Small-scale H-Darrieus turbine ( HDT ) often struggles to reach self-sustained power producing speed due to low start-up torque. Low torque is sometimes manifested in the form of torque plateau or ‘ dead band ’. To improve torque development, turbine design variables such as blade chord-to-radius ratio ( c/r ) and solidity ( σ ) play critical role. To understand the effect of c/r only, this study analyses turbines with identical σ but different c/r using unsteady computational fluid dynamics ( CFD) . Results show that larger c/r enhances torque by influencing the leading-edge flow and vortex formation and convection. Two mechanisms are identified: (i) amplification of the variation of incidence angle along blade chord, effectively acting as aerofoil-camber morphing, and (ii) high blade pitch rate effect, especially at low λ (<1) where intra-cycle pitching is significant. These findings highlight the sensitivity of torque generation to c/r , offering design guidance for improving HDT start-up performance.

Abstract The dynamics of partially molten mantle are central to the thermochemical evolution of terrestrial bodies, and partially molten plumes driven by melt buoyancy have been recognized as a crucial ingredient. Recent numerical models of the lunar mantle, however, have revealed a distinct finger-like structure, “magma finger”, that forms through a mechanism different from these plumes. To clarify the magma finger phenomenon and its relation to partially molten plumes, we performed a linear perturbation analysis and two-dimensional simulations of magma–matrix flow in a horizontal layer, where melt percolates through the convecting matrix. Our study shows that the upward migration of magma takes place in two regimes, depending on the competition between the two kinds of flows both driven by melt buoyancy: the Stokes flow of matrix and the percolation flow of melt. When the retention number $${R}_{t}$$ R t , defined by the ratio of the velocity of the former flow to the latter, is large, the magmatism–mantle upwelling (MMUb) feedback dominates the convective flow: buoyancy of melt generated by decompression during matrix upwelling boosts the upwelling itself. When a solid layer overlies the partially molten layer, the MMUb feedback induces partially molten plumes that ascend through the solid layer. At lower $${R}_{t}$$ R t , in contrast, a perturbation in the melt content in the partially molten layer propagates upward by a melt percolation-dominated instability: the perturbation induces a spatial variation in the rate of matrix expansion/contraction due to upward magma migration, shifting the perturbation upward. When a solid layer is overlaid, the melt percolation-dominated instability causes an instability along the layer boundary, generating magma fingers that extend upward into the solid layer. The calculated threshold in $${R}_{t}$$ R t for the onset of the MMUb feedback suggests that the feedback is responsible for the volcanism that generated the Large Igneous Provinces while being unimportant for hotspot volcanism on the Earth. Since $${R}_{t}$$ R t increases with decreasing matrix viscosity, volcanism caused by the MMUb feedback is likely more important in earlier terrestrial planets with hotter, softer mantles. Magma fingers are, in contrast, expected to have developed in the lunar mantle if a partially molten layer has developed at its base. Graphical Abstract

This study investigates the heat-flux enhancement of convection flows inside a fluid layer bounded from the top and bottom by two inhomogeneous porous layers. The porous matrix is made of solid materials with very high diffusivity. The numerical results reveal that, compared with the traditional convection system, the heat flux is greatly increased when the thickness of porous layer is large enough. At small Rayleigh numbers, the enhancement is the result of the increase in effective diffusivity in the fluid-saturated porous layers and the reduction in flow friction at the porous interface. For large Rayleigh numbers, the permeable motions across the interfaces generate strong convective flux, which greatly increases the total heat flux. For the latter parameter range, the exponent of the power-law scaling between the Nusselt number and the Rayleigh number exceeds 1/2, which is the value of the ultimate scaling. Our findings are not only of great potential in heat management in various industrial applications but also imply that, in many natural systems with imperfect boundaries, the global heat flux may be much stronger than the prediction by using a convection system with perfect boundaries.

The present study explores combined free-forced convective flow and entropy generation in a constant-volume double lid-driven trapezoidal cavity. All configurations of the isosceles trapezoidal cavity were meticulously designed to possess identical leg lengths and constant volume, ensuring that the same amount of heat is transferred from the cavity’s legs. The cavity has left and right lid-driven walls capable of oscillating upward and downward, while all other domain boundaries remain stationary. The left wall is sustained at a consistently high temperature, whereas the right wall is kept at a stable low temperature, and the upper and lower horizontal walls are thermally insulated. The modelling of this problem was carried out based on the finite volume technique. The obtained results were carefully validated against existing literature related to similar problems. The influence of relevant parameters such as Richardson number (0.01 ≤ Ri ≤ 100), aspect ratio (0.4 ≤ AR ≤ 1) and three distinct moving arrangements (Case-A, Case-B and Case-C) were examined. The findings revealed that heat transport was restricted at high Ri for all the presented aspect ratios, especially for Case-C. For all the presented aspect ratios and cases, entropy generation decreases as Ri increases, with the lowest values ​​observed for Case-A. Trapezoidal cavities with AR = 0.4, 0.6, and 0.8 generate lower entropy than the square cavity at high Ri, but higher entropy at low Ri.

Brinkman-Forchheimer model for unsteady mixed convective magnetohydrodynamics flow of couple stress fluid through swarm of particles at high magnetic Reynold number: Cell model technique

How the aspect ratio of a rectangular heat source influences convective flow structures: Implications on city-scale heat and pollutants dispersion

Retraction notice to “Electromagnetic free convective flow of a radiative, chemically reactive hybrid nanofluid over a moving vertical surface: With effects of porous medium” [Journal of Radiation Research and Applied Sciences, 18 (2) (2025), 101365

Ferrofluids flowing over a hydrophobic surface are important in enhancing heat transfer properties for mechanical devices and reducing friction on the surface for efficient use in lubrication. This effort investigates the motion of water-based ferrofluid on a vertical hydrophobic stretching sheet exposed to a magnetic field. In this flow, natural convection and temperature flow in the system are demonstrated. A non-dimensional transformation is used to change the mathematical model into a set of nonlinear formulations of differential equations. Due to the hydrophobic surface, the slip effects are considered. Finally, the system of nonlinearly coupled equations is simulated using the finite element technique. All the aspects of the numerical solution are validated with the previously published literature. The significance of surface roughness, magnetostatic field, and Prandtl number on the velocity profiles, convective boundary layer, and temperature is explained. The hydrophobic surface, the velocity slip parameter enhances the convective boundary layer and roughness factor plays a crucial role in the heat transfer enhancement and self-cleaning purposes in biomedical applications.

This study investigates the combined heat and mass transfer in mixed convection flow along vertical and inclined flat plates embedded in a porous medium. A mathematical problem is articulated based on the governing conservation laws and the prescribed coordinate system. The resultant system of collective nonlinear partial differential equations is reduced to a set of ordinary differential equations using a stream function formulation. The boundary value problem is solved numerically using a fourth-order Runge–Kutta method with appropriate iterative procedures to ensure convergence. The analysis emphasizes the influence of significant dimensionless parameters, together with the modified mixed convection parameter for heat and mass transfer [Formula: see text] and [Formula: see text], the Prandtl number [Formula: see text], the Schmidt number [Formula: see text], and the porous medium parameter [Formula: see text]. Numerical outcomes are accessible for velocity, temperature, and concentration distributions for assisting and opposed flow situations. Furthermore, the effects on engineering quantities such as skin friction, Nusselt number, and Sherwood number are examined in detail. The outcomes reveal that increasing [Formula: see text] and [Formula: see text] parameters significantly enhances skin friction and heat transfer rate in opposing flow, while offering additional resistance in assisting flow. The porous medium parameter is found to strongly regulate boundary layer thickness and flow resistance. These findings provide useful physical insights into mixed convection heat transfer in porous structures, with relevance to geophysical, environmental, and industrial applications.

Abstract We investigate how rotating convection responds to the imposition of a latitudinally varying heat flux at the base of the convective layer. This study is motivated by the solar near-surface shear layer, whose flows are thought to transition from a buoyancy-dominated regime near the photosphere to a rotation-dominated regime at depth. Here, we conduct a suite of spherical 3D, nonlinear simulations of rotating convection that operate in either the buoyancy-dominated (high-Rossby-number, high-Ro) or rotation-dominated (low-Rossby-number, low-Ro) regime. At the base of each model convection zone, we impose a heat flux whose latitudinal variation is opposite to the variation that the system would ordinarily develop. In both the low- and high-Ro regimes, a strong thermal wind balance is sustained in the absence of forcing. With a larger flux variation, this balance becomes stronger at high latitudes and weaker at low latitudes. The resulting differential rotation weakens in response, and at sufficiently high forcing, its latitudinal variation reverses for both low- and high-Ro systems. At fixed forcing, there exists a Rossby number above which the convective flows efficiently mix heat laterally, and the imposed flux variation does not imprint to the surface. At sufficiently high Ro, thermal wind balance is no longer satisfied. We discuss these results within the context of the Sun’s near-surface region, which possesses a weakened differential rotation when compared to the deep convection, along with little-to-no variation of photospheric emissivity in latitude.

The interplay of free convection with mass transfer on an unsteady, viscous, incompressible fluid flow over an oscillating infinite vertical plate in the presence of radiation has been attempted to be investigated analytically. The fluid is seen as a gray, non-scattering medium that emits and absorbs radiation. The dimensionless governing equations have been solved using the Laplace transform approach. With the aid of various graphs, the expressions for the velocity, temperature, and concentration profiles, as well as for the skin friction, Nusselt number, and Sherwood number are obtained and examined for various physical parameters, such as the thermal Grashof number, mass Grashof number, Schmidt number, Prandtl number, radiation parameter, and time.

This work investigates the MHD nonlinear convection flow of a Jeffrey fluid over a vertical surface, considering cross-diffusion, nonlinear radiation, heat generation, thermophoresis, and convective boundary conditions. The governing PDEs are reduced to nonlinear ODEs using similarity transformations and solved via the RKF-45 method. Validation against published results shows excellent agreement. Parametric analysis reveals that the Deborah number increases velocity and boundary layer thickness, while the Dufour and Soret effects enhance temperature and concentration profiles, respectively. The findings provide useful insights into heat and mass transfer in non-Newtonian MHD flows relevant to engineering applications.

This paper develops a Group transformation to formulate the laminar natural convection phenomenon, which involves a magnetic field perpendicular to the surface, incompressible fluid, viscosity, as well as a vertically oriented cone on a surface in which the variations in thermal flux are governed by a power function of the length from the cone tip (x=0). The ODEs with corresponding appropriate conditions are reduced from non-dimensional governing PDEs with boundary conditions. The R-K approach based on the shooting technique was used to solve the non-linear ODEs. We visually inspected the temperature and velocity fields for different Prandtl numbers (Pr), the exponent m value, and the magnetic parameter (M) values.

Purpose The growing demands for efficient cooling systems, lubrication and anti-friction properties motivate the investigation of advanced heat transfer in fluid dynamics. The purpose of this study is to investigate the convective flow of ternary hybrid nanofluids around a vertical cylinder, considering the effects of a porous medium, magnetic field, thermal radiation, viscous dissipation and Darcy–Forchheimer influence on heat transfer and fluid velocity. Design/methodology/approach Introduce the similarity transformations to reduce the system of governing partial differential equations (PDEs) to a system of nonlinear ordinary differential equations (ODEs), which are then converted into linear first-order ODEs. The bvp4c solver in MATLAB is used to crack the transformed ODEs and for the graphical illustrations. Findings The combined effects of radiation, Biot number and Eckert number significantly enhance the heat transfer capabilities of ternary hybrid nanofluids, achieving a 17.533% improvement over nanofluids alone. The effects of porosity, Darcy–Forchheimer influence and the magnetic field on fluid motion and skin friction are also investigated and presented in detail. This study has broad applications in cooling systems for power plants, as well as in anti-friction properties for transportation, automotive, precision machinery, robotics engineering and lubrication in rotating machinery, polymers and textile engineering. Originality/value From the literature survey, it is noted that the simultaneous effects of magnetic field, thermal radiation, viscous dissipation and convective boundary conditions on Darcy–Forchheimer flow of ternary hybrid nanofluids around a vertical cylinder have not been investigated so far, and this study addresses this gap. Further, the results are validated and compared with the existing results as a special case.

Abstract Nanofluids with enhanced thermal properties are critical for applications involving intense radiation in industrial and biomedical fields. This study models the mixed convection flow of human blood‐based nanofluids containing single‐walled (SWCNTs) and multi‐walled carbon nanotubes (MWCNTs) along a vertical surface using a fractional‐order approach with the constant proportional Caputo (CPC) operator. Semi‐analytical solutions for temperature, velocity, and concentration are obtained via Laplace transforms, with inversion computed using Stehfest and Tzou methods. Results show that thermal radiation increases blood–SWCNT temperature by up to 12%, while blood–MWCNTs exhibit higher velocity. Activation energy significantly influences concentration profiles. These findings inform the design of advanced nanofluid thermal systems for heat exchangers, solar collectors, microelectronics, and biomedical applications.

The current study mainly explores unsteady, laminar and mixed convection boundary layer flow of Casson ternary hybrid nanofluid in Dary-Forchheimer porous medium about a rotating sphere with slip velocity condition. The study considers quadratic thermal radiation and Cattaneo-Christov heat flux model subjected to convective heating condition with entropy generation for efficient heat transfer and irreversible processes. The non-dimensional similarity variables are employed to convert the governing equations, nonlinear partial differential equations into nonlinear coupled ordinary differential equations. An implicit finite difference approach known, as Keller-box method numerically applied to solve the flow problem. The main findings for thermal and flow behavior of ternary hybrid nanofluid containing silver, titanium and alumina nanoparticles with blood as base fluid are presented through graphical and tabular forms. The outcomes depict that the magnetic field, inertia constant, unsteady and material parameter increases the velocity field, while angular velocity decreases. Moreover, the presence of thermal radiation and convective heat parameters highly optimize the thermal distributions of boundary layer, whereas the coefficient of heat transfer decreases. Conversely, thermal time relaxation and unsteadiness parameters lead to a decrease in temperature field and thermal boundary layer thickness for hybrid and ternary hybrid nanofluids. Entropy production reduces as magnetic parameter strengthen and increase with the Brinkmann number and convection parameter. The findings are confirmed a strong correlations with previous literature. Moreover, Response Surface Methodology and sensitivity analysis are established to quantify the effects of input parameters on thermal performance with values [Formula: see text] = 99.99%, and [Formula: see text]-adjusted = 99.98%, which confirm reliability of the result. The sensitivity analysis depicted that heat transfer rate is high sensitivity to heat generation, moderate sensitivity to nanoparticle volume fraction, and low sensitivity to radiation parameter with their maximum point 1.4178, 0.9898, and 0.4425, respectively. Further, ternary hybrid nanofluid reveals that greater heat transfer enhancement rate of [Formula: see text] than heat transfer enhancement of hybrid nanofluid [Formula: see text] at maximum value.

Effects of the melting phenomenon on combined (natural and forced) convection flow adjacent to a vertical plate within a saturated porous medium filled with hybrid nanoparticles such as copper and aluminum, later serving as base fluid, are investigated in this work. The mathematical modeling of the problem reduced the nonlinear partial differential equations into a set of nonlinear ordinary differential equations through similarity transformation. Solutions to these boundary value problems are obtained using the shooting method in Maple software for various values of the concentration of hybrid nanoparticles, mixed (natural and forced) convection parameter, and melting parameter. Results indicate that the solution has two branches within a specific range of the above parameters. Additionally, findings reveal that the process of solid-liquid phase transition enhances the thermal conductivity of hybrid nanofluids and expedites the expansion of boundary layers.

In this work the non-homogeneous model for the nanofluid flow is formulated to examine the consequences of Fick’s and Fourier’s laws on bioconvective MHD couple-stress nanoliquid flows across a stretching surface under the significances of multiple stratified conditions and activation energy. Both the concentrations of motile microbes and solid nanoparticles are unified flow system. Furthermore, the collective effects of the Cattaneo–Christov (CC) heat flux and thermal radiation are also analyzed. To remove the complexity from the mathematical model, the similarity conversions are presented properly to change the resulting system of PDEs into a nonlinear set of ODEs. The transform set of ODEs is then numerically solved through the parametric continuation method (PCM) in MATLAB software. To validate our results, the outcomes are compared with bvp4c package. It can be perceived that the fluid velocity decreases with the impact of mixed convection and magnetic effects. The energy field enriches with the variation of thermophoresis effect, thermal radiation, buoyancy ratio factor, and Rayleigh number. Furthermore, the mass profile diminishes under the consequences of Lewis number, whereas enhanced with the effect of thermophoresis factor and concentration stratification Biot number.

Abstract This study investigates the linear stability of mixed convection
flow of an Oldroyd-B viscoelastic fluid in a vertical porous channel
subjected to differential heating. To understand how thermal properties
influence stability, two representative Prandtl numbers, Pr = 0.7
and Pr = 7 are considered. The governing equations for basic flow and
generalised eigenvalue problem, based on the viscoelastic form of the
volume averaged Navier-Stokes equations, are solved using a spectral
collocation approach. The analysis shows that variations in Reynolds
number strongly impact the critical Grashof number (Gr′), the propagation
speed of disturbances, and the overall instability mechanisms.
The results further highlight that flow stability is governed by a delicate
balance between fluid elasticity, buoyancy-driven forces, and the
permeability of the porous medium. The fluids with lower Prandtl
number display a stronger sensitivity to elasticity effects and further,
the fluid elasticity has significant impact on the disturbance convection
patterns inside the channel. The nature of instability is commonly
found to be thermal-bouyant for the range of parameters considered
in this study.

Double diffusive convection in flow along heated and non-uniform cylinder with nonlinear kinematics