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This review is about non-Newtonian nanofluid applications for convection in cavities under a magnetic field. Convection in cavities is an important topic in thermal energy system, and diverse applications exist in processes such as drying, chemical processing, electronic cooling, air conditioning, removal of contaminates, power generation and many others. Some problems occur in symmetrical phenomena, while they can be applicable to applied mathematics, physics and thermal engineering systems. First, brief information about nanofluids and non-Newtonian fluids is given. Then, non-Newtonian nanofluids and aspects of rheology of non-Newtonian fluids are presented. The thermal conductivity/viscosity of nanofluids and hybrid nanofluids are discussed. Applications of non-Newtonian nanofluids with magnetohydrodynamic effects are given. Different applications of various vented cavities are discussed under combined effects of using nanofluid and magnetic field for Newtonian and non-Newtonian nanofluids. The gap in the present literature and future trends are discussed. The results summarized here will be beneficial for efficient design and thermal optimization of vented cavity systems used in diverse energy system applications. [ABSTRACT FROM AUTHOR]

Natural convection heat transfer phenomena in nanofluid-filled square cavities with various temperature boundary conditions are studied computationally. From electronic cooling to building ventilation systems, such phenomena have numerous practical applications, and accurate simulations are crucial for developing new designs. Towards that end, the Navier–Stokes equations of incompressible flows are considered with thermal coupling. The base fluid is pure water, the nanoparticles are copper (Cu), cupric oxide (CuO), or aluminum oxide (Al 2 O 3), and the nanofluids are assumed to be homogeneous. It is well known that, in the standard finite element method framework, inappropriate selection of interpolation functions, e.g., (bi-)linear equal-order-interpolation velocity-pressure (e.g., P 1 P 1 and Q 1 Q 1) elements, yields nonphysical oscillations in the flow field for simulating incompressible flows, particularly for high Rayleigh numbers. In this study, in order to overcome such numerical instability issues, the streamline-upwind/Petrov–Galerkin (SUPG) and pressure-stabilizing/Petrov–Galerkin (PSPG) finite element formulations are utilized. The SUPG/PSPG-stabilized (SUPS) formulation is also enhanced with the least-squares on incompressibility constraint (LSIC). A comprehensive set of numerical test computations is considered for the values of the Rayleigh numbers ranging from 10 3 to 10 6 and a broad range of volume fractions of nanoparticles from ϕ = 0.025 to ϕ = 0.2. Incompressible flow solvers are developed in-house and executed in parallel. Numerical simulations and comparisons with reported studies reveal that the proposed formulation performs quite well even at high Rayleigh numbers, and it does not exhibit any significant local or globally spread numerical instabilities. It is also noted that this is achieved without employing any adaptive mesh strategies and using only linear and equal-order interpolation functions, which in turn saves computational time. [ABSTRACT FROM AUTHOR]

This work examines steady convection heat transfer and entropy generation in a wavy cubical container with Al2O3-water nanofluid and the solid cylinder. An isothermal embedded heater of finite width is located within the left vertical surface center of the container. All surfaces are insulated, except that the right wavy surface is kept cold, and the left wall is partially heated. The Boussinesq approximation is assumed, and three-dimensional simulations of governing equations have been applied to utilize the Galerkin weighted residual finite-element approach. Numerical results for the three-dimensional patterns of nanofluid flow, iso-temperature surfaces, and isentropic lines are given. The local Nusselt number adjacent to the left and interface surfaces within the container and solid cylinder and Bejan number have been examined for different values of the Rayleigh number, nanoparticle volume fraction, number of undulations and heater length, and cylinder radius. The results indicate that the optimal local heat transfer between the solid cylinder and container declines with the increased cylinder radius, which yields an imperfect nanofluid flow circulation. [ABSTRACT FROM AUTHOR]

Current communication candidly explicates the incremental aspect of generated entropy in apermeablesquare enclosure. Porosity aspects are mathematically formulated by Darcy-Forchheimer model, whereas the Lorentz force law is manifested to enclose magnetic field effectiveness. Water is capitalized as base fluid and nanoparticles composed of silver with different nanoparticles volume fractions are obliged. Thermal buoyancy is generated within the flow domain by provision of heat to left boundary. Description about physical modeling of the problem is manipulated in the form of PDEs with boundary constraints. Finite element procedure is used as a solution procedure to sort out the characteristics of flow problem. Variation in thermophysical attributes is presented through stream patterns, isothermal plots against flow contributing variables. Convective heat transfer through boundaries is measured through Nusselt number calculations. [ABSTRACT FROM AUTHOR]

• Wall elasticity and porosity of the channel with TEG installed system are studied. • When porous layer height and permeability are increased, TEG power rises up to 32%. • The length of porous layer in the flow direction has slight impact on TEG power. • 15% increment of TEG power is obtained with nanofluid. • Computational cost is reduced from 2.5 h to 2 min with the multi-POD method. Effects of wall elasticity and porosity of the channel on the performance characteristics of TEG module integrated system are explored numerically with finite element method. A porous layer in the lower channel is introduced with hybrid nanoparticles in the fluid. Effects of different values of elastic modulus of the top and bottom channel walls (5 × 10 3 ≤ E 1 , E 2 ≤ 10 10), Darcy number (5 × 10 − 4 ≤ Da ≤ 5 × 10 − 1 ), porous layer height (0.2H ≤ py ≤ 0.8H) and length in flow direction (0.25L ≤ px ≤ 0.85L), Reynolds number (200 ≤ Re ≤ 1000) and hybrid nanoparticle volume fraction (0 ≤ ϕ ≤ 2 %) on the convection and power generation are analyzed. The presence of elastic walls may affect the flow field in local regions but the overall impact on the power variation is slight while 2.8 % variation is obtained. The presence of the porous layer altered the power generation features while increasing the permeability and height of the porous layer resulted in higher thermoelectric power generation. The increment amounts are 32 % for the highest permeability and 17 % for the highest porous layer height. The length of porous layer in the flow direction has slight impact on power generation features while introducing nano-sized particles further enhanced the power by about 15 % at the highest ϕ. The computational cost of generated power is drastically reduced from 2.5 h for full coupled model to two minutes by using a multi-POD approach. [ABSTRACT FROM AUTHOR]

The problem of steady natural convection in a bottom-heated semi-elliptical enclosure has been investigated numerically for a wide range of geometric and flow configurations using the finite volume method. The results are presented for varying Rayleigh numbers, Ra, in the range 1 × 102 ≤ Ra ≤ 5 × 104 and different values of aspect ratio, A = 1, 0.75, 0.5, and 0.25, where the aspect ratio, A, is defined as the ratio of lengths of the semi-minor axis to the semi-major axis of the semi-elliptical enclosure. It has been found that the steady-state solution appears in the form of single or multiple pairs of counter-rotating convection cells depending on the values of physical parameters. For A = 1, 0.75, and 0.5, as the value of Rayleigh number exceeds a critical value, natural convective flow inside the semi-elliptical enclosure exhibits multiple steady solutions with varying pairs of counter-rotating convection cells; however, such multiplicity of steady solutions could not be found for the cases of A = 0.25. The parametric variations of heat transfer and entropy generation rates are studied in detail. It is observed that the average Nusselt number associated with the natural convection in the semi-elliptical cavity is governed by several parameters: aspect ratio, Rayleigh number, number of convection cells, and intensity of convective motion inside the convection cells. The entropy generation due to viscous dissipation is found to be negligible as compared to the entropy generation due to conduction. [ABSTRACT FROM AUTHOR]

The application of hybrid nanoparticles with the purpose of enhancing thermal processes is an important technology that could have ramifications for a wide range of interventions used in a variety of industries. In this research paper, the impact of a ternary hybrid type nanofluid on heat energy transfer and free convection flow in a square closed space is explored using numerical simulations with different wall conditions. The wall at the bottom side of the closed space is heated uniformly, the vertical wall at the left side is linearly heated or uniformly heated, and the vertical wall at the right side is either linearly heated or cooled, while the wall at the top is thermally insulated. The equations controlling the flow and heat energy transfer are resolved using the finite element method with quads and triangles as elements. With varying values of nanoparticle volume percentage and Rayleigh number, numerical results for the mean Nusselt numbers of various fluids are analysed in detail, along with the profiles of streamlines and isotherms. [ABSTRACT FROM AUTHOR]

• The Lewis number impacts the onset of thermo-bioconvection. • The hybrid nanofluid enhances the heat transfer in case of thermos-bioconvective flow in a porous horizontal cylindrical annulus. • The waviness parameters impact the flow pattern and the heat transfer rate. • An increase of the bioconvection Rayleigh number enhances the fluid velocity due to extra buoyancy forces. Transport phenomena related to thermo-bioconvection have recently emerged as an intriguing area of study because of their multi-physical applications such as bio-energy systems, food industries, solar collectors, pollutant dispersion in aquifers, biological wastes processing, chemical catalytic converters, geothermal energy usage, petroleum oil reservoirs, enhanced oil recovery, thermal energy storage, chemical processing equipment, fuel cell technology, medical application, microfluidic devices, and others. In this context, it is highly challenging to design and regulate a system with multi-physical transport in a complex geometry. The goal of the current study is to analyze the thermo-bioconvective heat transfer induced by a gradient of temperature and a motile of phototactic microorganisms with the presence of two types of nanoparticles inside a wavy-walled horizontal cylindrical porous annulus. The originality of this investigation is analyzing the influence of microorganisms, waviness parameters and hybrid nanofluid on thermo-convective instabilities. The effects of the wall waviness parameters, bioconvection Rayleigh number (R a b), thermal Rayleigh number (R a T), nanoparticles volume fraction ϕ and Lewis number (L e) on the flow structure, temperature, and isoconcentrations of microorganisms are investigated and explained in detail. The key findings showed that the Lewis number impacts the onset of thermo-convection and bioconvection and convection phenomena begins rapidly for small values of Lewis number. The nanoparticles enhance the heat transfer in case of thermo-bioconvective flow in a horizontal porous cylindrical system. The average Nusselt number N u ¯ decreases as the wall waviness parameters, amplitude λ , and undulation number η increase. It was also shown that thermo-convective instabilities may develop depending on thermal Rayleigh number, bioconvection Rayleigh number, nanoparticles volume fraction and wall waviness parameters. [ABSTRACT FROM AUTHOR]

In this study, thermal and phase change process in a circular porous vented cavity (P-VC) are numerically analyzed with finite element method considering magnetic field and inner surface rotation during nanofluid convection. The control of convective heat transfer and thermal management in porous cavities are crucial in applications for electronic cooling, heat exchangers, convective drying, and many other heat transfer devices. The numerical analysis is carried out for various values of the relevant parameters (Reynolds number—Re, rotational Reynolds number—Rew, Hartmann number—Ha, opening ratio—Ri) as follows: 500 ≤ Re ≤ 2000 , − 5000 ≤ Rew ≤ 5000 , 0 ≤ Ha ≤ 80 , 1 ≤ Ri ≤ 3. The phase change process often accelerates with higher Re when rotations are active. The rotations cause the full phase transition time (TR) to decrease by roughly 15% at the highest Re. The phase change process speeds up when both CW and CCW rotations are used at their highest values. The impacts of Ha on the TR variation is found as 33%. The thermal performances are slightly influenced by the variation of inner surface rotations and magnetic field strength. However, highest impact on thermal process and phase change is obtained when varying the inlet port size. The TR variation becomes 57% while heat transfer enhancement factor is obtained as 3.5. The optimal parameter combination to provide the highest thermal performance is (Ha, Rew, Ri) = (30.85, −4145, 2.98). • Thermal and phase change process in a circular porous vented cavity are numerically analyzed. • Finite element method was considered under magnetic field and inner surface rotation during nanofluid convection. • The optimal parameter combination to provide the highest thermal performance is (Ha, Rew, Ri)=(30.85, -4145, 2.98). [ABSTRACT FROM AUTHOR]

In this study, mixed convection of nanofluids in a three dimensional cavity with two inner adiabatic rotating circular cylinders were analyzed by using finite element method. Vertical surfaces are kept at constant temperature while other walls and rotating cylinder surfaces were taken as adiabatic. The three dimensional cavity was filled with water and various types of nanoparticles (Cu, Al 2 O 3 and TiO 2 ). The water-Cu nanofluid provided the highest heat transfer rate and at the highest value of Rayleigh number, 4 % higher average heat transfer rate is obtained when compared to other particles. When cylinders rotate, depending on the rotational direction either enhancement or deterioration of average Nusselt number is observed. For the highest value of rotational speed of the cylinders, 8.5 % discrepancy between the average Nusselt number is observed for the nanofluid with Cu and Al 2 O 3 nanoparticles. For Cu-water nanofluid at the highest volume fraction as compared to base fluid, 38.10 % of enhancement in the average heat transfer is obtained. A correlation for the average Nusselt number in polynomial form was developed which is a function of Rayleigh number and angular rotational speed of the cylinders. [ABSTRACT FROM AUTHOR]

Natural convection in a CuO-water nanofluid filled horizontal partitioned annulus formed by two isothermal surfaces under the influence of an inclined magnetic field was numerically investigated. A conductive partition with varying thickness and thermal conductivity was placed within the annulus. Finite element method was utilized to solve the governing equations. The influence of the Rayleigh number (between 10 4 and 10 6 ), Hartmann number (between 0 and 40), magnetic inclination angle (between 0° and 90°), thermal conductivity of the partition (between 0.06 and 60) and solid volume fraction of the nanoparticle (between 0 and 0.04) on the fluid flow and heat transfer characteristics were studied for various thickness values of the partition. Local and average Nusselt number along the inner surface enhance as the value of the thickness of the partition and Rayleigh number and magnetic inclination angle (up 45°) increase and as the value of Hartmann number decreases. The influence of the thickness of the conductive partition is more pronounced in the conduction dominated regime when Rayleigh number is low and Hartmann number is high. Average heat transfer enhances with thermal conductivity of the partition and this is more effective for a thicker partition. Almost a linearly varying relation exists between the average Nusselt number and solid nanoparticle volume fraction and the slope of the curve is slightly higher for a thick partition. [ABSTRACT FROM AUTHOR]

In this study, a numerical study of natural convection ferrofluid filled trapezoidal enclosure was performed under the influence of a magnetic dipole source. The left inclined wall of the cavity is heated and the right inclined wall is kept at constant temperature lower than that of the heater. Other horizontal walls of the trapezoidal enclosure are assumed to be adiabatic. The governing equations are solved with finite element method. The influence of the Rayleigh number, inclination angle of the side walls, strength of the magnetic dipole, horizontal and vertical location of the magnetic dipole on fluid flow and heat transfer are numerically investigated. It is observed that increasing values of Rayleigh number and inclination angles enhance the heat transfer. The external magnetic field parameters (strength and location) can be used to control the heat transfer and fluid flow inside the trapezoidal cavity. [ABSTRACT FROM AUTHOR]

A three dimensional computational solution has been obtained to investigate the natural convection and entropy generation of nanofluid-filled open cavities with an adiabatic diamond shaped obstacle. In the model, the finite volume technique was used to solve the governing equations. Based on the configuration, the cavity is heated from the left vertical wall and the diamond shape was chosen as adiabatic. Effects of nanoparticle volume fraction, Rayleigh number (103ὄ Ra ὄ 106) and width of diamond shape were studied as governing parameters. It was found that the geometry of the partition is a control parameter for heat and fluid flow inside the open enclosure. [ABSTRACT FROM AUTHOR]

In this article, entropy generation due to natural convection in entrapped trapezoidal cavities filled with nanofluid under the influence of magnetic field was numerically investigated. The upper (lower) enclosure is filled with CuO-water (Al2O3-water) nanofluid. The top and bottom horizontal walls of the trapezoidal enclosures are maintained at constant hot temperature while other inclined walls of the enclosures are at constant cold temperature. Different combinations of Hartmann numbers are imposed on the upper and lower trapezoidal cavities. Numerical simulations are conducted for different values of Rayleigh numbers, Hartmann number and solid volume fraction of the nanofluid by using the finite element method. In the upper and lower trapezoidal cavities magnetic fields with different combinations of Hartmann numbers are imposed. It is observed that the averaged heat transfer reduction with magnetic field is more pronounced at the highest value of the Rayleigh number. When there is no magnetic field in the lower cavity, the averaged Nusselt number enhances as the value of the Hartmann number of the upper cavity increases. The heat transfer enhancement rates with nanofluids which are in the range of 10% and 12% are not affected by the presence of the magnetic field. Second law analysis of the system for various values of Hartmann number and nanoparticle volume fractions of upper and lower trapezoidal domains is performed. [ABSTRACT FROM AUTHOR]

A numerical work has been conducted to explore the effects of opening parameters on melting of phase change material (PCM) during natural convection in a partially open enclosure. A finned heater is located on bottom wall while the remaining parts are insulated. Paraffin wax is used as PCM and two-dimensional time dependent analysis is performed by using the finite volume method for the parameters of location of opening and temperature difference. The governing parameters for the study are chosen for the range of Ra = 1.45 × 108 ≤ Ra ≤ Ra = 1.97 × 108, 0.25 ≤ w/H ≤ 0.75 and 0.25 ≤ c/H ≤ 0.75. It is found that both opening ratio and opening length are effective parameter on melting time and these can be used as control parameters for improving the energy efficiency. Also, heat transfer can be controlled by using PCM inserted block and opening parameters. Among different cases of opening ratios and locations of opening, the most favorable configuration is obtained at Ra = 1.97 × 108, w/H = 0.25, c/H = 0.25 while average heat transfer enhancement by about 60% is achieved. At the lowest and highest value of Rayleigh numbers, the most favorable location of the opening is obtained at c/H = 0.25 in order to have the highest reduction amount of phase completion time. [ABSTRACT FROM AUTHOR]

In this study, relationships of Nusselt–Rayleigh–Fourier type are proposed for the case of air-filled hemispherical cavity whose dome is oriented downwards and maintained isothermal. Its disk is subjected to a constant heat flux and inclined at an angle varying between 90° (vertical position) and 180° (disk horizontal with dome oriented downwards). The numerical approach is performed in transient regime by means of the finite volume method for Rayleigh numbers in the range of 104 −5×108. These results are confirmed at steady state by measurements done for some configurations in a previous study for the same Rayleigh and inclination ranges. Otherwise, they complete other surveys considering inclination angles varying between 0° (horizontal cavity with dome oriented upwards) and 90° (vertical cavity) for a wider range of Rayleigh numbers. The correlations allow thermal control of devices submitted to natural convection in hemispherical cavities during the time preceding the steady state after their switch on. [ABSTRACT FROM AUTHOR]

Abstract: A computational numerical work has been done to see the effects of magnetic field on natural convection for a trapezoidal enclosure. Both inclined walls and bottom wall have constant temperature where the bottom wall temperature is higher than the inclined walls. Top wall of the cavity is adiabatic. To investigate the effects, finite element method is used to solve the governing equations for different parameters such as Rayleigh number, Hartmann number and inclination angle of inclined wall of the enclosure. It is found that heat transfer decreased by 20.70% and 16.15% as φ increases from 0 to 60 at Ra=105 and 106 respectively. On the other hand, heat transfer decreased by 20.28% and 13.42% as Ha increases from 0 to 50 for Ra=105 and 106 respectively. [Copyright &y& Elsevier]

In this numerical work, effects of joule heating on natural convection in non-linearly heated square enclosure from right vertical wall were investigated for different Rayleigh numbers and Hartmann numbers. The cavity was considered with adiabatic horizontal walls and cooled left wall. Finite volume method was used to solve governing equations. The calculations have been performed for different Rayleigh numbers (Ra = 104, 5x104 and 105), Joule parameter (J = 0.0, 3.0 and 5.0) and Hartmann number (Ha = 0, 10, 20 and 50). Obtained results are illustrated with streamlines, isotherms, temperature and velocity profiles and mean Nusselt number. It is found that the flow becomes weaker near the right corner of the cavity due to non-isothermal boundary condition. Both Hartmann number and Joule parameter have important effect on heat transfer and fluid flow. [ABSTRACT FROM AUTHOR]

Two-dimensional study has been performed for the buoyancy induced flow in a stepwise opening cavity heated from the left vertical wall. The governing equations subject to the imposed boundary conditions are solved by using the higher order finite element technique. A finite element method involving the cubic polynomials (ℙ 3) has been implemented for the discretization of velocity, temperature and concentration fields while the pressure is approximated by utilizing the quadratic (ℙ 2) finite element space of functions. The adaptive Newtons method is availed for the linearization of the discrete system of algebraic equations and the corresponding linear system in each step is computed using the Gaussian elimination method. The governing parameters are chosen as Rayleigh number 103 ≤ Ra ≤ 107, Darcy number 10−6 ≤ Da ≤ 10−2, buoyancy ratio 0.1 ≤ Br ≤ 1, aspect ratio 0.5 ≤ AR ≤ 1 and Brownian motion parameter 0.1 ≤ Nb ≤ 1. It is noted that both heat and mass transport are function of the aspect ratio. Heat transfer is increased and mass transfer is reduced by decreasing the geometrical ratio depending on the different studied parameters. [ABSTRACT FROM AUTHOR]

[Display omitted] • Casson Sodium alginate based MWCNT nanofluid is considered in a wavy enclosure for the first time. • Natural convection is analyzed in the presence of adiabatic/hot/cold obstacle. • The dimensional velocities, streamlines and isotherms are discussed thoroughly. • FEM simulations are done with thermal radiation. Nanofluids are considered a better alternative to conventional fluids in many industrial situations and unfolding new opportunities for various applications owing to the optical and thermal properties of additive nanosized materials. In this study, the thermal and hydraulic characteristics of a Casson-based (sodium alginate) multiwall carbon nanotube (MWCNT) nanofluid were computationally investigated inside a wavy square enclosure containing a circular-shaped obstacle. The square enclosure comprised two cooled vertical walls and a wavy adiabatic top wall. The central part of the bottom wall comprised a heated wavy structure, and the remaining parts exhibited a flat and adiabatic structure. The Navier–Stokes (N–S) equations and boundary conditions were established using the non-Newtonian Casson fluid model and Rosseland thermal radiation. The present problem was numerically simulated using the Galerkin finite element method for three types of obstacles, namely, adiabatic, hot, and cold. The impacts of Casson parameter (0.001 ≤ β ≤ 0.1), Rayleigh number (103 ≤ Ra ≤ 106), nanoparticle volume fraction (0.01 ≤ φ ≤ 0.1) and radiation parameter (1 ≤ Rd ≤ 4) are analysed. A numerical code validation was performed using the available benchmark results. The characteristics of the convective radiation heat transport were clearly analyzed through the stream function and isotherm plots. For all types of obstacles, the mean Nusselt number along the heated wavy wall increased with the Casson parameter, MWCNT volume fraction, Rayleigh number, and radiation parameter. Conclusion : The heat and flow characteristics of a Casson-based MWCNT nanofluid inside a wavy square enclosure were investigated. The mean Nusselt number was higher (lower) in the presence of cold (hot) obstacles. [ABSTRACT FROM AUTHOR]

• MHD mixed convection lid-driven cavity problem is investigated numerically. • The square cavity is partially heated from the bottom plate covering 40% of its length. • One side of the cavity has streamlined geometry to control heat and fluid flow. • If there is no corner vortex, chamfer can also block the main stream and decrease heat transfer up to 11%. In this study, MHD mixed convection lid-driven cavity problem is investigated to find thermal effects of chamfer on the corner of the cavity. For this purpose, open source CFD software, OpenFOAM's existing solver is modified to add Lorentz Force to the momentum equation. Simulation parameters consist of different Richardson numbers (0.01 ≤ Ri ≤ 100), Hartmann numbers (0 ≤ Ha ≤ 75), magnetic field angle values (0° ≤ γ ≤ 90°), different chamfer radii (0.1 ≤ r * ≤ 0.3) and Lid Motion Direction (LMD) as positive and negative. The square cavity is partially heated from the bottom plate covering 40% of its length and the rest of the bottom plate is considered as adiabatic along with the side walls. Top plate an isothermal moving lid and its temperature is lower than the bottom plate. It is observed that chamfer presence can increase the heat transfer but effectiveness of chamfer is limited and dependent on the size of corner vortices and chamfer radius. For a square cavity, only 0.39% increase in the average Nusselt number is obtained at maximum. If there is no corner vortex, chamfer can also block the main stream and decrease heat transfer up to 11%. Lid motion direction can increase the effectiveness of the chamfer, depending on the corner vortex size and at γ = 45 °, reverse lid motion direction increases average Nusselt number up to 57.2% compared to the positive lid motion direction. [ABSTRACT FROM AUTHOR]

Magnetohydrodynamics forced convection of CNT-water nanofluid in a layered U-shaped vented cavity involving a porous region is investigated under the impact of wall corrugation. The numerical study is performed by using the finite volume method. Impacts of Reynolds number (between 100 and 1000), Hartmann number (between 0 and 50), Darcy number (between 10−4 and 5 × 10−2), porous layer height (between 0.1H and 0.5H), height (between 0 and 0.5H) and number of triangular waves (between 1 and 16) and curvature (between 0.01H and 0.2H) at the U-turn of the vented cavity on the convective heat transfer features are examined. The flow field and heat transfer are affected by variations in the Reynolds number, magnetic field strength and permeability of the porous medium. The average Nusselt number increases significantly with higher magnetic field strength and at Hartmann number of 50, the amount of enhancement is 112% while the impact is reverse for highest value of Darcy number of the porous compound. The corrugation of the bottom wall which is a triangular wave was found to be used as an effective tool for fluid flow and heat transfer features. The average heat transfer rate reduces with higher number of corrugation waves (68.2% reduction) while it first increases then reduces with higher height of the corrugation. The curvature of the neck in the U-shaped cavity reduced the heat transfer rate which is 15.5% at the highest value. [ABSTRACT FROM AUTHOR]

• The entropy production due to natural convection in an annular passage between horizontal confocal elliptic cylinders is studied. • Al 2 O 3 -Cu/water hybrid nanofluid is used. • Increasing of Ra number or use of hybrid nanoparticles in the pure water increases the heat transfer. A numerical analysis on entropy production due to natural convection in an annular passage between horizontal confocal elliptic cylinders is studied. The Al 2 O 3 -Cu/water hybrid nanofluid is using as a test fluid. The flow by natural convection in the annulus is driven by a gradient of temperature between an internal uniformly heated elliptical cylinder and a cold external elliptical cylinder. The full basic equations describing steady laminar flow of incompressible and Newtonian fluid under the Boussinesq approximation are expressed in the elliptical coordinates system and discretized by the finite volume method using an in-house FORTRAN code. The investigation is carried out to examine the influences of Rayleigh number and hybrid nanoparticles volume fraction on thermo-hydrodynamic characteristics, heat transfer and entropy generation inside the annulus. Obtained results showed that increase of Rayleigh number or use of hybrid nanoparticles in the pure water increases the natural convective flow and the heat transfer rate within the annulus, as well as both thermal and frictional entropy generation. Also, at lower Rayleigh, most of the entropy generation is due to the thermal irreversibility, whereas, at higher Rayleigh, the main contributor to the total entropy generation is that due to the frictional irreversibility. Image, graphical abstract [ABSTRACT FROM AUTHOR]

In this study, natural convection and entropy generation analysis of nanofluid in an inclined cavity including a curved shaped conductive partition are performed under the impact of inclined magnetic field by using Galerkin weighted residual finite element method. Numerical simulations are performed for various values of Rayleigh number (between 10 4 and 10 6), inclination angle of the cavity (between 0 o and 180 o), Hartmann number (between 0 and 50), orientation angle of the magnetic field (between 0 o and 90 o), curvatures of the conductive partition (between 0.01 and 0.1), conductivity ratio (between 0.01 and 100) and solid nanoparticle volume fraction (between 0 and 0.03). The average Nusselt number increases with higher values of Rayleigh number, inclusion of nano sized particles whereas it is reduced with higher values of Hartmann number. When the value of Hartmann number is increased from 0 to 50, 32% and 34% of average Nusselt number reduction is obtained for water and nanofluid. The cavity inclination angle has significant effects on the convective heat transfer characteristics. When the radii of the vertical and horizontal elliptic curved partitions are increased to 0.3H, 23% and 3.8% deterioration of average Nusselt number is obtained while significant enhancement in the heat transfer is observed when the conductivity of the partition is increased. The second law analysis was included in the study and entropy generation rate was found to vary with different parameters. Contributions of solid and fluid domains to the entropy generation rate were determined. • Natural convection and entropy generation of nanofluid in an inclined cavity are performed. • Curved shaped conductive partition was used with magnetic field effects. • The cavity inclination angle and curved partition have significant effects on Nu. • Nu increases with higher Ra number, φ and Kr whereas it is reduced with higher Ha number. • Contributions of domains to the entropy generation change with Ha and size of partition. [ABSTRACT FROM AUTHOR]

In this study, mixed convective flow of nanofluid in an inclined L-shaped cavity which has elastic walls is numerically analyzed under the effects of internal heat generation and magnetic field by using the finite element technique with the Arbitrary-Lagrangian–Eulerian method. Simulations are performed for different values Richardson number (between 0.03 and 30), inclination angle of the cavity (between 0°and 180°), Hartmann number (between 0 and 50), orientation angle of the magnetic field (between 0°and 90°), internal Rayleigh number (between 1 0 4 and 1 0 6), solid nanoparticle volume fraction (between 0 and 0.04), flexible wall elastic modulus (between 1 0 4 and 1 0 8) and aspect ratio (between 0.2 and 0.7) of the L-shaped cavity. It was observed that the effects of elastic wall on the convective heat transfer features are significant for the lowest value of Richardson number and lowest values of elastic modulus while 11% of discrepancy is obtained in the average Nusselt number when cavity with elastic and rigid walls is compared. The impact of the magnetic inclination angle is significant when compared to magnetic field strength for the variation of the average Nusselt number. Cavity inclination angle has significant impacts on the variation of the average Nusselt number for water and nanofluid. A higher size of the cold wall (aspect ratio) increases the heat transfer rate while the internal Rayleigh number reduces it. Enhancement in the average Nusselt number is about 15%–19% at highest nanoparticle volume fraction of the nanofluid while the trends in the convective heat transfer features with respect to changes in the pertinent parameters are similar for water and nanofluid. • FSI of nanofluid mixed convection in an L-shaped with MHD and IHD was studied. • Elastic wall effects on the Nu are significant for the lowest value of Ri number. • Impact of γ on Nu is significant when compared to Ha number. • The average Nu enhancement is in the range of 15–19% at the highest φ value. • Significant changes in flow and thermal fields are seen with change of ω value. [ABSTRACT FROM AUTHOR]

This work explores the magneto-bioconvection flow of silver(Ag)‑magnesium oxide(MgO)-water hybrid nanoliquid in a porous cavity considering the effect of gyrotactic microorganisms. The novelty of this work is to examine the magnetic force on bioconvection flow in a porous cavity containing obstacle, oxytactic bacteria and occupied by a hybrid nanofluid. A streamlined square obstacle is inserted in the flow field. For the modeling of porous medium, Brinkman-Forchheimer extended Darcy's model is considered. In order to simulate the governing system of dimensionless equations, a higher Galerkin finite element method (GFEM) is implemented. The resulting discrete algebraic systems are treated using the adaptive Newton's method. The validity and reliability of designed solver is ensured by recomputing the numerical and experimental data available in the literature. The flow structure, heat and mass transport are analyzed for the controlling parameters such as Hartmann number (Ha = 0 − 100), bioconvection Rayleigh number (R b = 10 − 100), Peclet number (Pe = 0.1 − 1), Richardson number (Ri = 0.1 − 5), Lewis number (Le = 1 − 10) and Darcy number (Da = 10−5 − 10−2). The obtained numerical approximations demonstrated that the variation of heat transfer becomes almost constant for varying the Peclet number. Whilst the Sherwood number is a decreasing function of Peclet number. The dimensions of streamlined obstacle can serve as a control parameter and it makes opposite impact on heat and mass transport. [ABSTRACT FROM AUTHOR]

In this study, the lid-driven cavity problem is investigated under mixed convection conditions by using Finite Volume Method (FVM). A porous block is placed in the middle of the domain with 0.1 porosity. A heater is placed on the edge of the porous block to imitate a local porous heater. In order to investigate the effects of the heater position on the problem physics, the heater is located in 4 different directions (left, right, top bottom) and 3 different orientations (clockwise, counterclockwise and middle). Mixed convection conditions are provided by three different Richardson numbers, 0.1 ≤ Ri ≤ 10 and porous block properties are applied by employing 4 different Darcy numbers 10−7 ≤ Da ≤ 10−1. It is observed that Darcy number can be used to control the vortex formation in the domain under specific configurations. Decrease in Darcy number can increase the average Nusselt number drastically, up to 10 times increase. Heater orientation can be used to control the heat transfer effectiveness, vortex shape and size. Heater orientation can increase the average Nusselt number by 324%. It is also shown that both heater location and orientation show a non-monotonic behavior for different flow parameters. [ABSTRACT FROM AUTHOR]

• The cavity is considered to be partially open and complex wavy walls enclosures. • Non-linear Boussinesq approximation is considered for the MHD natural convection of ferrofluids. • This work express the benefits of the do-nothing boundary condition at the open wall. • Best location of aperture for the fluid flow is in middle of the right wall while putting the aperture at top of the right wall is the best for the heat transfer. • The nonlinear Boussinesq parameter has positive effects on the ferrofluid movement, maximum values of entropy generation due to fluid friction and average Nusselt number. In the current contribution, a numerical investigation of natural convection with nonlinear Boussinesq approximation is considered for a ferrofluid flows inside an inclined, and partial open cavity. The vertical walls of the cavity are wavy where the aperture part lies in the right one. The left wall is considered to be uniformly heated whereas the remaining parts of the cavity are adiabatic. The nonslip boundary condition is assumed for all the boundaries except the aperture part where the directional do-nothing boundary condition is introduced to ensure the theoretical studies which leads to a conservative kinetic energy. The problem is modeled and the resulting partial differential equation system, after converting it to a non-dimensional form using a suitable transformation variables, is solved based on the Galerkin finite element method. The entropy generation analysis is presented for the local entropy generation due to heat transfer, local entropy generation due to fluid friction as well as their contribution to Bejan number. An intensive computation is carried out for wide ranges of the governing parameters namely; the Rayleigh number Ra , Hartmann number Ha , nanoparticle volume fraction ϕ , amplitudes of the two superimposed sinusoidal functions α i , non-linear Boussinesq parameter ξ , length of the aperture B R and its position b R. The obtained results are shown in terms of the streamlines, isotherms, local entropy generation due to heat transfer, local entropy generation due to fluid friction contours as well as average Bejan and Nusselt number. Over all, most of the governing parameters have a significant impacts in the flow and heat transfer rate as shown in the discussion section. [ABSTRACT FROM AUTHOR]

In this paper, laminar natural convection heat transfer was numerically investigated in cubical air-filled enclosures with partitions attached to the walls with different positions. Steady-state governing equations were solved using the Boussinesq approximation by the finite volume method. Two cases were considered that the partitions were placed perpendicular (Case 1) and parallel (Case 2) to the active walls, respectively. The opposing lateral walls of the enclosure are heated and cooled while the other walls are adiabatic. The effect of the two inclined partitions attached to the bottom and top adiabatic walls at the different positions on the heat transfer rate was examined. The dimensionless partition heights and positions were h/H = 0.1, 0.2 and 0.3, and c/H = 0.25, 0.5 and 0.75, respectively. The inclination of the partitions was θ =3°, 4°, and 5°. The air (Pr = 0.7) streamlines and the temperature fields were obtained for the Rayleigh numbers 103 ≤ Ra ≤ 106 for both cases studied. The mean dimensionless heat transfer ratio (Nusselt number) over the cold wall for both cases was also obtained. The effects of the dimensionless parameters considered on the heat transfer for both cases were concluded. It was seen that the parameters considered are important for Case 2 whereas they did not play a major role for Case 1. • The effect of dual partitions on the laminar natural convection in a cubical enclosure was investigated. • The parameters are the dimensionless heights, positions and inclinations of the partitions. • Novel correlations are derived for the cubical enclosure with dual partitions. [ABSTRACT FROM AUTHOR]

A numerical study of MHD natural convection in an upright porous cylindrical annulus filled with magnetized nanomaterial is made by using the specificity of nanoliquids to improve the phenomenon of heat transport. The upper and lower walls are thermally insulated, whereas the outer wall is kept at a lesser temperature. The finite volume method is used to treat the governing equations via computer code with Fortran programming. The results obtained are given for the values of the Rayleigh number between 103 and 106, aspect ratio A r = 2, radii ratio λ = 2, Hartmann number (0 ≤ Ha ≤ 80), Darcy number (10−5 ≤ Da ≤ 10−2), porosity ratio (0.1 ≤ ε ≤0.9), and the nanoparticles volume fraction (0 ≤ φ ≤ 0.1). The transferred thermal flux, in laminar natural convection, increases with the growth of the nanoparticle concentration, the Darcy number, the porosity, the Rayleigh number and, the length of the source. [ABSTRACT FROM AUTHOR]

This work studies the thermogravitational transmission and thermal radiation of micropolar nanoliquid within a porous chamber in the presence of the uniform magnetic influence. The model includes the single-phase nanofluid approach, local thermal equilibrium approximation and Darcy law for the processes within the porous structure. The Galerkin finite element method with the structured non-uniform mesh is used to calculate the formulated equations. The key characteristics are the Darcy–Rayleigh number Ra = 10–1000, Darcy number Da = 10−5–10−1, porosity ε = 0.1–0.9, nanoparticles concentration φ = 0–0.04, radiation parameter R d = 0–2, vortex viscosity characteristic Δ = 0–2, and Hartmann number Ha = 0–50. It has been ascertained the energy transport intensification with thermal radiation parameter, Darcy–Rayleigh number, porosity and nanoparticles concentration. Also, the results indicate that the average Nusselt number reduces with an increment of the Hartmann number for high values of the Rayleigh number, while for low magnitudes of the Rayleigh number a weak change of the average Nusselt number can be found. [ABSTRACT FROM AUTHOR]