A numerical study of heat and mass transport by double-diffusive magnetoconvection in an electrically conducting fluid under sinusoidal/non-sinusoidal rotational modulation

In this paper, we study the effects of rotational modulation on heat and mass transport due to double-diffusive magnetoconvection in an electrically conducting fluid. In the study, different modes of rotational modulation are considered. Using a perturbation method, a Ginzburg–Landau equation which is nonautonomous is obtained for the modulation amplitude. The effect of rotational modulation on the heat and mass transfer is studied. For the investigation of the effect of buoyancy ratio on the onset of convection, the system of Lorenz type equations is solved using the recent multistage spectral relaxation method. Furthermore, the influence of other fluid parameters on thermal convection and heat and mass transport is analyzed and presented graphically. We find among other results that the effect of increasing the Taylor number is to reduce the Nusselt and Sherwood numbers. A comparison between the sinusoidal and non-sinusoidal modes of rotational modulation on their influence on heat and mass transport in a magneto-diffusive fluid layer is made. We show that the square wave rotational modulation is the most destabilizing type of modulation in the sense that it leads to the early onset of thermal instabilities while the triangular modulation is the most stabilizing type of modulation. The effect of the buoyancy ratio on the nature of the flow pattern has been determined using streamlines, isotherms, and isoconcentrations.     

Nonlinear thermohaline convection in rotating fluids

Linear and weakly nonlinear properties of thermohaline convection in rotating fluids are investigated. Linear stability analysis is studied by plotting graphs for different values of physical parameters relevant to the Earth’s outer core and oceans. We have derived a nonlinear two-dimensional Landau–Ginzburg equation with real coefficients near the onset of stationary convection at the supercritical pitchfork bifurcation and shown the occurrence of Eckhaus and zigzag instabilities. We have studied heat transfer by using Nusselt number which is obtained from Landau–Ginzburg equation at the onset of stationary convection for the steady case. A coupled two-dimensional Landau–Ginzburg type equations with complex coefficients near the onset of oscillatory convection are derived and the stability regions of travelling and standing waves discussed.     

Heat and mass transfer for oscillatory convection in a binary viscoelastic fluid layer subjected to temperature modulation at the boundaries

Weak nonlinear hydrodynamic thermal instability analysis has been performed for double diffusive oscillatory mode of convection in a horizontal layer of viscoelastic fluid, heated from below. Employing complex non-autonomous Ginzburg–Landau equation, effects of various viscoelastic parameters on thermal instability have been investigated. The weak nonlinear analysis reveals that values of viscoelastic parameters have significant effect on the instability. The present study is to investigate the effect of time-periodic temperature modulation on heat and mass transfer, where controlling convection external to the system is important. Sinusoidal profile is taken to modulate the temperature of the boundaries. It is found that the variation of Nusselt number and Sherwood number with respect to the slow time scale becomes rapid as either increasing Rs, Pr, λ, δ or decreasing Γ, ε, Ω. Further, it is found that in-phase temperature modulation has negligible effect, while out of phase temperature modulation and only lower plate temperature modulation have oscillatory effects on heat and mass transport.     

Modified stability analysis of double-diffusive convection in viscoelastic fluid layer saturating porous media

The present analysis mathematically investigates the thermohaline convection problem in viscoelastic fluid layer saturating porous media by utilizing the modified Boussinesq approximation. By performing linear stability analysis, the Darcy–Rayleigh numbers for stationary and oscillatory modes of convection are derived. The effects of different parameters describing the problem are studied numerically. In nonlinear stability analysis, the heat and mass transfer rates in the form of Nusselt and Sherwood numbers, respectively, are obtained for oscillatory convection using the derived Ginzburg–Landau equation. From the results, it is observed that overstability is the preferred mode of instability in linear stability. It is found that in linear double-diffusive convection problems, the stress relaxation imparts a destabilizing effect whereas the strain retardation time, the coefficient of specific heat variation due to temperature, and the concentration gradient have a stabilizing effect on the system's stability. The numerical values of heat and mass transfer rates varied with the coefficient of specific heat showing that the heat transport decreases while the mass transport increases. Also, the stress relaxation time, the concentration gradient, and the gravity modulation's amplitude increase while the strain retardation time decreases the heat and mass transfer rates. The wavelength of oscillations remains unaltered with the variation of specific heat variation due to temperature. The modulation frequency does not affect the heat/mass transfer rate; though, the wavelength of oscillations decreases with increasing frequency.     

Forced convection magnetohydrodynamic flow past a circular cylinder by considering the penetration of magnetic field inside it

A numerical investigation is carried out to analyze forced convection heat transfer in magnetohydrodynamic (MHD) flow past a circular cylinder by considering the penetration of magnetic field inside it. The coupled Navier–Stokes and Maxwell equations are solved along with the energy equation using fourth-order compact finite difference scheme. We have found that the actual decrease in the rate of heat transfer upon the increase in magnetic field is almost double than what is presented in earlier studies where magnetic field is not considered to penetrate inside the cylinder. A non-monotonic behavior of local Nusselt number and mean Nusselt number with interaction parameter is observed which is in good agreement with experimental findings. Validity of heat transfer with quasi static MHD (QSMHD) flow suggests that the heat transfer results of QSMHD flow can be reproduced from our full MHD model in the limit of vanishing magnetic Reynolds number.     

On oscillatory rotating convection of a couple-stress fluid with helical force

Linear and weakly nonlinear stability analyses of thermosolutal convection in a couple-stress fluid with effects of helical force and rotation are performed. The governing nondimensional equations are solved using the normal modes. We have shown the effect of the helical force parameter, solutal Rayleigh number, Couple stress parameter, Lewis number, Taylor number, and Prandtl number on stationary and oscillatory convection regions and presented graphically. Solutal Rayleigh number, Couple stress parameter, Lewis number, and Taylor number have a stabilizing effect on the system whereas the helical force parameter has a destabilizing effect on the system. To study heat transport by convection we have derived the Ginzburg–Landau equation.     

Rayleigh–Benard convection in rotating fluids

Linear and weakly nonlinear properties of Rayleigh–Benard convection in rotating fluids are investigated. Linear stability analysis is studied to investigate analytically the effect of Coriolis force on gravity-driven convection for idealised stress-free boundary conditions. We have derived a nonlinear one-dimensional Landau–Ginzburg equation with real coefficients near the onset of stationary convection at the supercritical pitchfork bifurcation. A coupled Landau–Ginzburg type equations with complex coefficients near the onset of oscillatory convection at the supercritical Hopf bifurcation are derived and discussed the stability regions of travelling and standing waves.     

Study of Brinkman–Bènard nanofluid convection with idealistic and realistic boundary conditions and by considering the effects of shape of nanoparticles

This study deals with linear and weakly non-linear stability analyses of Brinkman–Bènard convection in nanoliquid-saturated porous enclosures. Water with a dilute concentration of molybdenum disulfide nanoparticles with 0.06 volume fraction and 30% glass fiber-reinforced polycarbonate as a porous medium with porosity 0.88 are considered to be a working medium. The analytical solution is obtained in the present study for idealistic and realistic boundary conditions, and their results are compared. An analytically intractable Lorenz model with quadratic nonlinearities is reduced to a tractable Ginzburg–Landau amplitude equation with cubic nonlinearity using the multiscale method. Nanoparticles with different shapes are considered in the study, and their effects on the onset and heat transfer are discussed in great detail graphically in the presence of other parameters arising in the problem.     

Magnetic and buoyancy effects on melting from a vertical plate embedded in saturated porous media

The magnetic and buoyancy effects on melting processes about a vertical wall embedded in a saturated porous medium are investigated. The Forchheimer extension is considered in the flow equations, and the magnetic work is included in the energy equation. A similarity solution for the transformed governing equations is obtained, and the combined effect of magnetic field on heat transfer rate is discussed. Numerical results for the velocity and temperature profiles as well as Nusselt number have been presented. The effect of inertial forces on flow and heat transfer in porous media is analyzed. The Nusselt number was found to decrease at the solid–liquid interface as the melting parameter increases.     

Effect of electromagnetic field on the thermal performance of longitudinal trapezoidal porous fin using DTM–Pade approximant

The heat transfer and thermal distribution through porous fins have gotten a lot of attention in recent years due to their extensive applications in the manufacturing and engineering field. In porous fins, the impact of magnetic field aids in improved heat transfer enhancement. Also, the combination of an electric effect and a magnetic field considerably enhances heat transfer. In this direction, the thermal distribution through a convective–radiative longitudinal trapezoidal porous fin with the impact of an internal heat source and an electromagnetic field is discussed in the present analysis. The governing heat equation is nondimensionalized with nondimensional terms, and the transformed nonlinear ordinary differential equation is solved analytically using the DTM–Pade approximant algorithm. Furthermore, the graphical discussion is presented to explore the impact of various nondimensional parameters, such as convection-conduction parameter, fin taper ratio, thermomagnetic field, radiation–conduction parameter, internal heat generation parameter, and thermoelectrical field on the temperature gradient of the fin. The investigation's key findings disclose that as the magnitude of the convection–conduction parameter, fin taper ratio, and radiation–conduction parameter increase, the thermal distribution through the fin reduces. The thermal distribution inside the fin increases for the heat-generating parameter, thermoelectric, and thermomagnetic fields.     

MHD nonlinear natural convection from a uniformly moving porous vertical plate with constant heat and mass flux in the presence of thermal radiation,diffusion-thermo,heat sink,and chemical reaction

An attempt has been made to investigate the problem of nonlinear free convection heat and mass transfer flow past an infinite vertical porous plate embedded in a porous medium by taking into account thermal radiation and heat sink with constant heat and mass flux. Transversely oriented and of uniform strength $B_0$, a magnetic field has been introduced to the fluid area. The nonlinear density variation with temperature as well as concentration are the basis for the current physical situation, which is explained by this mathematical model. Exact solutions are derived for momentum equation, energy equation, and species continuity equation under the relevant boundary conditions. The dimensionless governing equations are analytically solved. The influence of various physical parameters, such as Dufour number, Schmidt number, thermal Grashof number, magnetic parameter, mass Grashof number, heat sink, thermal radiation, Prandtl number, chemical reaction parameter on the flow, and transport characteristic, has been presented graphically and in tabular form. The novelty of the present investigation is that here both constant heat and mass flux at the plate are taken into account in addition to thermal radiation and heat sink. The findings of the mathematical study demonstrate that velocity, temperature, and skin friction intensify with a rise in the Dufour number this is due to the fact that the convection current becomes stronger as the Dufour number rises. Fluid's concentration declines as the Schmidt number grows, or the concentration rises as the mass diffusivity rises. Fluid temperature is enhanced with high thermal diffusivity. Frictional resistance on the plate hikes due to thermal buoyancy force.     

Experimental study of pool boiling heat transfer of water‐based magnetic fluid on a horizontal heater

The effect of mass concentration of magnetic particles and an applied magnetic field on pool boiling heat transfer of water‐based magnetic fluid on a horizontal heater was investigated. The experimental results show that high‐concentration magnetic fluid deteriorates boiling heat transfer, while middle‐ and low‐concentration magnetic fluid enhances the boiling heat transfer. There was an optimum concentration in which the enhancement of boiling heat transfer was the best. Conclusions were the same with an applied magnetic field that enhances the boiling heat transfer of magnetic fluid further. © 2005 Wiley Periodicals, Inc. Heat Trans Asian Res, 34(3): 180–187, 2005; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.20054     

Natural convection MHD mass transfer through an infinite vertical porous plate in the existence of radiation embedded in porous medium

This research focuses on studying the effects of heat and mass transfer convective flow passing through an infinite vertical plate embedded in porous media under radiation and chemical reaction with constant heat and mass flux. A magnetic field of strength is functional throughout the fluid region. The novelty of the present work is to examine the heat and mass transfer magnetohydrodynamics flow in the presence of thermal radiation. The equations governing the flow, heat and mass transfer are solved analytically using the perturbation technique. Expressions for velocity, temperature, concentration, skin-friction, Nusselt, and Sherwood numbers are obtained. The influence of physical parameters on the flow domain is described graphically and in tabular form. It is found that increase in radiation parameter reduces the velocity and temperature. Moreover, internal friction of the plate decreased with increasing values of radiation parameter.     

玉米热风干燥特性模拟研究

针对玉米热风干燥时内部发生的传热传质过程,以单个玉米为研究对象,构建了三维多组分干燥仿真模型.玉米由表皮、硬质胚乳、软质胚乳和胚四部分组成,扩散系数各不相同,以傅里叶导热方程、菲克扩散方程作为控制方程,表面水分蒸发作为边界条件,利用COMSOL Multiphysics模拟研究了整个干燥过程中内部温度场与浓度场的变化情...     

Heat transport in magnetohydrodynamic physiological blood flow through a constricted artery

In this paper, we study how the magnetohydrodynamic (MHD) pulsatile flow of blood and heat transfer works through a constricted artery with a flexible wall. The human circulatory network consists of veins and arteries that sometimes contain constrictions, allowing the impact of the applied magnetic field on flow fields to be observed. The walls of the flowing medium are considered to be a function of time. The flowing blood is hypothesized as shear-thinning fluid, emulating Yeleswarapu's viscosity replica. Additionally, we consider the energy equation to understand the impact of a magnetic field on heat transfer rates for such flows. The vorticity transport equation along with the stream function equation is obtained using the vorticity–stream function technique. Numerical solutions of the governing nonlinear MHD equations and energy equation in addition to physically pertinent flow conditions were achieved by adapting a finite difference scheme. Considerable attention has been paid to ensure an accurate comparison between the current and previous results. The two sets of numbers appear to match closely. For an even deeper understanding of the flow and heat transport process, the effects of height of stenosis and diverse physiological parameters on time-averaged wall shear stress (TAWSS), rate of heat transport, and so on are explored in depth through their graphical depiction. In the vicinity of the constriction, it is observed that the separation becomes longer with increasing constriction height. Higher magnetic force strength leads to a reduction in separation length. Newtonian fluids transfer heat more rapidly in their narrowing regions and downstream than fluids with non-Newtonian behavior.     

Radiation and slip effects on MHD point flow of nanofluid towards a stretching sheet with melting heat transfer

In the present paper, the melting heat transfer of a nanofluid over a stretching sheet is investigated. Magnetohydrodynamic stagnation point flow with thermal radiation and slip effects is considered for this study. The governing model of the flow is solved by Runge–Kutta fourth-order method using appropriate similarity transformations. Temperature and velocity fields are presented for various flow pertinent parameters. Nondimensional physical parameters such as Prandtl number, radiation parameter, Brownian motion parameter, Lewis number, thermophoresis parameter, magnetic parameter, and melting parameter on fluid velocity, heat, concentration, skin friction, Sherwood number, and Nusselt number are presented graphically and discussed numerically. Heat transfer rate can be increased by increasing slip, melting, or radiation parameter. Mass transfer increases for greater values of melting parameter or slip parameter while radiation parameter shows the opposite impact on mass transfer.     

Heat transfer and buoyancy‐driven convective MHD flow of nanofluids impinging over a thin needle moving in a parallel stream influenced by Prandtl number

The current study focuses on investigating the influence of transverse magnetic field, variable viscosity, buoyancy, variable Prandtl number, viscous dissipation, Joulian dissipation, and heat generation on the flow of nanofluids over thin needle moving in parallel stream. The theory of nanofluids that includes the Buongiorno model featured by slip mechanism, such as Brownian motion and thermophoresis, has been implemented. Further, convective boundary condition and zero mass flux condition are considered. The nondimensionally developed boundary layer equations have been solved by Runge–Kutta–Fehlberg method with shooting technique for different values of parameters. The most relevant outcomes of the present study are that the augmented magnetic field strength, viscosity parameter, buoyancy ratio parameter, and the size of the needle undermine the flow velocity, establishing thicker velocity boundary layer while Richardson number and Brownian motion show opposite trend. Another most important outcome is that increase in the size of the needle, viscous dissipation, convective heating, and heat generation upsurges the fluid temperature, leading to improvement in thermal boundary layer. The effects of different natural parameters on wall shear stress and heat and mass transfer rates have been discussed.     

Enhancement of Heat Transfer with Porous/Solid Insert for Laminar Flow of a Participating Gas in a 3-D Square Duct

In recent years, porous or solid insert has been used in a duct for enhancing heat transfer in high temperature thermal equipment, where both convective and radiative heat transfer play a major role. In the present work, the study of heat transfer enhancement is carried out for flow through a square duct with a porous or a solid insert. Most of the analyses are carried out for a porous insert. The hydrodynamically developing flow field is solved using the Navier–Stokes equation and the Darcy–Brinkman model is considered for solving the flow in the porous region. The radiative heat transfer is included in the analysis by coupling the radiative transfer equation to the energy equation. The fluid considered is CO₂ with temperature dependent thermophysical properties. Both the fluid and the porous medium are considered as gray participating medium. The increase in heat transfer is analyzed by comparing the bulk mean temperature, Nusselt number, and radiative heat flux for different porous size and orientation, Reyonlds number, and Darcy number.     

Effects of mass transfer and free convection on the unsteady mhd flow past a vertical porous plate with constant suction

Effects of free convection currents and mass transfer on the unsteady flow of an electrically conducting and viscous incompressible fluid past an infinite vertical porous plate subjected to uniform suction, in the presence of transverse magnetic field, have been studied taking into account that the external flow velocity varies periodically with time in magnitude but not in direction. The effect of the induced magnetic field has been neglected. Approximate solutions to the transient flow, the amplitude and the phase of the skin-friction and the rate of heat transfer have been derived. During the course of the discussion, the effects of the Grashoff number Gr, the modified Grashoff number Gc (depending on the concentration difference), the Schmidt number Sc, the Eckert number Ec, the magnetic field parameter M, and the frequency ω have been discussed.     

An axisymmetric bioheat transfer analysis through a unified model

A unified model is developed for the analysis of heat transfer (radiation and non-Fourier conduction) in an axisymmetric participating medium. The proposed model includes three different variants of hyperbolic–parabolic heat conduction models, that is, the single phase lag model, dual phase lag model, and the Fourier (no phase lag) model. The radiating-conducting medium is radiatively absorbing, emitting, and isotropically scattering. Significance of all the above mentioned models on the heat transfer characteristics is investigated in a two-dimensional axisymmetric geometry. The equation of transfer and the coupled non-Fourier conduction-radiation equation are solved via finite volume method. A fully implicit scheme is used to resolve the transient terms in the energy equation. For spatial resolution of radiation information, the STEP scheme is applied. Tri-diagonal-matrix-algorithm is used to solve the resulting set of linear discrete equations. Effects of two important influencing parameters: the scattering albedo and the radiation- conduction parameter are studied on the temporal evolution of temperature field in the radiatively participating medium. The non-Fourier effect of heat transport captured well with the proposed unified model. A good agreement can be found between the proposed model predictions and those available in the literature. It is also found that when the phase lag of the temperature gradient and the heat flux are the same, it reduces to conventional Fourier conduction-radiation and the wave behavior diminishes. However, the reduction to this Fourier model fails in the presence of constant blood perfusion and metabolic heat generation.