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In the present research, the stagnation point flow of EMHD Casson nanofluids over a stretchable electromagnetic plate is considered. Flow over the Riga plate is considered to analyze the Electromagnetic influences on fluid flow. Also, permeability, radiation, chemical reaction and heat source attributes are considered in this study. The guiding equations of the problem are transformed to nonlinear ODE using suitable similarity transformations. The numerical investigation of the flow is studied by implementing the Keller Box procedure using MATLAB. Validation of the numerical method is analyzed by comparing it with the previous studies. Also, calculated numerical observations of the local Nusselt and Sherwood parameters are of interest. An increase in the velocity outlines is detected for augmented observations of modified Hartmann number and unlike trends are noted for Casson, permeability, Prandtl number and suction factors. Temperature enhancement is witnessed for radiation, heat source, thermophoresis, Brownian diffusion and Biot number cases. Opposite trends are perceived in the case of suction constant. Concentration profiles are increasing for the alterations of thermophoresis parameter and declined in case of radiation, heat source, Brownian diffusion and Lewis number. [ABSTRACT FROM AUTHOR]

This paper presents computational analyses of the effects of the nanoparticle's shapes, heat, and mass transmission on the radiative nanofluid flow over a stretching Riga plate. Various nanoparticles shapes are considered, namely bricks- shaped, cylinder- shaped, platelets- shaped, and disk- shaped; those are governed using values of constants A and B in the correlations of the nanofluid dynamic viscosity. Besides, several significant influences are assumed such as constant Lorentz force, non-linear thermal radiation, viscous dissipation, heat generation, and convective boundary conditions. The solution methodology is based on similarity analyses and the obtained system is solved numerically. The entropy generation in all the aforementioned cases is examined. The given outcomes are represented in terms of the profiles of velocity, temperature, system entropy, and heat transfer rate together with the contours of the streamlines and isotherms. The findings disclosed that the sphere-shaped nanoparticles give higher values of the skin friction coefficient - C f Re 1 / 2 while the platelets-shaped cause lower values of - C f Re 1 / 2 . Additionally, the system irreversibility is enhanced as the thermal radiation coefficient R d , solid volume fraction φ , Brinkman number Br , or space-dependent heat source coefficient Q E is enhanced. [ABSTRACT FROM AUTHOR]

This paper explores the heat and mass transfer by hybrid nanofluids flow over a spinning disk in the presence of oxytactic microorganisms. During this study, the Soret and Dufour together with Lorentz force impacts are considered. The worked nano-mixture is assumed to be having time-dependent dynamic viscosity and thermal conductivity and its components are methanol-based hybrid nanofluid comprising CuO and MgO nanoparticles. The disk surface is permeable and various aspects such as thermal radiation, heat generation and Arrhenius activation energy are taken into account. The governing equations are treated numerically and suitable similar transformations are introduced. The obtained results revealed that both of the velocity and temperature gradients are enhanced as the absolute values of unsteadiness parameter and nanoparticles concentrations are rising. However, the flow is slowdown as the temperature-dependent variable viscosity parameter is growing. [ABSTRACT FROM AUTHOR]

At the current model, MHD natural convection has been numerically inspected around five circular thermal gates subjected to the non-Fourier heat flux. Streamlines experience many twists due to the addressed heat sources. In other words, streamline vortices appear as agitated groups through the cavity. When the frequency of the wavy sides increases, streamlines heaviness disperses widely, and the convection is enforced. Besides, given that there is no leading line for the force's action, the buoyancy force style exhibits peculiar behavior. Particularly, the convection regime is greatly supported by the heat generation parameter. In addition, the hybrid nanofluid provides a good chemical inertness for the electrical and thermal conductivity as to the molecular structure of the fluid particle. On the other hand, by lowering the heat exchange rate regardless of fluid flow behavior, the local thermal non-equilibrium condition maintains the system's internal energy overall, keeps the system in a static thermodynamic case, and creates isolation zones through the cavity. Moreover, the average heat transfer at the relevant porous model is not entirely dependent on the average fluid flow because porosity is proportional to flow intensity but conversely proportional to the average Nusselt number on the left, right, and bottom sides. Incidentally, the fact that the isotherm summit is near the isolated surface even though it is not connected to the heat sources indicates that the heat sources release separate energy batches that float along specific paths inside the cavity. Furthermore, the mechanism of independent energy batches is confirmed by the fact that many isotherm groups share the same values as the undulation parameter increases. [ABSTRACT FROM AUTHOR]

Mathematical simulation of biological fluids is of upmost significance due to its numerous medical uses. Interpreting various biological flows necessitates a thorough knowledge of the peristaltic mechanism. This paper presents a computational study for the peristaltic pumping within vertical asymmetric channels filled with BN‐EG nanofluid under the influence of temperature‐dependent electrical conductivity and thermal radiation. Experimental study showed that the nanofluid created by suspending Boron Nitride particles in a combination of Ethylene Glycol exhibited non‐Newtonian characteristics. Further, the Carreau's fluid model provides accurate predictions about the rheological properties of BN‐EG nanofluid. Various configurations of the outer boundaries are considered, namely, square wave, multi‐sinusoidal wave, trapezoidal wave, and triangular wave. A uniform magnetic field together with nanoparticles and mass concentrations, joule heating, first‐order chemical reaction as well as viscous dissipation are considered. Influences of the Dufour and Soret numbers are examined, and the cases of biological scientific assumptions which is known as low Reynolds number and long wavelength are applied. All the computations are obtained numerically using Mathematica symbolical software (ND‐Solve), and the obtained results are presented in terms of the axial velocity u, heat transfer rate Z, concentration profile Ω, temperature profile θ, extra stress tensor Sxy${S}_{xy}$, pressure gradient dpdx$\frac{{dp}}{{dx}}$, pressure rise Δpλ${\mathrm{\Delta p}}_{{\lambda}}$ and stream function ψ. The major outcomes revealed that the maximizing in electrical conductivity coefficient, variable viscosity coefficient and magnetic field parameter is better to obtain a higher rate of the heat transfer while the increase in thermo‐diffusion effects as well as linear thermal radiation coefficient causes a reduction in the rate of heat transfer. [ABSTRACT FROM AUTHOR]

This article presents a computational study for the peristaltic pumping within vertical irregular divergence channels filled with magnetic six-constant Jeffrey nanofluids. Various configurations of the outer boundaries are considered, namely, square wave, trapezoidal wave, multisinusoidal wave, and triangular wave. An induced magnetic field together with nanoparticles and mass concentration are considered. Influences of the Dufour and Soret numbers are examined, and the cases of long wavelength and low Reynolds number are applied. All the computations are obtained numerically via MATHEMATICA symbolical software (built-in command ND-Solve), and the obtained results are presented in terms of the axial velocity u , current density J z , the function of magnetic force Φ , axially induced magnetic field h x , nanoparticle fraction profile Ω , concentration profile γ , temperature profile θ , extra stress tensor S x y , pressure gradient d p d x , pressure rise Δ p λ , and stream function ψ. The major outcomes revealed that the square wave shape gives higher pressure gradients near the inlet and outlet parts while the multisinusoidal wave gives periodic behaviors of d p d x. Also, higher axial-induced magnetic fields are given at the higher values of the magnetic Reynolds number. [ABSTRACT FROM AUTHOR]

This study aims to examine the impacts of the variable nanofluid properties on the compressible flow over an inclined irregular surface. The density, dynamic viscosity and thermal conductivity of the nano liquid are assumed to be dependent on the temperature, and the viscous dissipation in this case is introduced. Sinusoidal formulations for the unsmoothed surface together with the governing system in case of G r L → ∞ are presented. The temperature on the edge is, also, variable and depending on the discerption function of the surface. The nonlinear radiation is taken into account, and the two-phase model for the nanofluid is applied. A fully implicit finite difference method (FDM) is used to solve the governing system. The major outcomes revealed that the skin friction coefficient and Nusselt number are rising as the compressibility parameter δ is altered. Also, the maximization of the thermal conductivity-variation β 1 is better for the velocity and temperature behaviors. [ABSTRACT FROM AUTHOR]

The heterogeneity of the porous medium properties is an important topic due to the important wide practical applications in the reservoir rocks and the petroleum reservoirs. This study aims to examine both the heterogeneity of the permeability, thermal conductivity and the nanofluid model on the dusty nanofluid within a three-dimensional cubic container. The convective transport is due to the buoyancy–driven flow resulting from two inner hot/cold cylinders separated by variable distance δ. The nanofluids are simulated by a non-homogeneous two phase model and the impact of a constant magnetic field in Z -direction is considered. Two systems of the governing equations are introduced for the dusty and nanofluid phase and the boundary conditions for the nanoparticle function are passively controlled. The major findings revealed that the flow structures can be well-controlled using the distance between the inner cylinders. Also, the heterogeneity in X − Y plane gives a higher rate of the heat transfer. Furthermore, the maximizing of the dusty parameter is better for enhancing the dusty temperature and velocities. [ABSTRACT FROM AUTHOR]

This computational analysis focuses on the effects of porous layer on the flow dynamics, heat transfer and hydrodynamic forces of hybrid nanofluid in a channel having an open cavity fixed with bottom wall in the presence of partial magnetic field. The set of PDEs governing the dynamics has been transformed to dimensionless form and simulated using higher order finite element method. In particular, P 3 / P 2 finite element pair is employed for the spatial discretization and Crank–Nicolson approach is utilized for the temporal discretization. The obtained equations has been linearized with adaptive Newtons method and linearized systems have been computed using the geometric multi-grid technique. The impact of parameters, for instance, Richardson number, thickness of porous layer and nanoparticle fraction is analyzed in the presence of partial magnetic field and porous layer on the hydrodynamic forces like lift and drag forces on the submerged bodies, being the important part of the fluid flow and heat transfer are also be analysed. It is noticed that the drag and lift coefficients are reduced as the nanoparticle fraction is altered while the local- and average-Nusselt number get higher values. [ABSTRACT FROM AUTHOR]

Mixed convection of ferrofluid in square configurations having various iso‐perimetric shaped obstacles has been investigated for fluid flow and heat transfer characteristics. The iso‐perimetric shapes are allowed to vary in size and tested at three different vertical positions subject to adiabatic and isothermal conditions. Simulations have been carried out for various choices of controlling parameters using the higher order mixed finite element method. In particular, the higher order and stable finite element pair of cubic and quadratic (ℙ3/ℙ2$$ {\mathrm{\mathbb{P}}}_3/{\mathrm{\mathbb{P}}}_2 $$) approximations on the hybrid grid is utilized to achieve the discretization of the governing non‐dimensional equations of mass, momentum and energy. The adaptive Newtons method is chosen to solve the discrete system of nonlinear equations. The present solver has been tested against a well‐known open source finite element analysis tool (FEAT2) and published results in the literature. The impact of governing parameters is investigated in the ranges as nanoparticles volume fraction ϕ(0%≤ϕ≤15%$$ \phi\ \Big(0\%\le \phi \le 15\% $$), the Richardson number Ri(0.01≤Ri≤5)$$ Ri\ \left(0.01\le Ri\le 5\right) $$, the perimeter of the obstacle Γ(0.2π≤Γ≤0.6π)$$ \Gamma\ \left(0.2\pi \le \Gamma \le 0.6\pi \right) $$, and positions of the obstacles C(0.25≤C≤0.75)$$ C\ \left(0.25\le C\le 0.75\right) $$. It is concluded that an increase in the perimeter of the inner obstacles causes a weakness in the fluid flow while a good thermal enclosure is obtained. Moreover, the isothermal obstacles enhance the average Nusselt number more than the adiabatic obstacles in all cases. [ABSTRACT FROM AUTHOR]

This paper aims to examine impacts of Cattaneo-Christov heat flux on the magnetohydrodynamic convective transport within irregular containers in the presence of the thermal radiation. Both of the magnetic field and flow domain are slant with the inclination angles and, respectively. The worked fluid is consisting of water (H2O) and Al2O3-Cu hybrid nanoparticles. The enclosures are filled with a porous medium, and the local thermal nonequilibrium (LTNE) model between the hybrid nanofluids and the porous elements are considered. Influences of various types of the obstacles are examined, namely, horizontal cold elliptic, vertical elliptic and cross section ellipsis. The solution methodology is depending on the finite volume method with nonorthogonal grids. The major outcomes revealed that the location (0:75; 0:5) is better for the rate of the flow and temperature gradients. The higher values of H-causes that the solid phase temperature has a similar behavior of the fluid phase temperature indicating to the thermal equilibrium state. Also, the fluid-phase average Nusselt number is maximizing by increasing Cattaneo-Christov heat flux factor. [ABSTRACT FROM AUTHOR]

A numerical investigation of the magnetohydrodynamics of a mixed convection of nano-enhanced phase change material (NEPCM) within a triangular chamber containing an elliptical heat source is presented in this article. The forced convection has resulted from the movement of the upper cavity, while the free convection is due to the temperature difference between the heat source and cold inclined sidewalls. Four cases are considered based on the directions of the moving of the upper wall parts, namely, Case 1, where the left part is moving in the positive direction of the X -axis and the right part moves in the opposite direction (1(+−)), Case 2, where the two parts move in the positive direction of the X -axis (2(++)), Case 3, where the two parts move in the negative direction of the X -axis (3(− −)), and Case 4, where the left part moves in the negative direction of the X -axis and the right part moves in the negative direction (4(−+)). The Galerkin finite element method (GFEM) is employed for addressing the governing equations of the system under study. The impacts of the Reynolds number (1 ≤ R e ≤ 100) , the inclination angle of the elliptic heat source (0 ≤ γ ≤ 90) , the nanoparticles volume fraction ϕ   (0 % ≤ ϕ ≤ 8 %) and the movement directions of the parts of the upper wall (four cases) are presented and discussed. The results suggested that increasing Re enhanced the heat transfer rate, while increasing Ha reduced it. The vertical positions of the elliptical heat source resulted in the maximum heat transmission rate. At the highest Re, changing the location of the heat source from horizontal ( γ = 0 ) to vertical ( γ = 90 ) enhanced the average Nusselt number by 60%, while choosing Case 1 for upper wall movement increased the average Nusselt number by 300% compared to Cases 2 and 3. [ABSTRACT FROM AUTHOR]

This study aims to investigate the magnetohydrodynamic flow induced by a moving surface in a nanofluid and the occurrence of suction and solar radiation effects using the Buongiorno model. The numerical findings are obtained using MATLAB software. The effects of various governing parameters on the rates of heat and mass transfer along with the nanoparticles concentration and temperature profiles are elucidated graphically. Non-unique solutions are discovered for a specific variation of the shrinking strength. The temporal stability analysis shows that only one of them is stable as time passes. Furthermore, raising the Brownian motion parameter reduces both the local Sherwood number and the local Nusselt number for both solutions. It is also observed that increasing the thermophoresis parameter reduces the rate of heat transfer, whereas the opposite trend is observed for the rate of mass transfer. [ABSTRACT FROM AUTHOR]

Numerical treatments based on the finite element method (FEM) are carried out for the entropy generation and convective process within inclined T‐shaped enclosures using the nano–encapsulated phase change materials (NEPCMs). The domain is filled by glass balls as a porous medium and the Brinkman‐extended non‐Darcy model is applied. For the worked mixture, the overall heat capacity of the encapsulated nanoparticles is estimated using the heat capacity of the core and shell and sine profiles are introduced for the latent heat of the change phase. Three different designs are performed for the considered geometry based on the aspect ratio of the boundaries. During the simulations, various values of the fusion temperature tf(0.05≤tf≤0.95)${t_f}\;({0.05 \le {t_f} \le 0.95})$, the inclination angle γ (0≤γ≤π/2)$({0 \le \gamma \le \pi /2})$ and different designs of the considered domain (D1,D2,D3)$({{D_1},\;{D_2},\;{D_3}})$ are taken into account and the Ryleigh‐Darcy number Ram$R{a_m}$ is varied between 102 and 104. The main outcomes disclosed that, for the fixed values of Ram(Ram=100)$R{a_m}\;({\;R{a_m} = \;100})$ and γ (γ=π3)$\gamma \; = \frac{\pi }{3})$, the increase in the fusion temperature tf${t_f}$ causes a shifting of the melting‐solidification zones from the top boundary to the bottom of the horizontal channel. [ABSTRACT FROM AUTHOR]

The present study looks at the heat transfer and the unsteady thin film flow of Al2O3 water nanofluid past an inclined stretching sheet having a buoyancy force effect. The boundary value problem solver (bvp4c) package in Matlab is utilized in solving the converted set of ordinary differential equations (ODEs). The multi-shape Al2O3 nanoparticles' impact with respect to the flow as well as heat transfer characteristics are studied and visually displayed for certain governing parameter values, which include the mixed convection, inclination angle, magnetic, slip, and Biot number. Thus, the skin friction coefficient and the local Nusselt number are also determined. Here, the platelet shape of Al2O3 nanoparticles possesses a high heat transfer and flow rate based on the outcomes. In addition, increasing the slip and magnetic parameters improves the temperature, whereas increasing the buoyancy and inclination angle parameters has reverse effects. The results also show that increasing the unsteadiness parameter and the magnetic parameter reduces the film thickness. [ABSTRACT FROM AUTHOR]

The flow, heat transfer, and melting-solidification behaviors within novel prismatic enclosures using the nano-encapsulated phase change materials (NEPCMs) are examined in this study. The flow area has nonfacing isothermal boundaries and it is filled by a homogeneous porous medium (glass balls). The Brinkman-extended non-Darcy formulations are applied while the latent heat of the change phase is computed using sine profiles. The host fluid is water, and the core and shell of the NEPCMs are nonadecane and polyurethane, respectively. The numerical simulations are carried out using the finite element method based on the characteristics-based split algorithm. The irreversibility of the system, flow, and thermal fields together with melting-solidification area is examined for wide ranges of the governing parameters. The major findings disclosed that the flow, heat transfer, and irreversibility of the system are affected by the fusion temperature and permeability of the medium. Also, an augmentation in values of N u avg up to 75% is obtained as ϕ is altered from 1% to 5%. Additionally, the heat transfer rate gets higher values at the lower values of the inclination angle. Furthermore, this numerical investigation is germane to the latent thermal energy storage units. [ABSTRACT FROM AUTHOR]

This paper aims to present a comprehensive study of the non‐linear peristaltic transport within a vertical uniform/non‐uniform channel filled with a Jeffery non‐Newtonian nanofluids in the presence of oxytactic microorganisms. The thermal conductivity of the used physiological fluids is varied linearly with the temperature while Arrhenius function is applied for the activation energy. The significance of electrical and magnetic fields together with a linear radiation and viscous dissipation are analyzed. The flow and heat transfer analysis has been performed under wall slip and compliant conditions. Additionally, optimization of the system entropy under the impacts of these aspects is examined. Numerical solutions for the governing system are introduced and profiles of the velocity u, temperature θ, nanoparticle distributions φ, heat transfer coefficient z and extra stress tensor distribution Sxy${S_{xy}}$ for the variations of the considered parameters are discussed. The main outcomes revealed that the maximizing of the Brinkman number Br$Br$ is better to get higher features of the extra stress tensor Sxy${S_{xy}}$. Also, the velocity u, density of the microorganisms ξ and the NP distributions in the interval −0.5

Study of the convective transport of the dusty nanofluid is germane to dust ladder air, fluidization, gas cooling systems to enhance heat transfer process, environmental pollution, dust collection, sedimentation, and petroleum industry. Therefore, we aim in this article to deal with the transient three dimensional (3 D) radiative-convective flows and heat transfer of dusty nanofluid within porous cubic enclosures. Two systems of the differential equations are formulated for the nanofluid and dusty phases and two SIMPLE (Semi Implicit Method for Pressure Linked Equation) techniques are carried out for the distributions of the nanofluid and dusty pressures. The porous elements are the glass balls and the non-Darcy model is applied for the porous medium. All the porous properties are constants and taken into account during all the computations. The radiation flux is assumed in the normal direction and components of the system are in the thermal equilibrium state. The mixture is consisting of water as a host fluid and alumina as nanoparticles. The main findings revealed that the dusty parameters have significantly impacts on the heat transfer and hence they are important factors in such types of flows. Also, the increase in the nanoparticles volume fraction from 0% to 10% gives an enhancement in the average Nusselt number up to 12.88%. [ABSTRACT FROM AUTHOR]

This contribution examines a highly forced convection situation due to the movements of two adjacent wavy and straight walls of two-sided wavy enclosures. An adiabatic obstacle is located within the domain and the top boundary is partially heated. The included porous medium is assumed to be radiant and the two-energy equations system is applied for this proposed. An inclined magnetic force together with heat generation sources is inclusive in the flow area. The governing equations have been solved utilizing the characteristic-based split algorithm under the spirit of finite-element method. Numerical outcomes for the flow and heat transfer for the fluid and solid phases are determined for miscellaneous combinations of the physical factors. Graphical and tabular findings pointing out interesting features of the physics of the problem are presented and discussed. The forced convection mode is dominant at higher values of the undulation parameter λ and low values of the Hartmann number Ha. Also, the radiative porous medium reduces the Nusselt coefficient for the solid phase. Furthermore, the rate of the heat transfer is reduced by 80% when the values of the Darcy coefficient are decreased from 10 - 2 to 10 - 5 . [ABSTRACT FROM AUTHOR]

The effect of magnetic field inclination and double lid‐driven on the mixed convection in a square cavity is investigated based on the local thermal non‐equilibrium model. The cavity was filled with a copper–water micropolar nanofluid saturated with a porous medium. The top and bottom walls are considered moving to the left or right directions at a constant velocity. In the current work, the ranges of parameters are as follow: Hartmann number (0 ≤ Ha ≤ 50), length of the heat source (0.2 ≤ B ≤ 0.8), Richardson number (0 ≤ Ri ≤ 10), Reynolds number (0 ≤ Re ≤ 100), location of the heat source (0.3 ≤ D ≤ 0.7), vortex to molecular viscosity ratio (0 ≤ Δ ≤ 2), Nield number (1 ≤ Q ≤ 100) and solid volume fraction (0 ≤ φ ≤ 0.1). It was found that the heat transfer decreases as the dimensionless heat source location and the Nield number increase. Also, the growing in the Nield number enhances the rate of the heat transfer for the porous phase and increases the thermal equilibrium state of the system. [ABSTRACT FROM AUTHOR]

Thermophoresis represents one of the most common methods of directing micromachines. Enhancement of heat transfer rates are of economic interest for micromachine operation. This study aims to examine the heat transfer enhancement within the shell and tube latent heat thermal storage system (LHTSS) using PCMs (Phase Change Materials). The enthalpy–porosity approach is applied to formulate the melting situation and various shapes of inner heated fins are considered. The solution methodology is based on the Galerkin finite element analyses and wide ranges of the nanoparticle volume fraction are assumed, i.e., (0% ≤ φ ≤ 6%). The system entropy and the optimization of irreversibility are analyzed using the second law of the thermodynamics. The key outcomes revealed that the flow features, hexagonal entropy, and melting rate might be adjusted by varying the number of heated fins. Additionally, in case 4 where eight heated fins are considered, the highest results for the average liquid percentage are obtained. [ABSTRACT FROM AUTHOR]

The unsteady natural-convection of Al2O3-water nanofluid form heated open T-pipe inside a cavity has been investigated by incompressible smoothed particle hydrodynamic (ISPH) method using non-homogenous two-phase Buongiorno's model. Different lengths and heights of T-pipe shape are considered. The side walls of the cavity are kept at cool temperature Tc and the horizontal walls are thermally insulated. The Lagrangian description of the controlling governing equations is discretized and solved using improved ISPH method. In this study, ISPH method is improved using kernel renormalization function for boundary treatment plus modification in the source term of pressure Poisson equation. The source term of pressure Poisson equation contains the velocity divergence plus density invariance multiply by relaxation coefficient. The calculations are performed for variable lengths of T-open pipe (0.2 ≤ Lb ≤ 0.6), variable widths of T-open pipe (0.02 ≤ Wb ≤ 0.16), (0.02 ≤ Wt ≤ 0.16), and variable concentration of nanoparticles volume fraction (1% ≤ φavg ≤ 10%). The obtained results showed that the maximum values of the stream function are reduced by 80.8% when φavg is increased from 1-10%. Additionally, as lengths and widths of the T-pipe are raised, the average Nusselt numbers at the vertical walls are enhanced. [ABSTRACT FROM AUTHOR]

Multiconvection modes together with the entropy generation due to Marangoni effects, movement of the side walls, and double-diffusive convection within liddriven enclosures filled by a porous medium are examined. The current flow domain is an inclined non-Darcy porous geometry having a top free surface where linear expressions in terms of the temperature and concentration are presented for the surface tension. The dynamic viscosity of the suspension has an exponential profile and the convective boundary conditions are taken into account. The finite volume method in which values of the pressure are computed using the SIMPLE algorithm is applied to solve the governing system. The non-Newtonian Bingham fluids are applied for different governing parameters, such as Grashof number, Reynolds number, Marangoni number, Darcy number, inclination angle of the cavity, Biot number, Bingham number, and geometrical parameters. It is observed that a rise in the Bingham number from 0 to 0.5 causes a decrease in the average Bejan number up to 4.77%. Also, the averaged and mixing temperatures are augmented as the inclination angle is altered, regardless values of the Biot number. [ABSTRACT FROM AUTHOR]

The local thermal non-equilibrium model (LTNEM) in case of a sinusoidal heating is applied to investigate the unsteady nanofluid flow and thermal fields inside an inclined enclosure filled with a thermally and hydrodynamically anisotropic porous medium. The Galerkin finite element method (GFEM) together with the Characteristic-based Split (CBS) Scheme is used to solve the dimensionless governing equations. Impacts of the controlling parameters are studied in two cases, namely, non-Darcy Regime in which values of the Darcy number and the Rayleigh number are, respectively, Da = 10-2, Ra = 105 and the Darcy regime where Da = 10-6, Ra = 109. Parametric studies are performed for wide ranges of the permeability ratio 0.1 ≤ K* ≤ 10, the Nield number 0 ≤ H ≤ 1000, the inclination angle 0 ≤ γ ≤ π/2, the nanoparticles volume fraction 0 ≤ Φ ≤ 4%, the inclination of the principal axes 0 ≤ ≤ π/2, the amplitude ratio 0 ≤ a ≤ 1 and the phase deviation 0 ≤ Φ ≤ π/2. The main outcomes revealed that the sinusoidal heating results in multicellular flow components inside the geometry. Also, the increase in the Nield number causes that the system converts from the LTNE state to local thermal equilibrium (LTE) state. For the non-Darcy regime, the convective process and the rate of the heat transfer are augmented as the inclination of the principal axes is increased. [ABSTRACT FROM AUTHOR]

Numerical simulations for the convective transport due to triangular fins within an inclined trapezoidal enclosure that is filled by a nanofluid layer and a non-Darcy pours layer are conducted. The local thermal non-equilibrium model between the nanofluid and porous phases in the porous layer is applied. Various cases based on the perimeter of the triangular fin are considered. Suitable grid transformations are introduced to map the non-uniform physical domain to a rectangular domain. The transformed governing equations are solved using a non-orthogonal finite volume method with SIMPLE algorithm. The given results revealed that the average Nusselt number is enhanced by 95.60% at the thermal conductivity ratio (Kr) = 0.1 and 68.46% at Kr = 1 and 11.23% at Kr = 10 when the Nield parameter is varied from 1 to 1000. Also, the nanofluid activity is supported in cases of higher values of the aspect ratio A and the trapezoidal angle Φ . [ABSTRACT FROM AUTHOR]

The entropy generation from convective hybrid nanofluid flow within the odd-shaped geometries using the finite element method is examined is examined. The flow domain is filled by variable porosity and permeability porous media. Also, the thermal conductivity is assumed to be heterogeneous, and the Brinkman extended non-Darcy model is applied to simulate the porous medium. The geometry is considered partially/fully filled by the porous medium and four cases are assumed, namely, only the horizontal channel is a porous (case 1), only the vertical channel is a porous (case 2), the entire domain is a porous (case 3) and the entire domain is a non-porous (case 4). Different designs of the odd-geometry are taken into account based on the aspect ratio. The characteristic-based split (CBS) based on semi-implicit (SI) scheme is used to treat the governing equations. Simulations are carried out for various values of the maximum Darcy parameter Da max , alumina-copper volume fraction ϕ Al , ϕ Cu and different conditions of the porous domain. It is noted that the case of the heterogeneous thermal conductivity maximizes the irreversibility from heat transfer and total entropy generation. Also, a weakness in values of the average Bejan number is obtained as the Rayleigh number is grown, regardless the porous conditions. [ABSTRACT FROM AUTHOR]

This work deals with natural convection flow resulting from rotating circular cylinders in a horizontal wavy cavity fully filled by nanofluid. The horizontal wavy cavity was saturated by three layers of heterogeneous porous media. Incompressible smoothed particle hydrodynamics (ISPH) method is used to solve the non-dimensional governing equations of the current physical problem. Three circular cylinders are carrying a hot temperature with a uniform circular velocity inside a horizontal wavy cavity. Effects of physical parameters including circular cylinder radius (0.05 ≤ R c ≤ 0.3) , Darcy parameter (10 - 3 ≤ Da ≤ 10 - 5) , Rayleigh number (10 3 ≤ Ra ≤ 10 5) , nanoparticles volume fraction (0 ≤ ϕ ≤ 6 %) , and paddle lengths (0.05 ≤ L paddl ≤ 0.2) on fluid flow and heat transfer were examined. Results revealed that an increase on radius of inner cylinders rises temperature distributions and nanofluid flow. A decrease on Darcy parameter weakens fluid flow. A growth on paddle lengths enhances velocity field in all the porous layers. In the current simulations, ISPH method showed a well performance in simulating natural convection flow of nanofluid inside a novel geometry (horizontal wavy cavity). [ABSTRACT FROM AUTHOR]

In this study, 3D-SIMPLE algorithm in the finite volume method (FVM) is introduced for investigating the convective flow of a power-law nanofluid within a cubic enclosure. The three-dimensional domain is filled by a heat-generating and 3D-heterogeneous porous media. The non-Newtonian power-law nanofluid is simulated using the two-phase model and case of the shear thickening fluids is considered. Three different levels of heterogeneous porous media and three values of power-law indices are investigated on the temperature, streamlines, nanoparticle volume fraction, isosurfaces of temperature and vertical velocity W. The obtained results indicated that with a homogeneous porous medium and Newtonian fluid, the temperature and nanoparticle volume fraction distributions are raising inside the cubic enclosure. Variations on the nanoparticle volume fraction under impacts of buoyancy ratio and thermophoresis parameters are reflecting the essential of the non-homogeneous distributions of the nanoparticle volume fraction. The maximum temperature rose in the cases of Newtonian fluid and homogeneous porous medium. [ABSTRACT FROM AUTHOR]

This paper presents numerical simulations for a MHD convective process in curved channels. The worked suspension consists of water as a based hybrid nanofluid and two types of the nanoparticles, namely, Cu and Al2O3. Two systems of the governing equations are formulated for the hybrid nanofluid and dusty phases. The hybrid nanofluid system is modeled in view of lubrication approach. The governing equations are mapped to a regular computational domain then they solved numerically using the fourth order Runge-Kutta method. The obtained findings revealed that the growing in the Hartmann number causes a reduction in both of the hybrid nanofluid and dusty velocities while the mixture temperature is enhanced. Also, the temperature distributions are supported when either the Grashof number or the amplitude ratio is altered. [ABSTRACT FROM AUTHOR]

Impacts of an inclined electromagnetic force on a mixed convective process in two‐sided lid‐driven geometries using the two‐energy equation model are examined in this study. The flow domain is filled by a porous medium and the local thermal nonequilibrium model is applied. Magnetic micropolar nanofluids are assumed as working fluids consisting of water as a base fluid and CuO as nanoparticles. The forced convection situation is due to the moving of the upper and lower walls in the right direction with a constant velocity. The used methodology depends on the finite volume method, together with the SIMPLE algorithm. The obtained outcomes are visualized using contours of the streamlines, isotherms for the nanofluid phase, isotherms for the solid phase, and angular velocity. The main findings revealed that the increase in lengths of the heated parts and the Nield number reduces the Nusselt number for the nanofluid phase. Also, the average heat transfer rate for the nanofluid and solid phases are boosted with the increase in the vortex viscosity. [ABSTRACT FROM AUTHOR]

In this paper, we introduced a numerical analysis for the effect of a magnetic field on the mixed convection and heat transfer inside a two-sided lid-driven cavity with convective boundary conditions on its adjacent walls under the effects of the presence of thermal dispersion and partial slip. A single-phase model in which the water is the base fluid and a copper is nanoparticles is assumed to represent the nanofluid. The bottom and top walls of the cavity move in the horizontal direction with constant speed, while the vertical walls of the cavity are stationary. The right wall is mentioned at relatively low temperature and the top wall is thermally insulated. Convective boundary conditions are imposed to the left and bottom walls of the cavity and the thermal dispersion effects are considered. The finite volume method is used to solve the governing equations and comparisons with previously published results are performed. It is observed that the increase in the Hartmann number causes that the shear friction near the moving walls is enhanced and consequently the horizontal velocity component decreases. [ABSTRACT FROM AUTHOR]

An unsteady convection-radiation interaction flow of power-law non-Newtonian nanofluids using the time-fractional derivative is examined. The flow domain is an enclosure that has a free surface located at the top boundaries. Also, the geometry is filled by aluminum foam as a porous medium and the overall thermal conductivity as well as the heat capacity are approximated using a linear combination of the properties of the fluid and porous phases. Additionally, the dynamic viscosity and thermal conductivity of the mixture are expressed as a function of velocity gradients with a fractional power. Marangoni influences are imposed to the top free surface while the bottom boundaries are partially heated. Steps of the solution methodology are consisting of approximation of the time fractional derivatives using the conformable definition, using the finite differences method to discretize the governing system and implementation the resulting algebraic system. The main outcomes reveled that as the fractional order approaches to one, the maximum values of the stream function, the bulk-averaged temperature and cup-mixing temperature are reduces, regardless values of the time. [ABSTRACT FROM AUTHOR]

In this paper, the Galerkin finite element method (FEM) together with the characteristic-based split (CBS) scheme are applied to study the case of the non-linear Boussinesq approximation within sinusoidal heating inclined enclosures filled with a non-Darcy porous media and nanofluids. The enclosure has an inclination angle and its side-walls have varying sinusoidal temperature distributions. The working fluid is a nanofluid that is consisting of water as a based nanofluid and Al2O3 as nanoparticles. The porous medium is modeled using the Brinkman Forchheimer extended Darcy model. The obtained results are analyzed over wide ranges of the non-linear Boussinesq parameter 0 ≤ ζ ≤1, the phase deviation 00 ≤ Φ ≤ 1800, the inclination angle 00 ≤ γ ≤ 900, the nanoparticles volume fraction 0%≤ φ ≤ 4%, the amplitude ratio 0 ≤ a ≤1 and the Rayleigh number 104 ≤ Ra ≤ 106. The results revealed that the average Nusselt number is enhanced by 0.73%, 26.46% and 35.42% at Ra =104, 105 and 106, respectively, when the non-linearBoussinesq parameter is varied from 0 to 1. In addition, rate of heat transfer in the case of a non-uniformly heating is higher than that of a uniformly heating. Non-linear Boussinesq parameter rises the flow speed and heat transfer in an enclosure. Phase deviation makes clear changes on the isotherms and heat transfer rate on the right wall of an enclosure. An inclination angle varies the flow speed and it has a slight effect on heat transfer in an enclosure. [ABSTRACT FROM AUTHOR]

Analyses of the entropy of a thermal system that consists of an inclined trapezoidal geometry heated by a triangular fin are performed. The domain is filled by variable porosity and permeability porous materials and the working mixture is Al2O3-Cu hybrid nanofluids. The porosity is varied exponentially with the smallest distance to the nearest wall and the permeability is depending on the particle diameter. Because of using the two energy equations model (LTNEM), sources of the entropy are entropy due to the transfer of heat of the fluid phase, entropy due to the fluid friction and entropy due to the porous phase transfer of heat. A computational domain with new coordinates (ξ,η) is created and Finite Volume Method (FVM) in case of the non-orthogonal grids is used to solve the resulting system. Various simulations for different values of the inclination angle, Hartmann number and alumina-copper concentration are carried out and the outcomes are presented in terms of streamlines, temperature, fluid friction entropy and Bejan number. It is remarkable that the increase in the inclination angle causes a diminishing of the heat transfer rate. Additionally, the irreversibility due to the temperature gradients is dominant near the heated fins, regardless of the values of the Hartmann number. [ABSTRACT FROM AUTHOR]

In this paper, numerical investigations for peristaltic motion of dusty nanofluids in a curved channel are performed. Two systems of partial differential equations are presented for the nanofluid and dusty phases and then the approximations of the long wave length and low Reynolds number are applied. The physical domain is transformed to a rectangular computational model using suitable grid transformations. The resulting systems are solved numerically using shooting method and mathematical forms for the pressure distributions are introduced. The controlling parameters in this study are the thermal buoyancy parameter Gr, the concentration buoyancy parameter Gc, the amplitude ratio, the Eckert number Ec, the thermophoresis parameter Nt and the Brownian motion parameter Nb and the dusty parameters Ds; αs. The obtained results revealed that an increase in the Eckert number enhances the temperature of the fluid and dusty particles while the nanoparticle volume fraction is reduced. Also, both of the temperature and nanoparticles volume fraction are supported by the growing of the Brownian motion parameter. [ABSTRACT FROM AUTHOR]

The present numerical investigation aims to analysis the enhancement heat transfer in the nanofluid filled-complex geometries saturated with a partially layered porous medium. The vertical walls of the cavity are taken as complex wavy geometries. The horizontal walls of the cavity are flat with insulated temperature. The complex wavy cavity is filled with a nanofluid and the upper half of the wavy cavity is saturated with the porous medium. In the analysis, the governing equations are formulated for natural convection under the Boussinesq approximation in various environments including pure-fluid, nanofluid, and porous medium. In this investigation, the effects of the Rayleigh number (103 ≤ Ra ≤ 105), Darcy parameter (10–6 ≤ Da ≤ 10–3), thermophoresis parameter (0.1 ≤ Nt ≤ 0.5), nanofluid buoyancy ratio (0.1 ≤ Nr ≤ 0.5), Brownian motion parameter (0.1 ≤ Nb ≤ 0.5), inclination angle (0° ≤ γ ≤ 90°), and geometry parameters α1 and R have been studied on the streamlines, temperature, nanoparticles volume fraction, local Nusselt number, and the local Sherwood number. It is found that, the performance of the heat transfer can be improved by adjusting the geometry parameters of the wavy surface. Overall, the results showed that the nanofluid parameters enhance the convection heat transfer and the obtained results provide a useful insight for enhancing heat transfer in two separate layers of nanofluid and porous medium inside complex-wavy cavity. [ABSTRACT FROM AUTHOR]

This paper studies the effect of fractional derivatives on the fractional convective flow of hybrid nanofluids in a wavy enclosure that has inlet and outlet parts near the left wall and is filled with a porous medium. The Caputo definition of the fractional derivatives is applied on the partial differential equations governing flow. The complex shape is mapped to a rectangular domain using appropriate transformations. The finite difference method is used to solve the resulting system. The results showed that an increase in order of the fractional derivatives causes a low activity of the fluid flow and a reduction in the rate of heat transfer. Also, an increase in the nanoparticles volume fractions reduces the activity of the fluid flow and, as a result, the rate of heat transfer is diminished. An enhancement in fluid motion and rate of the heat transfer is obtained by increasing the amplitude of the wavy wall. [ABSTRACT FROM AUTHOR]

In this paper, numerical investigations for magnetohydrodynamic natural convection from two heating systems inside fined triangular enclosures filled with an isotropic porous medium using the nanofluids are performed. The two heating modes are represented by two cases, namely, case 1 a triangular enclosure with a heated part at the left wall and including a cold fin at the bottom wall and case 2 in which a cold part at the left wall and a heated fin located at the bottom wall. The copper is considered as nanoparticles and the Darcy model is applied to the porous medium. The triangular physical model is transformed to a rectangular computational model using suitable grid transformations and then the finite-volume method is applied to solve the resulting system. The key parameters in this study are the height, width and locations of the fin, different lengths and locations of the active part, nanoparticles volume fraction, heat generation/absorption parameter, and the Hartmann number. The results revealed that the increase in height of the fins decays the nanofluid flow in case 1, but in case 2, it accelerates the fluid motion. In addition, the increase in width and height of the fin enhances the rate of the heat transfer regardless the heating mode. [ABSTRACT FROM AUTHOR]

A steady laminar two-dimensional magneto-hydrodynamics mixed convection flow in a square inclined cavity filled with Cu–water nanofluid is investigated numerically by using the finite difference method. The left and right vertical sidewalls of the cavity are considered adiabatic and move upward, while a partial slip flow condition is imposed on these walls. The horizontal top wall is considered cold and stationary, while a part of the stationary bottom wall is subjected to a uniform heat source and the remaining parts of it are considered adiabatic. An adiabatic obstacle is located in the center of the cavity and an external magnetic field is applied parallel to the horizontal x-axis. Parametric studies of the influence of various parameters such as Hartmann number, inclination angle of the cavity, dimensionless heat generation/absorption coefficient, obstacle aspect ratio, dimensionless length and location of the heat source, and solid volume fraction on the fluid flow and heat transfer have been performed. Comparisons with previously published numerical work are performed, and good agreements between the results are observed. It is found that the nanofluid was better than water to enhance the heat transfer when the effect of the magnetic field is weak, while the water is better than the nanofluid when its effect is strong. Moreover, the results indicated that the partial slip has a significant effect on the above-mentioned parameters. [ABSTRACT FROM AUTHOR]

This paper presents a revised model for the titled "Unsteady Mixed Nano- Bioconvection Flow in a Horizontal Channel with Its Upper Plate Expanding or Contracting" [18]. In this paper, the authors used a two phase model for the nanofluid presented in International Journal of Thermal Sciences 77 (2014), Mar., pp. 126-129 [15] in which the nanofluid particle volume at the wall is passively rather than actively controlled. Here, we observed that the boundary conditions are not satisfied in all curves of the nanoparticle volume fraction, i. e. the curves do not match the boundary conditions presented in eq. (19). The second note is that all values of are positive which contradicts with the results presented in [15]. Since the equations are coupled then it can be said that not only the behaviors of are wrong but also all the results presented in that paper is not correct. The main reason for conducting this investigation is performing a revision for the mentioned paper and presenting a set of curves to show the corrected behaviors for dependent variables. [ABSTRACT FROM AUTHOR]

A steady laminar two-dimensional magneto-hydrodynamic natural convection flow in an inclined trapezoidal enclosure filled with a fluid-saturated porous medium is investigated numerically using a finite difference method. The left and right vertical sidewalls of the trapezoidal enclosure are maintained at a cold temperature. The horizontal top wall is considered adiabatic while the bottom wall is subjected to isoflux heating. A volumetric internal heat generation or absorption is embedded inside the trapezoidal enclosure while an external magnetic field is applied on the left sidewall of the enclosure. In the current work, the following parametric ranges of the non-dimensional groups are used: Hartmann number is varied as $0 \le Ha \le 50$, Darcy number is taken as $Da = 10^{-3}$, 10−4, and 8 × 10−5, Rayleigh number is varied as $10^3 \le Ra \le 10^5$, Prandtl number is considered constant at Pr = 0.7, the dimensionless internal heat generation or absorption parameter is varied as Δ = −0.2, 0, 1, and 2.0, while the trapezoidal enclosure inclination angle is varied as $0^\circ \le \psi \le 90^\circ$. The results indicated a strong flow circulation occurs when the Darcy and the Rayleigh numbers are high. In addition, it is found that the Hartmann number, internal heat generation or absorption parameter and inclination angle have an important role on the flow and thermal characteristics. It is also found that when the enclosure inclination angle and Hartmann number increase the average Nusselt number along the hot bottom wall decreases. © 2012 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library (wileyonlinelibrary.com/journal/htj). DOI 10.1002/htj.21013 [ABSTRACT FROM AUTHOR]