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Flow around a solid sphere finds utility in numerous single- and two-phase engineering applications, such as sport balls, combustion systems, silt conveyance in waterways, hydraulic conveying, pneumatic equipment, food and chemical manufacturing. Therefore, this paper aims to examine the Casson nanofluids flow and heat transfer over a solid sphere that is saturated in an isotropic porous material in the presence of Stefan blowing and slip conditions. The forced situation is due to the presence of a stagnation point while the surface of the sphere is subjected to thermal slip conditions. Besides, various significant impacts are taken into account such as Lorentz force, thermal radiation, heat source/sink, and activation energy. The solution technique is based on non-similar transformations and implicit finite difference method with the Blottner algorithm. It is remarkable that, for all values of the activation parameter, the growth of Stefan number reduces the gradients of the velocity, temperature, and nanoparticle concentration. Also, the presence of the thermal slip factor reduces the temperature distributions. Additionaly, an increase in either the Casson parameter or Darcy number enhances the flow while both temperature and concentration are diminishing. Furthermore, there is an improvement in values of the Nusselt number up to 50.57 % when the magnetic parameter is varied from 0 to 6. [ABSTRACT FROM AUTHOR]

Examining the behaviors of power-law nanofluid flow and the rate of heat transfer over different surfaces has received great attention due to its numerous industrial applications, such as polymer solutions, molten plastics, pulps, and foods. Also, the investigators focused on the case of constant viscosity, while in several practical situations, the dynamic viscosity of the power-law suspension is variable. So this study aims to examine non-similar solutions for the coupled flow of power-law non-Newtonian nanofluids over a truncated cone. The dynamic viscosity is varied according to the Reynolds viscosity model, and an exponential decaying form is considered for the internal heat generation. The non-Darcy model, where the quadratic drag is significant, is applied to formulate this situation, and the medium's permeability is varied according to the modified Ostwald-de-Waele power law model. Both the Arrhenius activation energy and non-linear thermal radiation impacts are considered. The solution methodology is based on the effective finite differences method with the Blottner scheme. The significant outcomes revealed that the rise in the power-law index n accelerates the flow and boosts the heat transfer rate. The values of the local Nusselt number in the case of the Darcy flow are higher than those of the non-Darcy case. Additionally, considering the case of variable dynamic viscosity, it is recommended to enhance the heat transfer rate. Furthermore, the rate of the heat transfer is enhanced by 29.1% viscosity parameter δ is varied from 0 to 0.5. [ABSTRACT FROM AUTHOR]

The purpose of the current study is to establish a novel mathematical model in the wave propagation in fibre-reinforced viscothermoelastic media of higher order. The governing equations of a fibre-reinforced viscothermoelastic media of higher order are solved analytically to determine mechanical displacement and stresses. Dispersion relation for Rayleigh-type, Love-type, and Stoneley-type wave has been derived using suitable boundary conditions, which is found to be complex in nature. The analysis included Rayleigh-type, Love-type, and Stoneley-type waves while the findings revealed a broader scope compared to previous research, which is encompassed by our results as special cases. Findings are compared with and without rotational effect, along with assessing the parameters for fiber-reinforced materials in the medium, it was observed that surface waves could not propagate in a fast rotating medium. These results are computed numerically and depicted graphically to highlight the effects of fiber reinforcement and rotation parameter on the surface wave speed. Certain particular cases of interest have been deduced from the current investigation. Numerical results and graphical analyses of surface waves were performed using MATLAB software. [ABSTRACT FROM AUTHOR]

Using substances of high latent heat such as phase change materials is a perfect technique in the energy storage units. Additionally, examining the heat transport and melting process for these materials is beneficial for a wide variety of solar-related applications. Therefore, this study aims to examine the time-dependent fractional melting process within inclined containers filled with Nanoparticles-enhanced Phase-Change Materials (NePCM) via the model of the enthalpy-porosity. The used NePCM is octadecane and the fractional derivatives are considered for all the time-dependent variables, namely, velocities, temperature and liquid fraction. The Caputo definition is applied to estimate the non-integer derivatives and the fractional order takes the values between 0.75 and 0.95. The solution methodology is depending on the Finite Volume technique with SIMPLE approach. The range of the Fourier number is between 0.05 and 0.4 and the resulting data is presented in terms of melting interface, liquid fraction, streamlines, isotherms and heat transfer rate. The main findings revealed that the influences of order of the fractional derivatives more significant at the higher values of the Fourier number and the melting interface points move towards the heated wall as order of the fractional derivatives is reduced. Also, at higher values of the fractional derivative's order (0.9), the maximizing of inclination angle causes a diminishing in the rate of the heat transfer. [ABSTRACT FROM AUTHOR]

The current numerical investigation focuses on the power-law nanofluids behaviors in slant wavy enclosures in the presence of thermal radiation. The entropy of the system together with the flow and thermal features are examined for several patterns of the side wavy walls, namely, Out-Out, In-In and In-out. The components of the suspension are multi-wall carbon nanotubes and ethylene glycol. The magnetic field is considered in the current study to be inclined and its components are expressed in terms of the enclosure inclination angle. The solution scheme is based on the Characteristic-Based Split (CBS) scheme and the resulting system is discretized using the finite element method (FEM). It is noted that the flow structures, temperature, and entropy features have strong responses for changing the patterns of the side walls. Also, for the non-inclined domain, an augmentation in the non-Newtonian fluid flow up to 44.2% is given as the radiation coefficient is altered from 0 to 5. [ABSTRACT FROM AUTHOR]

In this paper, by means of the finite element method, the MHD free convection flow of non-Newtonian nanoliquid inside a halved annulus enclosure considering a constant heat flux is being applied to the straight walls has been analyzed. The enclosure is loaded with water and nanoparticles of alumina (Al 2 O 3) the combination of these tows produces a liquid that shows shear-thinning behavior. The governing parameters of this study are the Rayleigh number (103 ≤ Ra ≤ 106), inclination angle (0 ≤ α ≤ 90), power-law index (0.6 ≤ n ≤ 1) and Hartmann number (0 ≤ Ha ≤ 100). The outcomes indicate that the inclination angle of the cavity and the Hartmann number can be considered as effective control parameters at different Rayleigh numbers. While the magnetic field is applied the velocity field retarded and hence convection heat transfer and the Nusselt number diminished, and the increment of power-law index prompts the heat transfer to drop. It is shown that the power-law index and Hartmann reduces the local Nusselt number. Also, the average Bejan numbers corresponding of active parameters are discussed in this study. [ABSTRACT FROM AUTHOR]

This research delves into the propagation of radial free harmonic waves in a poroelastic cylinder, conceptualized as a magnetically and rotationaly influenced hollow structure. The primary aim is to elucidate the magnetic field's and rotation impact on the vibrational behavior of such systems. The investigative method encompasses the resolution of motion equations, formulated as partial differential equations, through the application of Lame's potential theory. This analytical process is augmented by the implementation of fitting boundary conditions, culminating in the derivation of a comprehensive expression for the complex dispersion equation, predicated on the premise that the wavenumber embodies a complex entity. The precision of the model is corroborated through a comparative analysis with established literature, underpinned by an exploration of diverse scenarios. The research employed MATLAB for both numerical and graphical assessments, focusing on the dispersion and displacement attributes. Dispersion relations within the poroelastic medium were computed, considering varied magnitudes of magnetic field intensity, rotation and angular velocities. The outcomes are articulated through complex-valued dispersion relations, transcendental formulations, and numerical resolutions employing MATLAB's bisection technique. These insights hold substantial significance for the theoretical advancement in orthopedic research, particularly concerning cylindrical poroelastic media. This study deduces that the radial vibrational patterns and the corresponding frequency equation within a poroelastic medium are profoundly modified by the magnetic field's interference and rotation. This study formulate a novel governing equation for a poroelastic medium, highlighting the significance of radial vibrations and investigating the impact of magnetic field and rotation. [ABSTRACT FROM AUTHOR]

The non-homogenous two-phase Buongiorno's nanofluids model is applied to investigate the convection process within cubic enclosures filled with homogenous/heterogeneous porous medium. The homogenous/heterogeneous properties are considered in the overall permeability and thermal conductivity of the porous elements. Different cases upon the type of the medium are considered, namely, homogeneous porous domain, heterogeneous porous domain in all directions, heterogeneous cavity with stratification in X - Y plane, heterogeneous cavity with stratification in X - Z plane and heterogeneous cavity with stratification in Y - Z plane. The worked mixture is Al 2 O 3 ewater nanofluid and the Brownian motion parameters, the thermophores parameter and the dynamic viscosity are variables. The SIMPLE algorithm together with the finite volume method are extended to the three dimensional case and applied to treat the governing equations. It is remarkable that the heterogeneous case in all directions (η 1 = η 2 = η 3 = 1.5) gives the largest values of the average Nusselt coefficient while the homogenous case has the lowest rate of the heat transfer. In all the considered porous cases, the growing in the Rayleigh and Darcy numbers enhances the average Nusselt number. [ABSTRACT FROM AUTHOR]

The flow and heat transfer fields of a nanofluid within V-shaped cavity are analyzed using the incompressible smoothed particle hydrodynamic (ISPH) scheme. Novel studies on a nanofluid-occupied V-shaped cavity with a partial layer heterogeneous porous medium were conducted. The bottom and top corners of the V-shaped enclosure have isothermal conditions while the remaining boundaries are considered adiabatic. Lengths of the heated and cold parts are assumed to be variables. The flow domain is filled with a partial layer porous medium. Three levels of the porous medium are taken into account, namely, horizontal heterogeneous, vertical heterogeneous and homogeneous porous media. Impacts of the wide ranges of the hot–cold partitions lengths L p (0.2 ≤ L p ≤ 1.5) , the nanoparticles volume fraction (0 % ≤ ϕ ≤ 5 %) , the Darcy number ( 10 - 2 ≤ D a ≤ 10 - 5 ) and the Rayleigh number ( 10 3 ≤ R a ≤ 10 5) on the features of the temperature and nanofluid flow are examined. The main outcomes disclosed that the average Nusselt number takes its maximum in case of the horizontal heterogeneous porous medium while the homogeneous porous medium case gives the lowest rate of the heat transfer. Therefore, for V-shaped cavity, the horizontal heterogeneous porous medium considers the best case of porous media. An augmentation on Rayleigh number rises the buoyancy force and accordingly the convective transport is enhanced. Further, the convective flow is enhanced as the hot–cold partitions lengths increase, regardless the porous case. [ABSTRACT FROM AUTHOR]

Numerical emulations are conducted to study the physical situation of a variable properties nanofluid inside enclosures with rough boundaries. Two cases are considered based on way of the heating in the enclosures, namely, case1 the enclosure is heated from inside using two heated and cross-section ellipsis at the center of the enclosure and case2 in which differentially heated enclosures are assumed. The numerical procedure which applied to solve the non-homogenous Buongiorno mathematical model is based on the control volume technique with SIMPLE algorithm. Wide ranges for the temperature differences, roughness parameter and Darcy number are considered and the dynamic viscosity of CuO nanofluid is expressed as a mathematical form of the temperature and nanoparticle volume fraction based on experimental results. The main results revealed that the average Nusselt is enhanced by 11% in case 1 and by 30% in case 2 when the temperature differences are increased by 10 °C. Also, the decrease in Darcy number causes that rate of the heat transfer is reduced regardless way of the heating. Moreover the increase in the roughness parameter reduces the maximum values of the stream function in all cases. [ABSTRACT FROM AUTHOR]

The main objective of this study is to simulate magnetohydrodynamics (MHD) ferro-convective flow in an inclined double-lid driven L-shaped enclosure with heated corners. The dimensionless forms of the partial governing equations are solved numerically using the Galerkin finite element method. The L-shaped enclosure is heated from the corner with variations on the heated lengths of the left and bottom walls. The other boundaries are insulated except the top and right boundaries of the L-walls, which are cooled with a lid-driven velocity. The magnetic field acts on the horizontal direction of an inclined L-shaped enclosure. Heat generation/absorption, shear forces through lid motion and magnetic forces are considered. Simulations are performed for several physical parameters including Richardson parameter Ri , an inclination angle α , Hartman parameter Ha , solid volume fraction ϕ and heat generation/absorption parameter Q. The results revealed that the isothermal distributions are increased strongly as the lengths of the heated corner increase. For a fixed value of the heat generation parameter (Q = 2) , the average Nusselt number is reduced by 4.66% when lengths of the active parts is varied from 0.2 to 0.8. Also, rate of the heat transfer is minimized by 30.66% in case of the ferrofluid with concentration 5% as the Hartmann number increases from 0 to 50. [ABSTRACT FROM AUTHOR]

This paper discusses the thermal stratification and suction/injection effects on the entropy generation and heat transfer due to convective boundary layer flow over a vertical stretching cylinder using Buongiorno's model for nanofluids. For the nanoparticle volume fraction, the boundary conditions are taken such that its normal fluxes are zero. The governing equations and the entropy equation are derived in cylindrical coordinates, in details. Similar transformations are used to convert the governing equation into ordinary differential equations and the resulting system is solved numerically using MATLAB function bvp4c. The obtained results are presented in terms of velocity profiles, temperature distributions, nanoparticle volume fraction, local entropy generation, skin friction coefficient and local Nusselt number. It is found that the minimum values of the entropy generation occur in the injection case, while the suction case maximizes the entropy generation. The increase in the thermal stratification parameter decreases the profiles of velocity temperature and nanoparticle volume fraction, while it enhances the entropy generation. [ABSTRACT FROM AUTHOR]

This paper discusses the problem of mixed convection in two-sided lid-driven enclosures saturated non-Darcy porous medium. The vertical walls of the cavity were kept thermally insulated. The bottom wall is cooled while the top wall is uniformly heated. The bottom and the top walls are moving in opposite direction. The governing equations were solved using finite volume method with SIMPLE algorithm. A new form for the heat function was derived. The obtained results were presented in contours maps for the streamlines, the isotherms and the heat function. The profiles of the horizontal velocity component and the maximum values of vertical velocity components as well as the mean Nusselt number were presented graphically. It is found that, for the low values of the Richardson number, the forced convection plays a dominant role in the flow region. The increase in inverse Darcy number leads to decrease the mean Nusselt number. [ABSTRACT FROM AUTHOR]

This paper discusses the magnetohydrodynamic rotating flow, heat and mass transfer of a laminar incompressible viscous electrically conducting fluid in the stagnation region of an impulsively rotating sphere in the presence of thermal radiation effect. Non-similar solution is presented and fourth order Runge–Kutta–Fehlberg method is used to solve the resulting non-similar equations. The results of the problem are presented in terms of velocity profiles in the x -direction, temperature distributions and concentration distributions as well as surface shear stresses in both x -and y -directions, heat transfer rate and mass transfer rate. It is found that the temperature distributions increases as the radiation parameter increases while the increase in the buoyancy ratio reduce the temperature distributions. Also, the rotation parameter has a positive effect on the flow, heat and mass transfer rates. Further, the increase in the buoyancy parameter causes an increase in the velocity profiles in velocity profiles in x -direction as well as the surface shear stress in the x -direction and rate of heat transfer. [ABSTRACT FROM AUTHOR]

This paper discusses the phenomenon of natural convection flow in an inclined, partially open enclosure filled with Al2O3-water nanofluid. In the cavity, the horizontal walls and the closed portions of the right wall are thermally insulated. Three thermal cases were considered for the left wall; in the first case, the left wall was considered to be uniformly heated; in the second case, a heat source was attached to the left wall; and in the third, the left wall had a heat sink. For case 2, there is a heat source attached to the left wall. For case 3, the left wall contains a heat sink. The partial differential equations governing the problem were solved numerically using the finite difference method. The obtained results were presented by the local Nusselt number, the average Nusselt number, streamlines, and isotherms with various pertinent parameters, namely, the Rayleigh number (10³≤Ra≤106), the solid volume fraction (0≤ϕ≤0.2), different lengths of the heat source/sink (0.2≤BL≤1), different locations of the heat source/sink (0.2≤bL≤0.8), different lengths of the aperture (0.2≤BR≤1.0), different locations of the aperture (0.2≤bR≤0.8), and an inclination angle (0deg≤ϑ≤π). It is found that, for all cases, the fluid features were strongly affected by changing the aperture length or the aperture location. Also, a clear increase in the mean Nusselt number could be obtained by increasing the Rayleigh number. Moreover, an enhancement in the average Nusselt number was found by increasing the nanoparticle volume fraction. A good natural convection could be obtained by increasing the heat source/sink length. Title the cavity by 60 deg leads to increase the absolute values of the stream function and a decrease in the maximum values of the maximum temperature. The best location of the heat source was found to be at the top of the left wall, whereas the best position of the aperture was found to be at the top of the right wall. [ABSTRACT FROM AUTHOR]

This paper aims to analyze the second law of the thermodynamic for the non-Newtonian power-law nanofluids flow between inclined polygonal/polygonal or polygonal/cylinder shapes. Multi-wall carbon nanotubes are incorporated in the ethylene glycol as a base fluid to formulate the worked suspension. Electromagnetic forces together with the thermal radiation are taken into account. Unusually, the magnetic field is assumed to be horizontal while the flow domain is inclined and a semi implicit treatment is presented for the magnetic terms. The solution methodology is depending on the Galerkin finite element method (FEM) and the Characteristic-Based Split (CBS) scheme. Various designs for the considered models are considered based on the areas and shapes of the inner polygonal/cylinder. The main outcomes revealed that area of the flow and power-law index N control in the convective and heat transfer process. Also, the fluid friction irreversibility takes its maximum values at high values of the power-law index. Furthermore, ratios of the increase in values of the entropy tools (S T + , S F + , S tot +) due to the variations of γ take their maximum at γ = 30 and low values of Ha. [ABSTRACT FROM AUTHOR]

A collocated finite volume method based simulation is performed to analyze the heat transfer enhancement in two-sided lid-driven cavities with the heat source embedded in the left side wall using Al2O3-water nanofluid. Four cases were considered depending on the direction of the movement of the walls. The relevant parameters in the present study are Richardson number (Ri=0.1-100), nanoparticles volume fraction (φ=0-4%), the heat source length (B=0.2, 0.4, 0.6, 0.8), and Reynolds number (Re=10−316.2278). Comparisons with previously published work on the bases of special cases are performed and found to be in an excellent agreement. It is found that the fluid flow and heat transfer characteristics depend strongly on the direction of the horizontal walls movement. Also, significant heat transfer enhancement can be obtained due to the presence of nanoparticles. [ABSTRACT FROM AUTHOR]

This work focuses on the numerical modeling of a steady, laminar natural convection flow in a triangular enclosure partially heated from below and with a cold inclined wall filled with Cu-water nanofluid having variable thermal conductivity and viscosity. The problem is formulated in terms of the vortices stream function formulation and the resulting governing equations are solved numerically using an efficient finite difference method. Various results for the streamline and isotherm contours, as well as the local and average Nusselt numbers, are presented for a wide range of Rayleigh numbers and volume fractions of nanoparticles. Different behaviors (enhancement or deterioration) are predicted in the average Nusselt number as the volume fraction of nanoparticles changes. The placement and length of the heat source along the bottom wall is observed to have significant effects on the behavior of the average Nusselt number. [ABSTRACT FROM AUTHOR]

In this work, the problem of transient MHD double-diffusive natural convection flow of a Newtonian fluid in a rectangular enclosure with linearly heated and concentrated walls in the presence of heat generation or absorption effects is investigated. The finite-difference method is employed to solve the dimensionless governing equations of the problem. The effects of governing parameters, namely the Hartmann number, Lewis number, buoyancy parameter and the heat generation or absorption parameter on the streamlines, isotherm and iso-concentration contours as well as the velocity components, local Nusselt number and the local Sherwood number are studied. Two cases are considered. The first case is when the cavity has both vertical walls heated and concentrated and the second case when the cavity has only its left wall heated and concentrated while the right wall is cooled and has no mass. The present results are validated by favourable comparisons with previously published results. All results are presented graphically and discussed. [ABSTRACT FROM AUTHOR]

The problem of unsteady Magnetohydrodynamic (MHD) flow with heat and mass transfer near the stagnation point of a three-dimensional (3D) porous body in the presence of heat source/sink and chemical reaction effect has been studied numerically using an efficient iterative implicit finite-difference method. The numerical results are validated by favourable comparisons with previously published work. Three forms for the free stream velocity distributions namely a constantly accelerating flow, a periodic fluctuating flow and an exponentially decelerating flow are considered. Numerical results for the velocity components in the x-and y-directions, temperature distribution and concentration distribution as well as the skin-friction coefficients and the Nusselt and Sherwood numbers are presented graphically for various parametric conditions and discussed. [ABSTRACT FROM AUTHOR]