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The aims of this study is to numerically investigate the thermal phenomena during magnetohydrodynamic (MHD) free convection in an oblique enclosure filled with porous media saturated with Cu–Al₂O₃/water hybrid nanofluid and heated at the left wavy wall. The thermophysical phenomena are explored thoroughly by varying the amplitude (λ) and undulation (n) of the wavy wall and the inclination of the enclosure (γ) along with other pertinent physical parameters. Darcy–Rayleigh number (Ra_m), Darcy number (Da), Hartmann number (Ha) and nanoparticle volumetric fraction (ϕ). The effect of all parameters has been analyzed and represented by using heatlines, isotherms, streamlines, average Nusselt number and local Nusselt number.

The finite volume method is used to work out the transport equations coupled with velocity, pressure and temperature subjected to non-uniform staggered grid structure after grid-sensitivity analysis by an indigenous computing code and the semi-implicit method for pressure linked equations (SIMPLE) algorithm. The solution process is initiated following an iterative approach through the alternate direction implicit sweep technique and the tridiagonal matrix algorithm (TDMA) algorithm. The iterative process is continued until successive minimization of the residuals (<1e-8) for the governing equations.

This study reveals that the increase in the heating surface area does not always favor heat transfer. An increase in the undulation amplitude enhances the heat transfer; however, there is an optimum value of undulation of the wavy wall for this. The heat transfer enhancement because of the wall curvature is revealed at higher Ra_m, lower Da and Ha and lower volume fraction of nanoparticles. In general, this augmentation is optimum for four undulations of the wavy wall with an amplitude of λ = 0.3. The heat transfer enhancement can be more at the cavity inclination   γ = 45°.

The technique of this investigation could be used in other multiphysical areas involving partial porous layers, conducting objects, different heating conditions, wall motion, etc.

This study is to address MHD thermo-fluid phenomena of Cu–Al₂O₃/water-based hybrid nanofluid flow through a non-Darcian porous wavy cavity at different inclinations. The amplitude and number of undulations of the wavy wall, permeability of the porous medium, magnetic field intensity, nanoparticle volumetric fraction and inclinations of the enclosure play a significant role in the heat transfer process. This analysis and the findings of this work can be useful for the design and control of similar thermal systems/devices.

Many researchers have examined the problem of buoyancy-induced free convection in a wavy-porous cavity packed with regular fluids or nanofluids. However, the effect of magnetic fields along with the amplitude (λ) at different undulations (n) of the heated wavy wall of an inclined enclosure is not attended so far to understand the transport mechanisms. Most often, the evolutions of the thermo-fluid phenomena in such complex geometries invoking different multiphysics are very intricate. Numerical implementations for simulations and subsequent post-processing of the results are also challenging.

The purpose of this paper is to assess steady, two-dimensional natural convection flow of a viscoelastic, incompressible, electrically conducting and optically thick heat-radiating nanofluid over a linearly stretching sheet in the presence of uniform transverse magnetic field taking Dufour and Soret effects into account.

The governing boundary layer equations are transformed into a set of highly non-linear ordinary differential equations using suitable similarity transforms. Finite element method is used to solve this boundary value problem. Effects of pertinent flow parameters on the velocity, temperature, solutal concentration and nanoparticle concentration are described graphically. Also, effects of pertinent flow parameters on the shear stress, rate of heat transfer, rate of solutal concentration and rate of nanoparticle concentration at the sheet are discussed with the help of numerical values presented in graphical form. All numerical results for mono-diffusive nanofluid are compared with those of double-diffusive nanofluid.

Numerical results obtained in this paper are compared with earlier published results and are found to be in excellent agreement. Viscoelasticity, magnetic field and nanoparticle buoyancy parameter tend to enhance the wall velocity gradient, whereas thermal buoyancy force has a reverse effect on it. Radiation, Brownian and thermophoretic diffusions tend to reduce wall temperature gradient, whereas viscoelasticity has a reverse effect on it. Nanofluid Lewis number tends to enhance wall nanoparticle concentration gradient.

Study of this problem may find applications in engineering and biomedical sciences,e.g. in cooling and process industries and in cancer therapy.

The purpose of this paper is to study the effects of chemical reaction, thermal radiation and Soret and Dufour effects of heat and mass transfer by natural convection flow about a truncated cone in porous media.

The problem is formulated and solved numerically by an accurate implicit finite-difference method.

It is found that the Soret and Dufour effects as well as the thermal radiation and chemical reaction cause significant effects on the heat and mass transfer charateristics.

The problem is relatively original as it considers Soret and Dufour as well as chemical reaction and porous media effects on this type of problem.

The purpose of this paper is to study the influence of magnetic field on entropy generation and natural convection inside an enclosure filled with a hybrid nanofluid and having a conducting wavy solid block. Also, the effect of fluid–solid thermal conductivity ratio is investigated.

The governing equations that are formulated in the dimensionless form are discretized via finite volume method. The velocity–pressure coupling is assured by the SIMPLE algorithm. Heat transfer balance is used to verify the convergence. The validation of the numerical results was performed by comparing qualitatively and quantitatively the results with previously published investigations.

The results indicate that the magnetic field and the conductivity ratio of the wavy solid block can significantly affect the dynamic and thermal field and, consequently, the heat transfer rate and entropy generation because of heat transfer, fluid friction and magnetic force.

To the best of the authors’ knowledge, the present numerical study is the first attempt to use hybrid nanofluid for studying the entropy generation because of magnetohydrodynamic natural convective flow in a square cavity with the presence of a wavy circular conductive cylinder. Irreversibilities due to magnetic effect are taken into account. The effect of fluid–solid thermal conductivity ratio is considered.

This study aims to focus on a thermo-fluid flow in a partially driven cavity (PDC) using Cu-water nanoliquid, magnetic field and porous substance. The cooling and sliding motion are applied on the upper half of the vertical walls and the bottom wall is heated. Thermal characteristics are explored to understand magnetohydrodynamic convection in a nanoliquid filled porous system from a fundamental viewpoint. The governing parameters involved to cater to the moving speed of the sidewalls and partial translation direction are the relative strength of thermal buoyancy, porous substance permeability, magnetic field intensity, nanoparticle suspension and orientation of the cavity.

The coupled transport equations of the problem are solved using an in-house developed finite volume-based computing code. The staggered nonuniform grids along the x and y directions are used. The SIMPLE algorithm technique is considered for the iterative solution of the discretized equations with the convergence check of the continuity mass defect below 10^–10.

The present study unveils that the heat transfer enhances at higher Ri with the increasing value of Re, irrespective of the presence of a porous substance or magnetic field or the concentration of nanofluid. Apart from different flow controlling parameters, the wall motions have a significant contribution to the formation of flow vortices and corresponding heat transfer. Orientation of the cavity significantly alters the transport process within the cavity. The upward wall velocity for both the sidewalls could be a better choice to enhance the high heat transfer (approximately 88.39% at Richardson and Reynolds numbers, respectively, 0.1 and 200).

Considering other multi-physical scenarios like porous layers, conducting block, microorganisms and the present investigation could be further extended to analyze a problem of complex flow physics.

In this study, the concept of partially driven wall motion has been adopted under the Cu-water nanoliquid, magnetic field, porous substance and oblique enclosure. All the involved flow-controlling parameters have been experimented with under a wide parametric range and associated thermo-flow physics are analyzed in detail. This outcome of this study can be very significant for designing as well as controlling thermal devices.

The convective process in a partially driven cavity (PDC) with the porous medium has not been investigated in detail considering the multi-physical scenarios. Thus, the present effort is motivated to explore the thermal convection in such an oblique enclosure. The enclosure is heated at its bottom and has partially moving-wall cold walls. It consists of various multi-physical conditions like porous structure, magnetic field, Cu–H₂O nanoliquid, etc. The system performance is addressed under different significant variables such as Richardson number, Reynolds number, Darcy number, Hartmann number, nanoliquid concentration and orientation of cavity.

Increasing heat transfer rate in spiral heat exchangers is possible by using conventional methods such as increasing number of fluid passes and counter flowing. In addition, newer ideas such as using pillows as baffles in the path of cold and hot fluids and using nanofluids can increase heat transfer rate. The purpose of this study is to simulate turbulent flow and heat transfer of two-phase water-silver nanofluid with 0-6 Vol.% nanoparticle concentration in a 180° path of spiral heat exchanger with elliptic pillows.

In this simulation, the finite volume method and two-phase mixture model are used. The walls are subjected to constant heat flux of q″ = 150,000 Wm⁻². The inlet fluid enters curves path of spiral heat exchanger with uniform temperature T_in = 300 K. After flowing past the pillows and traversing the curved route, the working fluid exchanges heat with hot walls and then exits from the section. In this study, the effect of radiation is disregarded because of low temperature range. Also, temperature jump and velocity slipping are disregarded. The effects of thermophoresis and turbulent diffusion on nanofluid heat transfer are disregarded. By using finite volume method and two-phase mixture model, simulations are performed.

The results show that the flow and heat transfer characteristics are dependent on the height of pillows, nanoparticle concentration and Reynolds number. Increasing Reynolds number, nanoparticle concentration and pillow height causes an increase in Nusselt number, pressure drop and pumping power.

Turbulent flow and heat transfer of two-phase water-silver nanofluid of 0-6 per cent volume fraction in a 180° path of spiral heat exchanger with elliptic pillows is simulated.

The purpose of this paper is to address the thermo-physical impacts of unsteady magneto-hydrodynamic (MHD) boundary layer flow of non-Newtonian tangent hyperbolic nanofluid past a moving stretching wedge. To delineate the nanofluid, the boundary conditions for normal fluxes of the nanoparticle volume fraction are chosen to be vanish.

The local similarity transformation is implemented to reformulate the governing PDEs into coupled non-linear ODEs of higher order. Then, numerical solution is obtained for the simplified governing equations with the aid of finite difference technique.

Numerical calculations point out that pressure gradient parameter leads to improve all skin friction coefficient, rate of heat transfer and absolute value of rate of nanoparticle concentration. As well as, lager values of Weissenberg number tend to upgrade the skin friction coefficient, while power law index and velocity ratio parameter reduce the skin friction coefficient. Again, the horizontal velocity component enhances with upgrading power law index, unsteadiness parameter, velocity ratio parameter and Darcy number and it reduces with rising values of Weissenberg number.

A numerical treatment of unsteady MHD boundary layer flow of tangent hyperbolic nanofluid past a moving stretched wedge is obtained. The problem is original.

The purpose of this study is to present the significance of Joule heating, viscous dissipation, magnetic field and slip condition on the boundary layer flow of an electrically conducting Boussinesq couple-stress fluid induced by an exponentially stretching sheet embedded in a porous medium under the effect of the magnetic field of the variable kind. The heat transfer phenomenon is accounted for under thermal radiation, Joule and viscous dissipation effects.

The governing nonlinear partial differential equations are transformed to the nonlinear ordinary differential equations (ODEs) by using some appropriate dimensionless variables and then the consequential nonlinear ODEs are solved numerically by making the use of the well-known shooting iteration technique along with the standard fourth-order Runge–Kutta integration scheme. The impact of emerging flow parameters on velocity and temperature profiles, streamlines, local skin friction coefficient and Nusselt number are described comprehensively through graphs and tables.

Results reveal that the velocity profile is observed to diminish considerably within the boundary layer in the presence of a magnetic field and slip condition. The enhanced radiation parameter is to decline the temperature field. The slip effect is favorable for fluid flow.

Till now, slip effect on Boussinesq couple-stress fluid over an exponentially stretching sheet embedded in a porous medium has not been explored. The present results are validated with the previously published study and found to be highly satisfactory.

The purpose of this paper is to solve the problem of steady, laminar, coupled heat and mass transfer by MHD natural convective boundary‐layer flow over a permeable truncated cone with variable surface temperature and concentration in the presence of thermal radiation and chemical reaction effects.

The governing equations are derived and transformed into a set of non‐similar equations which are then solved by an adequate implicit finite difference method.

It is found that the presence of thermal radiation, magnetic field and chemical reaction have significant effects on the rates of heat and mass transfer. The variation of the wall temperature and concentration exponent contribute to significant changes in the Nusselt and Sherwood numbers as well.

The titled problem with the various considered effects has not been solved before and it is of special importance in various industries. The problem is original.

The purpose of this study is two phase modeling of Water/Cu nanofluid forced convection in different arrangements of elliptical tube banks in a two-dimensional space.

The arrangements of tube banks have been regarded as equal spacing triangle (ES), equilateral triangle (ET) and the rotated square (RS). The obtained results indicate that, among the investigated arrangements, the RS arrangement has the maximum value of heat transfer with cooling fluid. Also, the changes of Nusselt number and the local friction factor are under the influence of three main factors including volume fraction of slid nanoparticles, the changes of fluid velocity parameters on the curved surface of tube and flow separation after crossing from a specified angle of fluid rotation.

In Reynolds number of 250 and in all arrangements of the tube banks, the behavior of Nusselt number is almost the same and the separation of flow happens in almost 155-165 degrees from fluid rotation on surface. In RS arrangement, due to the strength of vortexes after fluid separation, better mixture is created and because of this reason, after the separation zone, the level of local Nusselt number graph enhances significantly.

In this research, the laminar and two-phase flow of Water/Cu nanofluid in tube banks with elliptical cross section has been numerically investigated in a two-dimensional space with different longitudinal arrangements. In this study, the effects of using nanofluid, different arrangements of tube banks and the elliptical cross section on heat transfer and cooling fluid flow among the tube banks of heat exchanger have been numerically simulated by using finite volume method.