Numerical simulation of natural convection within wavy square enclosure filled with nanofluid under magnetic field using EFGM with parallel algorithm

Purpose This paper aims to study the flow and heat transfer inside a wavy enclosure filled with Cu-water nanofluid under magnetic field effect by parallel implemented meshfree approach. Design/methodology/approach The simulation has been carried out for a two-dimensional model with steady, laminar and incompressible flow of the nanofluid filled inside wavy enclosure in which one of the walls is sinusoidal such that the amplitude (A = 0.15) and number of undulations (n = 2) are fixed. A uniform magnetic field B0 has been applied at an inclination angle γ. The governing equations for the transport phenomena have been solved numerically by implementing element-free Galerkin method (EFGM) with the sequential as well as parallel approach. The effect of various parameters, namely, nanoparticle volume fraction (φ), Rayleigh number (Ra), Hartmann number (Ha) and magnetic field inclination angle (γ) has been studied on the natural convection flow of nanofluid. Findings The results are obtained in terms of average Nusselt number calculated at the cold wavy wall, streamlines and isotherms. It has been observed that the increasing value of Rayleigh number results in increased heat transfer rate while the Hartmann number retards the fluid motion. On the other hand, the magnetic field inclination angle gives rise to the heat transfer rate up to its critical value. Above this value, the heat transfer rate starts to decrease. Originality/value The implementation of the magnetic field and its inclination has provided very interesting results on heat and fluid flow which can be used in the drug delivery where nanofluids are used in many physiological problems. Another important novelty of the paper is that meshfree method (EFGM) has been used here because the domain is irregular. The results have been found to be very satisfactory. In addition, parallelization of the scheme (which has not been implemented earlier in such problems) improves the computational efficiency.

The dynamics of 3-min wavefronts and their relation to sunspot magnetic fields

We present a study of wave processes occurring in solar active region NOAA 11131 on 10 December 2010, captured by the Solar Dynamics Observatory in the 1600 Å, 304 Å and 171 Å channels. For spectral analysis, we employed pixelized wavelet filtering together with a developed digital technique based on empirical mode decomposition. We studied the ∼3-minute wave dynamics to obtain relationships with the magnetic structuring of the underlying sunspot. We found that during development of wave trains the motion path occurred along a preferential direction, and that the broadband wavefronts can be represented as a set of separate narrowband oscillation sources. These sources become visible as the waves pass through the umbral inhomogeneities caused by the differing magnetic field inclination angles. We found the spatial and frequency fragmentation of wavefronts, and deduced that the combination of narrowband spherical and linear parts of the wavefronts provide the observed spirality. Maps of the magnetic field inclination angles confirm this assumption. We detect the activation of umbral structures as the increasing of oscillations in the sources along the front ridge. Their temporal dynamics are associated with the occurrence of umbral flashes. Spatial localization of the sources is stable over time and depends on the oscillation period. We propose that these sources are the result of wave paths along the loops extending outwards from the magnetic bundles of the umbra. This article is part of the Theo Murphy meeting issue ‘High-resolution wave dynamics in the lower solar atmosphere’.

Hydromagnetic natural convection from a horizontal porous annulus with heat generation or absorption

The problem of unsteady laminar, two-dimensional hydromagnetic natural convection heat transfer in a concentric horizontal cylindrical annulus filled with a fluid-saturated porous medium in the presence of a transverse magnetic field and fluid heal generation effects is studied numerically. It is assumed that the inner and outer walls of the cylindrical annulus are maintained at uniform and constant temperatures Ti and To respectively. The model consists of the heat equation and the equations of motion under the Darcy law. The derived problem with the stream function-temperature formulation is solved numerically using the alternating direction implicit method. This investigation concerns the effect of magnetic field inclination angle, Hartmann number and heat generation on the heat transfer and the flow pattern. The obtained numerical results are presented graphically in terms of streamlines and isotherms. It was found that the heat transfer mechanisms and the flow characteristics depend strongly on the magnetic field inclination angle, Hartmann number and heat generation..

MHD free convection flow in an inclined square cavity filled with both nanofluids and gyrotactic microorganisms

Purpose This paper aims to study the magnetohydrodynamic (MHD)-free convection flow in an inclined square cavity filled with both nanofluids and gyrotactic microorganism. Design/methodology/approach The benefits of adding motile microorganisms to the suspension include enhanced mass transfer, microscale mixing and anticipated improved stability of the nanofluid. The model includes equations expressing conservation of total mass, momentum, thermal energy, nanoparticles, microorganisms and oxygen. Physical mechanisms responsible for the slip velocity between the nanoparticles and the base fluid, such as Brownian motion and thermophoresis, are accounted for in the model. Findings It has been found that the Hartmann number suppresses the heat and mass transfer, while the cavity and magnetic field inclination angles characterize a non-monotonic behavior of the all considered parameters. A rise of the Hartmann number leads to a reduction of the influence rate of the magnetic field inclination angle. Originality/value The present results are original and new for the study of MHD-free convection flow in an inclined square cavity filled with both nanofluids and gyrotactic microorganisms.

Effects of Hall Current and Magnetic Field Inclination on Hydromagnetic Natural Convection Flow in a Micro-Channel With Asymmetric Thermal Boundary Condition

This study examines the impact of induced magnetic field and Hall current on steady fully developed hydromagnetic natural convection flow in a micro-channel under the action of an inclined magnetic field. The mathematical model responsible for the present physical situation is presented in a dimensionless form under relevant boundary conditions. The governing coupled equations are solved exactly. A parametric study of some physical parameters is conducted and a representative set of numerical results for the velocity field, the induced magnetic field, induced current density, volume flow rate, and skin friction on the micro-channel surfaces are illustrated graphically. It is observed that magnetic field inclination plays an important role in flow formation inside the micro-channel. Numerical computation reveals that the increase in inclination angle reduces the hydromagnetic drag leading to enhancement in primary fluid velocity, while the impact is just converse on the secondary fluid velocity. Furthermore, the increase in Hall current parameter increases the magnitude of the fluid velocity in both primary and secondary flow directions.

Estimates of Surface Waves Using Subsurface EM-APEX Floats under Typhoon Fanapi 2010

Seven subsurface Electromagnetic Autonomous Profiling Explorer (EM-APEX) floats measured the voltage induced by the motional induction of seawater under Typhoon Fanapi in 2010. Measurements were processed to estimate high-frequency oceanic velocity variance associated with surface waves. Surface wave peak frequency fp and significant wave height Hs are estimated by a nonlinear least squares fitting to , assuming a broadband JONSWAP surface wave spectrum. The Hs is further corrected for the effects of float rotation, Earth’s geomagnetic field inclination, and surface wave propagation direction. The fp is 0.08–0.10 Hz, with the maximum fp of 0.10 Hz in the rear-left quadrant of Fanapi, which is ~0.02 Hz higher than in the rear-right quadrant. The Hs is 6–12 m, with the maximum in the rear sector of Fanapi. Comparing the estimated fp and Hs with those assuming a single dominant surface wave yields differences of more than 0.02 Hz and 4 m, respectively. The surface waves under Fanapi simulated in the WAVEWATCH III (ww3) model are used to assess and compare to float estimates. Differences in the surface wave spectra of JONSWAP and ww3 yield uncertainties of <5% outside Fanapi’s eyewall and >10% within the eyewall. The estimated fp is 10% less than the simulated before the passage of Fanapi’s eye and 20% less after eye passage. Most differences between Hs and simulated are <2 m except those in the rear-left quadrant of Fanapi, which are ~5 m. Surface wave estimates are important for guiding future model studies of tropical cyclone wave–ocean interactions.