Circular rotation of different structures on natural convection of nanofluid-mobilized circular cylinder cavity saturated with a heterogeneous porous medium.

The incompressible smoothed particle hydrodynamics (ISPH) method is utilized for studying the circular rotations of three different structures, circular cylinder, rectangle and triangle centered in a circular cylinder cavity occupied by Al2O3 nanofluid. The novelty of this work is appearing in simulating the circular rotations of different solid structures on natural convection of a nanofluid-occupied a circular cylinder. The circular cylinder cavity is suspended by heterogeneous/homogeneous porous media. The embedded structures are taken as a circular cylinder, rectangle and triangle with equal areas. The first thermal condition considers the whole structure is heated, the second thermal condition considers the half of the structure is heated and the other is cooled and the third thermal condition considers the quarter of the structure is heated and the others are cooled. The outer boundary of cylinder cavity is cooled. Due to the small angular velocity ω=3.15 (low rotational speeds), then the natural convection case will be considered only. The results are representing the temperature, velocity fields. The simulations revealed that the presence of the inner hot/cold structures affects on the velocity distributions and temperature field inside a circular cylinder cavity. The triangle shape has introduced the highest temperature distributions and maximum values of the velocity fields compare to other shapes inside a circular cylinder cavity. The homogeneous porous level reduces the maximum values of velocity field by 25% compared to the heterogeneous porous level.

A Comprehensive Review of Nanofluid Heat Transfer in Porous Media.

In the present paper, recent advances in the application of nanofluids in heat transfer in porous materials are reviewed. Efforts have been made to take a positive step in this field by scrutinizing the top papers published between 2018 and 2020. For that purpose, the various analytical methods used to describe the flow and heat transfer in different types of porous media are first thoroughly reviewed. In addition, the various models used to model nanofluids are described in detail. After reviewing these analysis methods, papers concerned with the natural convection heat transfer of nanofluids in porous media are evaluated first, followed by papers on the subject of forced convection heat transfer. Finally, we discuss articles related to mixed convection. Statistical results from the reviewed research regarding the representation of various parameters, such as the nanofluid type and the flow domain geometry, are analyzed, and directions for future research are finally suggested. The results reveal some precious facts. For instance, a change in the height of the solid and porous medium results in a change in the flow regime within the chamber; as a dimensionless permeability, the effect of Darcy's number on heat transfer is direct; and the effect of the porosity coefficient has a direct relationship with heat transfer: when the porosity coefficient is increased or decreased, the heat transfer will also increase or decrease. Additionally, a comprehensive review of nanofluid heat transfer in porous media and the relevant statical analysis are presented for the first time. The results show that Al2O3 nanoparticles in a base fluid of water with a proportion of 33.9% have the highest representation in the papers. Regarding the geometries studied, a square geometry accounted for 54% of the studies.

Dissipative MHD free convective nanofluid flow past a vertical cone under radiative chemical reaction with mass flux.

Recently, Nanoparticles have supplied diverse challenges to several scientific issues. Nanoparticles dispersed in a variety of conventional fluids can change the flow and heat transmission properties of the fluids. The mathematical technique is used in this work to investigate the MHD water-based nanofluid flow via an upright cone. The heat and mass flux pattern is used in this mathematical model to examine MHD, viscous dissipation, radiation, chemical reactions and suction/injection processes. The finite difference approach was used to find the solution to the basic governing equations. A combination of nanofluids comprising nanoparticles including aluminum oxide (Al[Formula: see text]O[Formula: see text]), silver (Ag), copper (Cu) and titanium dioxide (TiO[Formula: see text]) with a volume fraction of nanoparticles (0, 0.01, 0.02, 0.03, 0.04), viscous dissipation ([Formula: see text]), MHD (M = 0.5, 1.0), radiation (Rd = 0.4, 1.0, 2.0), chemical reaction ([Formula: see text]) and heat source/sink ([Formula: see text]) . The mathematical findings of velocity, temperature, concentration, skin friction, heat transfer rate as well as Sherwood number distributions are analyzed diagrammatically using non-dimensional flow parameters. It has been discovered that by increasing the value of the radiation parameter, velocity and temperature profiles enhance. The production of safe, high-quality products for consumers across the world depends on vertical cone mixers, from food to medicine, household cleansers to personal hygiene products. Every vertical cone mixer type we provide was especially developed to meet the demands of industry. As the mixer warms up on the slanted surface of the cone while vertical cone mixers are being utilized, the effectiveness of the grinding may be felt. The temperature is transferred along the cone's slant surface as a consequence of the mixture being mixed quickly and repeatedly. This study describes the heat transmission in these events and their parametric properties. The heated cone's temperature is then convective to its surroundings.

Coupled plasmons in aluminum nanoparticle superclusters.

Metallic nanoparticles can self-assemble into highly ordered superclusters for potential applications in optics and catalysis. Here, using first-principles quantum mechanical calculations, we investigate plasmon coupling in superclusters made of aluminum nanoparticles. More specifically, we study/compare the plasmon coupling in close-pack FCC (face-centered-cubic) and non-close-pack BCC (body-centered-cubic) superclusters. We demonstrate that the optical properties of these clusters can be fine-tuned with respect to the packing arrangement. As a key result of this work, plasmon coupling is found to be enhanced (diminished) in FCC (BCC) superclusters due to constructive (destructive) plasmon coupling. Our quantum calculations would help in the design of Al-based superclusters beneficial for plasmonics applications.

Analysis of entropy production in a bi-convective magnetized and radiative hybrid nanofluid flow using temperature-sensitive base fluid (water) properties.

The heat transport characteristics, flow features, and entropy-production of bi-convection buoyancy induced, radiation-assisted hydro-magnetic hybrid nanofluid flow with thermal sink/source effects are inspected in this study. The physical characteristics of hybrid nanofluids (water-hosted) are inherited from the base liquid (water) and none has considered the physical characteristics of base liquid (water) in the study of temperature-sensorial hybrid nanofluid investigations, though the water physical characteristics are not constants in temperature variations. So, the temperature-sensorial attributes of base liquid (water) are taken into account for this hybrid nanofluid ([Formula: see text]) flow analysis. The mathematical forms of the flow configuration (i.e., the set of coupled, nonlinear PDE form of governing equations) are solved by utilizing the subsequent tasks: (i) congenial transformation; (ii) quasilinearization; (iii) methods of finite differences to form block matrix system, and (iv) Varga's iterative algorithm. The preciseness of the whole numerical procedure is ensured by restricting the computation to follow strict convergence conditions. Finally, the numerically extracted results representing the impacts of various salient parameters on different profiles ([Formula: see text]), gradients, and entropy production are exhibited in physical figures for better perception. A few noticeable results are highlighted as: velocity graph shows contrast behaviour under assisting and opposing buoyancy; temperature ([Formula: see text]) is dropping for heightening heat source ([Formula: see text]) surface friction remarkably declines with the outlying magnetic field ([Formula: see text]); thermal transport confronts drastic abatement under radiation ([Formula: see text]), and [Formula: see text]; the characteristics Reynolds and Brinkman numbers promote entropy. Furthermore, the bounding surface acts as a strong source of [Formula: see text]-production. Summarizations are listed at the end to quantify percentage variations.

Three-Dimensional Study of Magnetohydrodynamic Natural Convection, Entropy Generation, and Electromagnetic Variables in a Nanofluid Filled Enclosure Equipped with Inclined Fins.

This article provides a numerical study on carbon nanotube-water nanofluid convection in a three-dimensional cavity under a magnetic field effect. Two walls are kept at a hot temperature, and the upper and lower horizontal walls are considered adiabatic. As a new configuration, the beneficial effect of using a nanofluid is coupled with the incorporation of cold V-shape obstacle placed in the cubic cavity; in addition, an external magnetic field is applied toward the horizontal x-axis direction. The finite element method based on the Galerkin's Weighted Residual technique is used to solve the three-dimensional governing equations. In this paper, the ranges of the parameters used are the Hartmann number, varied from 0 to 100, Rayleigh number from 103 to 105, nanofluid volume fraction between 0% and 4.5%, and the body V-shaped opening angle varied from 0 to 80°. The effect of the obstacle shape and the added nanoparticle concentration on the flow behaviors, the different instabilities generated, and the heat transfer exchanged were exposed. An enhancement in heat transfer was recorded by increasing the obstacle opening angle and the volume fraction of the carbon nanotubes. Special attention has also been devoted to the calculation of the different kinds of entropy generations.

Significance of Rosseland's Radiative Process on Reactive Maxwell Nanofluid Flows over an Isothermally Heated Stretching Sheet in the Presence of Darcy-Forchheimer and Lorentz Forces: Towards a New Perspective on Buongiorno's Model.

This study aimed to investigate the consequences of the Darcy-Forchheimer medium and thermal radiation in the magnetohydrodynamic (MHD) Maxwell nanofluid flow subject to a stretching surface. The involvement of the Maxwell model provided more relaxation time to the momentum boundary layer formulation. The thermal radiation appearing from the famous Rosseland approximation was involved in the energy equation. The significant features arising from Buongiorno's model, i.e., thermophoresis and Brownian diffusion, were retained. Governing equations, the two-dimensional partial differential equations based on symmetric components of non-Newtonian fluids in the Navier-Stokes model, were converted into one-dimensional ordinary differential equations using transformations. For fixed values of physical parameters, the solutions of the governing ODEs were obtained using the homotopy analysis method. The appearance of non-dimensional coefficients in velocity, temperature, and concentration were physical parameters. The critical parameters included thermal radiation, chemical reaction, the porosity factor, the Forchheimer number, the Deborah number, the Prandtl number, thermophoresis, and Brownian diffusion. Results were plotted in graphical form. The variation in boundary layers and corresponding profiles was discussed, followed by the concluding remarks. A comparison of the Nusselt number (heat flux rate) was also framed in graphical form for convective and non-convective/simple boundary conditions at the surface. The outcomes indicated that the thermal radiation increased the temperature profile, whereas the chemical reaction showed a reduction in the concentration profile. The drag force (skin friction) showed sufficient enhancement for the augmented values of the porosity factor. The rates of heat and mass flux also fluctuated for various values of the physical parameters. The results can help model oil reservoirs, geothermal engineering, groundwater management systems, and many others.

Impact of packing arrangement on the optical properties of C60 cluster aggregates.

The packing arrangement of organic π-conjugated molecules in a nanoscale material can have a strong impact on their optical properties. Here, using real-time-propagation time dependent density functional theory (rt-TDDFT) calculations with the support of transition contribution maps, we study how modifications in the packing arrangement (cubic-like and chain-like aggregates composed of eight C60 molecules) and packing density (assembled at close distances with center-to-center inter-fullerene distances (d) varying from 9 Å to 11 Å) of C60 molecules affect the optical properties of cluster aggregates. The important conclusions drawn from this work are summarized as follows. For d = 9 Å, the charge transfer excitons produced by cubic and chain-like C60 cluster aggregates have highly different optical characteristics, as evidenced by the transition contribution maps. On the other hand, for d = 10 Å and 11 Å, both kinds of aggregates produce qualitatively similar optical features with the emergence of Wannier-like delocalized excitons having distinct degrees of localization and spatial distribution. The theoretical findings in this study elucidate the optical excitations in C60 cluster aggregates and could help in the design of more efficient organic devices.

Entropy production and mixed convection within trapezoidal cavity having nanofluids and localised solid cylinder.

The entropy production and mixed convection within a trapezoidal nanofluid-filled cavity having a localised solid cylinder is numerically examined using the finite element technique. The top horizontal surface moving at a uniform velocity is kept at a cold temperature, while the bottom horizontal surface is thermally activated. The remaining surfaces are maintained adiabatic. Water-based nanofluids ([Formula: see text] nanoparticles) are used in this study, and the Boussinesq approximation applies. The influence of the Reynolds number, Richardson number, nanoparticles volume fraction, dimensionless radius and location of the solid cylinder on the streamlines, isotherms and isentropic are examined. The results show that the solid cylinder's size and location are significant control parameters for optimising the heat transfer and the Bejan number inside the trapezoidal cavity. Furthermore, the maximum average Nusselt numbers are obtained for high R values, where the average Nusselt number is increased by 30% when R is raised from 0 to 0.25.

Impacts of Amplitude and Local Thermal Non-Equilibrium Design on Natural Convection within NanoflUid Superposed Wavy Porous Layers.

A numerical study is presented for the thermo-free convection inside a cavity with vertical corrugated walls consisting of a solid part of fixed thickness, a part of porous media filled with a nanofluid, and a third part filled with a nanofluid. Alumina nanoparticle water-based nanofluid is used as a working fluid. The cavity's wavy vertical surfaces are subjected to various temperature values, hot to the left and cold to the right. In order to generate a free-convective flow, the horizontal walls are kept adiabatic. For the porous medium, the Local Thermal Non-Equilibrium (LTNE) model is used. The method of solving the problem's governing equations is the Galerkin weighted residual finite elements method. The results report the impact of the active parameters on the thermo-free convective flow and heat transfer features. The obtained results show that the high Darcy number and the porous media's low modified thermal conductivity ratio have important roles for the local thermal non-equilibrium effects. The heat transfer rates through the nanofluid and solid phases are found to be better for high values of the undulation amplitude, the Darcy number, and the volume fraction of the nanofluid, while a limit in the increase of heat transfer rate through the solid phase with the modified thermal ratio is found, particularly for high values of porosity. Furthermore, as the porosity rises, the nanofluid and solid phases' heat transfer rates decline for low Darcy numbers and increase for high Darcy numbers.

Impact of two-phase hybrid nanofluid approach on mixed convection inside wavy lid-driven cavity having localized solid block.

INTRODUCTION: Mixed convection flow and heat transfer within various cavities including lid-driven walls has many engineering applications. Investigation of such a problem is important in enhancing the performance of the cooling of electric, electronic and nuclear devices and controlling the fluid flow and heat exchange of the solar thermal operations and thermal storage. OBJECTIVES: The main aim of this fundamental investigation is to examine the influence of a two-phase hybrid nanofluid approach on mixed convection characteristics including the consequences of varying Richardson number, number of oscillations, nanoparticle volume fraction, and dimensionless length and dimensionless position of the solid obstacle. METHODS: The migration of composite hybrid nanoparticles due to the nano-scale forces of the Brownian motion and thermophoresis was taken into account. There is an inner block near the middle of the enclosure, which contributes toward the flow, heat, and mass transfer. The top lid cover wall of the enclosure is allowed to move which induces a mixed convection flow. The impact of the migration of hybrid nanoparticles with regard to heat transfer is also conveyed in the conservation of energy. The governing equations are molded into the non-dimensional pattern and then explained using the finite element technique. The effect of various non-dimensional parameters such as the volume fraction of nanoparticles, the wave number of walls, and the Richardson number on the heat transfer and the concentration distribution of nanoparticles are examined. Various case studies for Al2O3-Cu/water hybrid nanofluids are performed. RESULTS: The results reveal that the temperature gradient could induce a notable concentration variation in the enclosure. CONCLUSION: The location of the solid block and undulation of surfaces are valuable in the control of the heat transfer and the concentration distribution of the composite nanoparticles.

Free Energy Surfaces and Barriers for Vacancy Diffusion on Al(100), Al(110), Al(111) Reconstructed Surfaces.

Metadynamics is a popular enhanced sampling method based on the recurrent application of a history-dependent adaptive bias potential that is a function of a selected number of appropriately chosen collective variables. In this work, using metadynamics simulations, we performed a computational study for the diffusion of vacancies on three different Al surfaces [reconstructed Al(100), Al(110), and Al(111) surfaces]. We explored the free energy landscape of diffusion and estimated the barriers associated with this process on each surface. It is found that the surfaces are unique regarding vacancy diffusion. More specically, the reconstructed Al(110) surface presents four metastable states on the free energy surface having sizable and connected passage-ways with an energy barrier of height 0.55 eV. On the other hand, the reconstructed Al(100)/Al(111) surfaces exhibit two/three metastable states, respectively, with an energy barrier of height 0.33 eV. The findings in this study can help to understand surface vacancy diffusion in technologically relevant Al surfaces.

Entropy Generation and Mixed Convection Flow Inside a Wavy-Walled Enclosure Containing a Rotating Solid Cylinder and a Heat Source.

The current study investigates the 2D entropy production and the mixed convection inside a wavy-walled chamber containing a rotating cylinder and a heat source. The heat source of finite-length h is placed in the middle of the left vertical surface in which its temperature is fixed at T h . The temperature of the right vertical surface, however, is maintained at lower temperature T c . The remaining parts of the left surface and the wavy horizontal surfaces are perfectly insulated. The governing equations and the complex boundary conditions are non-dimensionalized and solved using the weighted residual finite element method, in particular, the Galerkin method. Various active parameters are considered, i.e., Rayleigh number R a = 10 3 and 10 5 , number of oscillations: 1 ≤ N ≤ 4 , angular rotational velocity: - 1000 ≤ Ω ≤ 1000 , and heat source length: 0 . 2 ≤ H ≤ 0 . 8 . A mesh independence test is carried out and the result is validated against the benchmark solution. Results such as stream function, isotherms and entropy lines are plotted and we found that fluid flow can be controlled by manipulating the rotating velocity of the circular cylinder. For all the considered oscillation numbers, the Bejan number is the highest for the case involving a nearly stationary inner cylinder.

Natural convection of [Formula: see text]-water nanofluid in a non-Darcian wavy porous cavity under the local thermal non-equilibrium condition.

This study investigates thermal natural convective heat transfer in a nanofluid filled-non-Darcian porous and wavy-walled domain under the local thermal non-equilibrium condition. The considered cavity has corrugated and cold vertical walls and insulated horizontal walls except the heated part positioned at the bottom wall. The transport equations in their non-dimensional model are numerically solved based on the Galerkin finite-element discretization technique. The dimensionless governing parameters of the present work are the nanoparticle in volume concentration, the Darcy number, number of undulations, modified heat conductivity ratio, dimensionless heated part length, and location. Comparisons with other published theoretical and experimental results show good agreement with the present outcomes. The findings indicate that the heater length, its position, and the waves number on the side vertical walls as well as the nanoparticles concentration can be the control parameters for free convective motion and heat transport within the wavy cavity.

Effects of a Rotating Cone on the Mixed Convection in a Double Lid-Driven 3D Porous Trapezoidal Nanofluid Filled Cavity under the Impact of Magnetic Field.

Effects of a rotating cone in 3D mixed convection of CNT-water nanofluid in a double lid-driven porous trapezoidal cavity is numerically studied considering magnetic field effects. The numerical simulations are performed by using the finite element method. Impacts of Richardson number (between 0.05 and 50), angular rotational velocity of the cone (between -300 and 300), Hartmann number (between 0 and 50), Darcy number (between 10 - 4 and 5 × 10 - 2 ), aspect ratio of the cone (between 0.25 and 2.5), horizontal location of the cone (between 0.35 H and 0.65 H) and solid particle volume fraction (between 0 and 0.004) on the convective heat transfer performance was studied. It was observed that the average Nusselt number rises with higher Richardson numbers for stationary cone while the effect is reverse for when the cone is rotating in clockwise direction at the highest supped. Higher discrepancies between the average Nusselt number is obtained for 2D cylinder and 3D cylinder configuration which is 28.5% at the highest rotational speed. Even though there are very slight variations between the average Nu values for 3D cylinder and 3D cone case, there are significant variations in the local variation of the average Nusselt number. Higher enhancements in the average Nusselt number are achieved with CNT particles even though the magnetic field reduced the convection and the value is 84.3% at the highest strength of magnetic field. Increasing the permeability resulted in higher local and average heat transfer rates for the 3D porous cavity. In this study, the aspect ratio of the cone was found to be an excellent tool for heat transfer enhancement while 95% enhancements in the average Nusselt number were obtained. The horizontal location of the cone was found to have slight effects on the Nusselt number variations.

Numerical study of heat generating γ Al 2 O 3 - H 2 O nanofluid inside a square cavity with multiple obstacles of different shapes.

A numerical research on uniformly heat generating γ Al 2 O 3 -H 2 O nanofluid filled square cavity with multiple obstacles of different shapes is carried out. The cavity is assumed to be heated at bottom and cooled by vertical walls with linearly varying temperature. An adiabatic condition is assumed at the top of the cavity. Circular, square and triangular shaped obstacles are considered. The mathematical model has been solved using Galerkin finite element method. Results are presented for streamlines, isotherms, local and mean Nusselt numbers. Multiple rotating cells are observed in the streamlines. It is found that the local and mean Nusselt numbers increase with nanoparticle volume fraction and higher heat transfer is achieved in the cavity with triangular obstacles.

Entropy Generation and Consequences of Binary Chemical Reaction on MHD Darcy-Forchheimer Williamson Nanofluid Flow Over Non-Linearly Stretching Surface.

The current article aims to present a numerical analysis of MHD Williamson nanofluid flow maintained to flow through porous medium bounded by a non-linearly stretching flat surface. The second law of thermodynamics was applied to analyze the fluid flow, heat and mass transport as well as the aspects of entropy generation using Buongiorno model. Thermophoresis and Brownian diffusion is considered which appears due to the concentration and random motion of nanoparticles in base fluid, respectively. Uniform magnetic effect is induced but the assumption of tiny magnetic Reynolds number results in zero magnetic induction. The governing equations (PDEs) are transformed into ordinary differential equations (ODEs) using appropriately adjusted transformations. The numerical method is used for solving the so-formulated highly nonlinear problem. The graphical presentation of results highlights that the heat flux receives enhancement for augmented Brownian diffusion. The Bejan number is found to be increasing with a larger Weissenberg number. The tabulated results for skin-friction, Nusselt number and Sherwood number are given. A decent agreement is noted in the results when compared with previously published literature on Williamson nanofluids.

Entropy Generation Analysis and Natural Convection in a Nanofluid-Filled Square Cavity with a Concentric Solid Insert and Different Temperature Distributions.

The problem of entropy generation analysis and natural convection in a nanofluid square cavity with a concentric solid insert and different temperature distributions is studied numerically by the finite difference method. An isothermal heater is placed on the bottom wall while isothermal cold sources are distributed along the top and side walls of the square cavity. The remainder of these walls are kept adiabatic. Water-based nanofluids with Al 2 O 3 nanoparticles are chosen for the investigation. The governing dimensionless parameters of this study are the nanoparticles volume fraction ( 0 ≤ ϕ ≤ 0.09 ), Rayleigh number ( 10 3 ≤ R a ≤ 10 6 ) , thermal conductivity ratio ( 0.44 ≤ K r ≤ 23.8 ) and length of the inner solid ( 0 ≤ D ≤ 0.7 ). Comparisons with previously experimental and numerical published works verify a very good agreement with the proposed numerical method. Numerical results are presented graphically in the form of streamlines, isotherms and local entropy generation as well as the local and average Nusselt numbers. The obtained results indicate that the thermal conductivity ratio and the inner solid size are excellent control parameters for an optimization of heat transfer and Bejan number within the fully heated and partially cooled square cavity.

Numerical Investigation of Mixed Convection and Entropy Generation in a Wavy-Walled Cavity Filled with Nanofluid and Involving a Rotating Cylinder.

This numerical study considers the mixed convection and the inherent entropy generated in Al 2 O 3 -water nanofluid filling a cavity containing a rotating conductive cylinder. The vertical walls of the cavity are wavy and are cooled isothermally. The horizontal walls are thermally insulated, except for a heat source segment located at the bottom wall. The dimensionless governing equations subject to the selected boundary conditions are solved numerically using the Galerkin finite-element method. The study is accomplished by inspecting different ranges of the physical and geometrical parameters, namely, the Rayleigh number ( 10 3 ≤ R a ≤ 10 6 ), angular rotational velocity ( 0 ≤ Ω ≤ 750 ), number of undulations ( 0 ≤ N ≤ 4 ), volume fraction of Al 2 O 3 nanoparticles ( 0 ≤ ϕ ≤ 0.04 ), and the length of the heat source ( 0.2 ≤ H ≤ 0.8 ) . The results show that the rotation of the cylinder boosts the rate of heat exchange when the Rayleigh number is less than 5 × 10 5 . The number of undulations affects the average Nusselt number for a still cylinder. The rate of heat exchange increases with the volume fraction of the Al 2 O 3 nanoparticles and the length of the heater segment.

MHD Free Convection and Entropy Generation in a Corrugated Cavity Filled with a Porous Medium Saturated with Nanofluids.

MHD free convection inside a triangular-wave-shaped corrugated porous cavity with Cu-water nanofluid is numerically studied with the finite element method. The influences of the Grashof number ( 10 4 ≤ Gr ≤ 10 6 ), Hartmann number ( 0 ≤ Ha ≤ 50 ), Darcy number ( 10 - 4 ≤ Da ≤ 10 - 1 ) and solid volume fraction of the nanoparticle ( 0 ≤ ϕ ≤ 0.05 ) on the convective flow features are examined. It is observed that increasing the Grashof number and Darcy number enhances the heat transfer, while the effect is opposite for the Hartmann number. As the corrugation frequency of the triangular wave increases, the local and averaged heat transfer rates decrease, which is more effective for higher values of Grashof and Darcy numbers. Normalized total entropy generation increases as the Darcy number and solid volume fraction of the nanoparticles increase and decreases as the Hartmann number increases both for flat and corrugated wall configurations.