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The purpose of this study is to theoretically analyze the laminar free convection heat transfer of nanofluids in a square cavity. The sidewalls of the cavity are subject to temperature difference, whereas the bottom and top are insulated. Based on the available experimental results in the literature, two new non-dimensional parameters, namely, the thermal conductivity parameter (Nc) and dynamic viscosity parameter (Nv) are introduced. These parameters indicate the augmentation of the thermal conductivity and dynamic viscosity of the nanofluid by dispersing nanoparticles.

The governing equations are transformed into non-dimensional form using the thermo-physical properties of the base fluid. The obtained governing equations are solved numerically using the finite element method. The results are reported for the general non-dimensional form of the problem as well as case studies in the form of isotherms, streamlines and the graphs of the average Nusselt number. Using the concept of Nc and Nv, some criteria for convective enhancement of nanofluids are proposed. As practical cases, the effect of the size of nanoparticles, the shape of nanoparticles, the type of nanoparticles, the type of base fluids and working temperature on the enhancement of heat transfer are analyzed.

The results show that the increase of the magnitude of the Rayleigh number increases of the efficiency of using nanofluids. The type of nanoparticles and the type of the base fluid significantly affects the enhancement of using nanofluids. Some practical cases are found, in which utilizing nanoparticles in the base fluid results in deterioration of the heat transfer. The working temperature of the nanofluid is very crucial issue. The increase of the working temperature of the nanofluid decreases the convective heat transfer, which limits the capability of nanofluids in decreasing the size of the thermal systems.

In the present study, a separation line based on two non-dimensional parameters (i.e. Nc and Nv) are introduced. The separation line demonstrates a boundary between augmentation and deterioration of heat transfer by using nanoparticles. Indeed, by utilizing the separation lines, the convective enhancement of using nanofluid with a specified Nc and Nv can be simply estimated.

By solving a long-wave evolution model numerically for power-law fluids, the authors aim to investigate the hydrodynamic and thermal characteristics of thermocapillary flow in an evaporating thin liquid film of pseudoplastic fluid.

The flow reversal attributed to the thermocapillary action is manifestly discernible through the streamline plots.

The thermocapillary strength is closely related to the viscosity of the fluid, besides its surface tension. The thermocapillary flow prevails in both Newtonian and pseudoplastic fluids at a large Marangoni number and the thermocapillary effect is more significant in the former. The overestimate in the Newtonian fluid is larger than that in the pseudoplastic fluid, owing to the shear-thinning characteristics of the latter.

This study provides insights into the essential attributes of the underlying flow characteristics in affecting the thermal behavior of thermocapillary convection in an evaporating thin liquid film of the shear-thinning fluids.

The purpose of this study is to adapt the incompressible smoothed particle hydrodynamics (ISPH) method with artificial intelligence to manage the physical problem of double diffusion inside a porous L-shaped cavity including two fins.

The ISPH method solves the nondimensional governing equations of a physical model. The ISPH simulations are attained at different Frank–Kamenetskii number, Darcy number, coupled Soret/Dufour numbers, coupled Cattaneo–Christov heat/mass fluxes, thermal radiation parameter and nanoparticle parameter. An artificial neural network (ANN) is developed using a total of 243 data sets. The data set is optimized as 171 of the data sets were used for training the model, 36 for validation and 36 for the testing phase. The network model was trained using the Levenberg–Marquardt training algorithm.

The resulting simulations show how thermal radiation declines the temperature distribution and changes the contour of a heat capacity ratio. The temperature distribution is improved, and the velocity field is decreased by 36.77% when the coupled heat Cattaneo–Christov heat/mass fluxes are increased from 0 to 0.8. The temperature distribution is supported, and the concentration distribution is declined by an increase in Soret–Dufour numbers. A rise in Soret–Dufour numbers corresponds to a decreasing velocity field. The Frank–Kamenetskii number is useful for enhancing the velocity field and temperature distribution. A reduction in Darcy number causes a high porous struggle, which reduces nanofluid velocity and improves temperature and concentration distribution. An increase in nanoparticle concentration causes a high fluid suspension viscosity, which reduces the suspension’s velocity. With the help of the ANN, the obtained model accurately predicts the values of the Nusselt and Sherwood numbers.

A novel integration between the ISPH method and the ANN is adapted to handle the heat and mass transfer within a new L-shaped geometry with fins in the presence of several physical effects.

The main purpose of this numerical study is to study on entropy generation in natural convection of nanofluid in a wavy cavity using a single-phase nanofluid model.

The cavity is heated non-uniformly from the wavy wall and cooled from the right side while it is insulated from the horizontal walls. The physical domain of the problem is transformed into a rectangular geometry in the computational domain using an algebraic coordinate transformation by introducing new independent variables ξ and η. The governing dimensionless partial differential equations with corresponding initially and boundary conditions were numerically solved by the finite difference method of the second-order accuracy. The governing parameters are Rayleigh number (Ra = 1000-100000), Prandtl number (Pr = 6.82), solid volume fraction parameter of nanoparticles (φ = 0.0-0.05), aspect ratio parameter (A = 1), undulation number (κ = 1-3), wavy contraction ratio (b = 0.1-0.3) and dimensionless time (τ = 0-0.27).

It is found that the average Bejan number is an increasing function of nanoparticle volume fraction and a decreasing function of the Rayleigh number, undulation number and wavy contraction ratio. Also, an insertion of nanoparticles leads to an attenuation of convective flow and enhancement of heat transfer.

The originality of this work is to analyze the entropy generation in natural convection within a wavy nanofluid cavity using single-phase nanofluid model. The results would benefit scientists and engineers to become familiar with the flow behaviour of such nanofluids, and will be a way to predict the properties of this flow for the possibility of using nanofluids in advanced nuclear systems, in industrial sectors including transportation, power generation, chemical sectors, ventilation, air-conditioning, etc.

The purpose of this paper is to perform numerical simulations based on the incompressible smoothed particle hydrodynamics (ISPH) method for thermo-diffusion convection in a hexagonal-shaped cavity saturated by a porous medium and suspended by a nano-encapsulated phase change material (NEPCM). Here, the solid particles are inserted into a phase change material to enhance its thermal performance.

Superellipse rotated shapes with variable lengths are embedded inside a hexagonal-shaped cavity. These inner shapes are rotated around their center by a uniform circular velocity and their conditions are positioned at high temperature and concentration. The controlling equations in a non-dimensional form were analyzed by using the ISPH method. At first, the validation of the ISPH results is performed. Afterward, the implications of a fusion temperature, lengths/types of the superellipse shapes, nanoparticles parameter and time parameter on the phase change heat transfer, isotherms, isoconcentration and streamlines were addressed.

The achieved simulations indicated that the excess in the length of an inner superellipse shape augments the temperature, concentration and maximum of the streamlines in a hexagonal-shaped cavity. The largest values of mean Nusselt number are attained at the inner rhombus shape with convex (n = 1.5) and the largest values of mean Sherwood number are attained at the inner rectangle shape with rounded corners (n = 4).

The ISPH method is developed to emulate the influences of the uniform rotation of the novel geometry shapes on heat/mass transport inside a hexagonal-shaped cavity suspended by NEPCM and saturated by porous media.

Sheet processing of magnetic nanomaterials is emerging as a new branch of smart materials’ manufacturing. The efficient production of such materials combines many physical phenomena including magnetohydrodynamics (MHD), nanoscale, thermal and mass diffusion effects. To improve the understanding of complex inter-disciplinary transport phenomena in such systems, mathematical models provide a robust approach. Motivated by this, this study aims to develop a mathematical model for steady, laminar, MHD, incompressible nanofluid flow, heat and mass transfer from a stretching sheet.

This study developed a mathematical model for steady, laminar, MHD, incompressible nanofluid flow, heat and mass transfer from a stretching sheet. A uniform constant-strength magnetic field is applied transversely to the stretching flow plane. The Buongiorno nanofluid model is used to represent thermophoretic and Brownian motion effects. A non-Fourier (Cattaneo–Christov) model is used to simulate thermal conduction effects, of which the Fourier model is a special case when thermal relaxation effects are neglected.

The governing conservation equations are rendered dimensionless with suitable scaling transformations. The emerging nonlinear boundary value problem is solved with a fourth-order Runge–Kutta algorithm and also shooting quadrature. Validation is achieved with earlier non-magnetic and forced convection flow studies. The influence of key thermophysical parameters, e.g. Hartmann magnetic number, thermal Grashof number, thermal relaxation time parameter, Schmidt number, thermophoresis parameter, Prandtl number and Brownian motion number on velocity, skin friction, temperature, Nusselt number, Sherwood number and nanoparticle concentration distributions, is investigated.

A strong elevation in temperature accompanies an increase in Brownian motion parameter, whereas increasing magnetic parameter is found to reduce heat transfer rate at the wall (Nusselt number). Nanoparticle volume fraction is observed to be strongly suppressed with greater thermal Grashof number, Schmidt number and thermophoresis parameter, whereas it is elevated significantly with greater Brownian motion parameter. Higher temperatures are achieved with greater thermal relaxation time values, i.e. the non-Fourier model predicts greater values for temperature than the classical Fourier model.

The present study aims to investigate the inverse-thermocapillary effect in an evaporating thin liquid film of self-rewetting fluid, which is a dilute aqueous solution (DAS) of long-chain alcohol.

A long-wave evolution model modified for self-rewetting fluids is used to study the inverse thermocapillary characteristics of an evaporating thin liquid film. The flow attributed to the inverse thermocapillary action is manifested through the streamline plots and the evaporative heat transfer characteristics are quantified and analyzed.

The thermocapillary flow induced by the negative surface tension gradient drives the liquid from a low-surface-tension (high temperature) region to a high-surface-tension (low temperature) region, retarding the liquid circulation and the evaporation strength. The positive surface tension gradients of self-rewetting fluids induce inverse-thermocapillary flow. The results of different working fluids, namely, water, heptanol and DAS of heptanol, are examined and compared. The thermocapillary characteristic of a working fluid is significantly affected by the sign of the surface tension gradient and the inverse effect is profound at a high excess temperature. The inverse thermocapillary effect significantly enhances evaporation rates.

The current investigation on the inverse thermocapillary effect in a self-rewetting evaporating thin film liquid has not been attempted previously. This study provides insights on the hydrodynamic and thermal characteristics of thermocapillary evaporation of self-rewetting liquid, which give rise to significant thermal enhancement of the microscale phase-change heat transfer devices.

The purpose of this study is to investigate the accuracy and applicability of the Flowfield Dependent Variation (FDV) method for large-eddy simulations (LES) of decaying isotropic turbulence.

In an earlier paper, the FDV method was successfully demonstrated for simulations of laminar flows with speeds varying from low subsonic to high supersonic Mach numbers. In the current study, the FDV method, implemented in a finite element framework, is used to perform LESs of decaying isotropic turbulence. The FDV method is fundamentally derived from the Lax–Wendroff Scheme (LWS) by replacing the explicit time derivatives in LWS with a weighted combination of explicit and implicit time derivatives. The increased implicitness and the inherent numerical dissipation of FDV contribute to the scheme’s numerical stability and monotonicity. Understanding the role of numerical dissipation that is inherent to the FDV method is essential for the maturation of FDV into a robust scheme for LES of turbulent flows. Accordingly, three types of LES of decaying isotropic turbulence were performed. The first two types of LES utilized explicit subgrid scale (SGS) models, namely, the constant-coefficient Smagorinsky and dynamic Smagorinsky models. In the third, no explicit SGS model was employed; instead, the numerical dissipation inherent to FDV was used to emulate the role played by explicit SGS models. Such an approach is commonly known as Implicit LES (ILES). A new formulation was also developed for quantifying the FDV numerical viscosity that principally arises from the convective terms of the filtered Navier–Stokes equations.

The temporal variation of the turbulent kinetic energy and enstrophy and the energy spectra are presented and analyzed. At all grid resolutions, the temporal profiles of kinetic energy showed good agreement with t^(−1.43) theoretical scaling in the fully developed turbulent flow regime, where t represents time. The energy spectra also showed reasonable agreement with the Kolmogorov’s k^(−5/3) power law in the inertial subrange, with the spectra moving closer to the Kolmogorov scaling at higher-grid resolutions. The intrinsic numerical viscosity and the dissipation rate of the FDV scheme are quantified, both in physical and spectral spaces, and compared with those of the two SGS LES runs. Furthermore, at a finite number of flow realizations, the numerical viscosities of FDV and of the Streamline Upwind/Petrov–Galerkin (SUPG) finite element method are compared. In the initial stages of turbulence development, all three LES cases have similar viscosities. But, once the turbulence is fully developed, implicit LES is less dissipative compared to the two SGS LES runs. It was also observed that the SUPG method is significantly more dissipative than the three LES approaches.

Just as any computational method, the limitations are based on the available computational resources.

Solving problems involving turbulent flows is by far the biggest challenge facing engineers and scientists in the twenty-first century, this is the road that the authors have embarked upon in this paper and the road ahead of is very long.

Understanding turbulence is a very lofty goal and a challenging one as well; however, if the authors succeed, the rewards are limitless.

The derivation of an explicit expression for the numerical viscosity tensor of FDV is an important contribution of this study, and is a crucial step forward in elucidating the fundamental properties of the FDV method. The comparison of viscosities for the three LES cases and the SUPG method has important implications for the application of ILES approach for turbulent flow simulations.

The purpose of this paper is to make a numerical study of natural convection of water‐based nanofluids in a square cavity when a discrete heat source is embedded on the bottom wall, applying a “nanofluid‐oriented” model for the calculation of the effective thermal conductivity (Xu‐Yu‐Zou‐Xu's model) and the effective dynamic viscosity (Jang‐Lee‐Hwang‐Choi's model). Another motivation is the numerical solution of the equations of the flow with a meshless method.

A meshless point collocation method with moving least squares (MLS) approximation is used. A test validation study of the numerical method takes place for pure water flow, as well for water/Al₂O₃ nanofluids. The influence of pertinent parameters such as Rayleigh number (Ra), the non‐uniform nanoparticle size keeping the mean nanoparticle diameter fixed, the volume fraction of nanoparticles and the location of heat source on the cooling performance are studied.

The presence of a discrete heat source, as well as the various thermal boundary conditions affects the characteristics of the nanofluid flow and heat transfer. When the ratio of minimum to maximum nanoparticle diameter is increased, the local Nusselt number is increased and the heat source temperature is decreased. The increase of solid volume fraction of nanoparticles causes the heat source maximum temperature to decrease and the Nusselt Number to increase.

The present study constitutes an original contribution to the nanofluid flow and heat transfer characteristics when a discrete heat source is presence. “Nanofluid‐oriented” models are used for the calculation of the effective thermal conductivity and dynamic viscosity.

This paper aims to perform the lattice Boltzmann simulation of conjugate natural convection heat transfer, heat flow visualization via heatlines approach and entropy generation in a partitioned medium filled with Ag-MgO (15-85%)/water.

The lattice Boltzmann method (LBM) is used to predict the dynamic and thermal behaviors. Experimental correlations for dynamic viscosity and thermal conductivity versus solid volume fraction are used. The study is conducted for the ranges of Rayleigh number 10³ ≤ Ra ≤ 10⁶, the partitioner thickness 0.01 ≤ δ ≤ 0.9, its position 0.15 ≤ X_s ≤ 0.85 and the hybrid nano-suspensions volume fraction 0% ≤ ϕ ≤ 2%.

The effects of varying of controlling parameters on the convective flow patterns, temperature contours, heat transfers, the heatlines and the entropy generation are presented. It has been found that the maximum rate of heat transfer enhancement occurs for low Ra numbers (10³) and is close to 13.52%. The solid thickness d and its horizontal position X_s have a substantial influence on the heat transfer rate, flow structure, heatline, total entropy generation and Bejan number. Besides, the maximum heat transfer is detected for high Ra and δ ≈ 1 and the percentage of augmentation is equal to 65.55% for ϕ = 2%. According to the horizontal position, the heat transfer remains invariant for Ra = 10³ and takes a maximum value near the active walls for Ra ≥ 10⁴. The total entropy generation increases with Ra and decreases with ϕ for Ra = 10⁶. The increase of ϕ from 0 to 2% leads to a reduction in close to 40.76%. For this value of Ra, the entropy is the maximum for δ = 0.4 and X_s = 0.35 and X_s = 0.65%. Moreover, as the Ra increases the Bejan number undergoes a decrease. The Bejan number is the maximum for Ra = 10³ independently to δ and X_s. The superior thermal performance manifests at low Ra and high value of δ independently to the positions of the conducting body.

The originality of this paper is to analyze the hybrid nano-additive effects on the two-dimensional conjugate natural convection in a partitioned medium using the LBM. The experimental correlations used for the effective thermal conductivity and dynamic viscosity give credibility to our study. Different approaches such as heatlines and entropy generation are used.