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Purpose The purpose of this paper is to study and analyze the converging/diverging channel flow and heat transfer with the multiple slips effect, which is a development of the Jeffery–Hamel problem using the mass-based hybrid nanofluid algorithm. Whereas transferring biological liquid by arteries is a vital issue, mathematical modeling of hybrid nanofluid flow containing titanium dioxide and silver as nanoparticles and blood as base liquid through a converging/diverging duct, which can be a useful analysis for the fields of drug delivery, has been investigated. Design/methodology/approach The present approach is based on the Tiwari–Das nanofluid method. In this modeling, the volume fraction of nanoparticles is replaced with nanoparticles masses. The partial differential equations of the mass, momentum and energy conservations are changed to the system of ordinary differential equations through the similarity solution method. The final governing equations are solved by Runge–Kutta–Fehlberg procedure and shooting method. Findings The effect of emerging parameters on the temperature, the velocity, the Nusselt number and the skin friction have been analyzed by graphical and tabular reports. It is observed that the opposition to hybrid nanofluid flow in the attendance of particles of nonspherical shapes is more enhanced than those in the attendance of particles of spherical shapes. This issue demonstrates that the rheology of a hybrid nanofluid is dependent on the shape of particles. Besides, backflow regimes form in the divergent channel for high values of Reynolds number, m2 and a. Indeed, this modeling for the hybrid nanofluid can be useful in different technologies and industries such as biological ones. It is worth mentioning that the excellent achievement of the mass-based algorithm for heat transfer and hybrid nanofluid flow is the most important success of this study. Originality/value The main originality is related to the development of the Jeffery–Hamel problem using the mass-based hybrid nanofluid algorithm. This new mass-based method is a single-phase hybrid nanofluid approach that the inputs are masses of nanoparticles and base liquid. Besides, considering the multiple slips effect and also pure blood as base fluid in this problem are also new.

Purpose This study aims to numerically examine the influence of various geometric parameters of a novel W-shaped porous cavity undergoing hybrid nanofluid-based magnetohydrodynamic mixed convection. The W-shaped cavity is modified from the classical trapezoidal cavity by constructing a triangular shape at its bottom. This cavity is isothermally active at the bottom, with different numbers and heights of the triangular peak (or undulation). The heated hybrid nanofluid (Cu–Al2O3–H2O) flow is cooled through the translating top wall. Inclined sidewalls are thermally insulated. To compare the impacts of change in geometric parameters, a square cavity under similar boundary conditions is also simulated. This study is carried out systematically addressing the various influences from a range of parameters like side angles (γ), number (m) and height (λ) of the bottom undulation, Reynolds number (Re), Richardson number (Ri), Darcy number (Da), Hartmann number (Ha), hybrid nanoparticles volume fraction (φ) on the overall thermal performance of the cavity. Design/methodology/approach Applying the finite volume approach, the transport equations involving multiphysical conditions like porous substance, hybrid nanofluid, magnetic field and shearing force are solved numerically by using a written FORTRAN-based code following the SIMPLE algorithm. The algebraic equations are solved over all the control volumes in an iterative process using the alternate direction implicit scheme and the tri-diagonal matrix algorithm. The converged solution of the iterative process is obtained when the relative error levels satisfy the convergence criterion of 10–8 and 10–10 for the maximum residuals and the mass defect, respectively. Findings It is revealed that an increase in the bottom undulation height always improves the thermal energy transfer despite the reduction of fluid volume. Thermal energy transfer significantly depends on the heating and cooling surface lengths, fluid volume in the cavity and the magnitude of the bottom undulation height of the W-shaped cavity. With the increase in bottom undulation height, effective heating length increases by ∼28%, which leads to a ∼15% reduction in the effective volume of the working fluid and a gain in heat transfer by ∼56.48%. In general, the overall thermal energy transport is improved by increasing Re, Ri and Da; whereas it is suppressed by increasing Ha. Research limitations/implications There are many opportunities for future research experimentally or numerically, considering different curvature effects, orientations of the geometry, working fluids, boundary conditions, etc. Furthermore, this study could be extended by considering unsteady flow or turbulent flow. Practical implications In many modern systems/processes pertaining to materials processing, continuous casting, food processing, chemical reactors, biomedical applications, etc. fine control in the transport process is a major concern. The findings of this analysis can effectively be useful for other applications for getting more control features in terms of achieving the operational objectives. The approach of the system analysis (considering geometrical size parameters to delve into the underlying transport physics) and the obtained simulated results presented in the work can usefully be applicable to similar thermal systems/devices such as materials processing, thermal mixing, chemical reactors, heat exchangers, etc. Originality/value From the well-documented and vast pool of literature survey, it is understood that there exists no such investigation on the considered geometry and study. This study contributes a lot to understanding magnetic field moderated thermofluid flow of a hybrid nanofluid in a porous medium filled W-shaped cavity, in consideration of different geometrical shape parameters (undulation peak numbers at bottom wall, peak heights, side angles and heating and cooling length). Findings brought by this study provide great insights into the design and operation under various ranges of multiphysical thermofluid-flow processing phenomena.

Purpose 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. Design/methodology/approach 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. Findings 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). Research limitations/implications 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. Practical implications 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. Originality/value 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.

Purpose 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 (Ram), 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. Design/methodology/approach 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 ( Findings 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 Ram, 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°. Research limitations/implications The technique of this investigation could be used in other multiphysical areas involving partial porous layers, conducting objects, different heating conditions, wall motion, etc. Practical implications 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. Originality/value 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.

Purpose Metal-cooled reactors generally use molten metals such as sodium, potassium or a combination of sodium and potassium because of their excellent heat transfer properties so that the reactor can operate at much lower pressures and higher temperatures. The purpose of this paper is to investigate the stability of natural convection in an inclined ring filled with molten potassium under the influence of a radial magnetism. Design/methodology/approach A numerical simulation of electrically conductive fluid natural convection stability is performed on an inclined cylindrical annulus under the influence of a radial magnetism. The upper and lower walls are adiabatic, while the internal and external cylinders are kept at even temperatures. The equations governing this fluid system are solved numerically using finite volume method. The SIMPLER algorithm is used for pressure-speed coupling in the momentum equation. Findings Numerical results for various effective parameters that solve the problem in the initial oscillatory state are discussed in terms of isobars, isotherms and flow lines in the annulus for a wide range of Hartmann numbers (0 ≤ Ha ≤ 80), inclination angles (0 ≤ γ ≤ 90°) and radii ratios λ ≤ 6. The dependency stability diagrams between complicated situations with the critical value of the Rayleigh number RaCr and the corresponding frequency FrCr are established on the basis of the numeric data of this investigation. The angle of inclination and the radii ratio of the annulus have a significant effect on the stabilization of the magneto-convective flux and show that the best stabilization of the natural oscillatory convection is obtained by the intensity of the strongest magnetic field, the high radii ratio and inclination of the annulus at γ = 30°. Practical implications This numerical model is selected for its various applications in technology and industry. Originality/value To the best of the authors’ knowledge, the influence of the inclination of the cylindrical annulus (ring), with various radii ratio, on natural oscillatory convection under a radial magnetism has never been investigated.