted under different height and baffle arrangement. The multi-phase thermal lattice Boltzmann based on the D3Q19 method was used for modeling fluid flow and temperature fields.

Streamlines, isotherms, nanofluid volume fraction distribution and Nusselt number along the wall surface for 104 < Ra < 108 have been demonstrated. Signal-to-noise ratios have been analyzed to predict optimal conditions of maximize and minimize the heat transfer rate. The results show that by choosing the appropriate height and arrangement of the baffles, the average Nusselt number can be changed by more than 57 per cent.

The value of this paper is surveying three-dimensional and two-phase simulation for nanofluid. Also using the Taguchi method for Predicting the optimal arrangement type of baffles in a multi-part enclosure. Finally statistical analysis of the results by using of two maximum and minimum target Function heat transfer rates.

The purpose of this paper is to find the approximate solutions of unsteady squeezing nanofluid flow and heat transfer between two parallel plates in the presence of variable heat source, viscous dissipation and inclined magnetic field using collocation method (CM).

The partial governing equations are reduced to nonlinear ordinary differential equations by using appropriate transformations and then are solved analytically by using the CM.

It is observed that the enhancing values of aligned angle of the magnetic causes a reduction in temperature distribution. It is also seen that the effect of nanoparticle volume fraction is significant on the temperature but negligible on the velocity profile.

To the best of the authors’ knowledge, no research has been carried out considering the combined effects of inclined Lorentz forces and variable heat source on squeezing flow and heat transfer of nanofluid between the infinite parallel plates.