Time-dependent Convection Research Articles

Time-Dependent Magnetohydrodynamic (MHD) Flow of an Exothermic Arrhenius Fluid in a Vertical Channel with Convective Boundary Condition

The current study examined the effects of magnetohydrodynamics (MHD) on time-dependent mixed convection flow of an exothermic fluid in a vertical channel. Convective heating and Navier’s slip conditions are considered. The dimensional nonlinear flow equations are transformed into dimensionless form with suitable transformation. For steady-state flow formations, we apply homotopy perturbation approach. However, for the unsteady-state governing equation, we use numerical technique known as the implicit finite difference approach. Flow is influenced by several factors, including the Hartmann number, Newtonian heating, Navier slip parameter, Frank-Kamenetskii parameter, and mixed convection parameter. Shear stress and heat transfer rates were also investigated and reported. The steady-state and unsteady-state solutions are visually expressed in terms of velocity and temperature profiles. Due to the presence of opposing force factors such as the Lorentz force, the research found that the Hartmann number reduces the momentum profile. Fluid temperature and velocity increase as the thermal Biot number and Frank-Kamenetskii parameter increase. There are several scientific and infrastructure capabilities that use this type of flow, such flow including solar communication systems exposed to airflow, electronic devices cooled at room temperature by airflow, nuclear units maintained during unscheduled shutoffs, and cooling systems occurring in low circumstances. The current findings and the literature are very consistent, which recommend the application of the current study.

Supercloseness analysis of a stabilizer free weak Galerkin finite element method for time dependent convection diffusion reaction equation

This paper considers a stabilizer-free weak Galerkin (SFWG) finite element method for the time-dependent convection diffusion reaction equation. We describe error estimate for both semidiscrete and fully discrete schemes and achieve the supercloseness convergence rate, which is two orders higher than the optimal order associated with SFWG finite element space (Pk(K),Pk+1(∂K),[Pk+1(K)]2). More precisely, we obtain O(hk+2+τ2) in L∞(H1) norm and O(hk+3+τ2) in L∞(L2) norm. Numerous numerical examples are provided to confirm the theoretical findings and efficiency of the proposed method.

Superconvergence error analysis of an efficient mixed finite element method for time-dependent natural convection problem

Superconvergence error analysis of an efficient mixed finite element method for time-dependent natural convection problem

Interpolated coefficient characteristic finite element method for semilinear convection–diffusion optimal control problems

In this paper, a fully discrete interpolated coefficient characteristic finite element approximation is proposed for optimal control problems governed by time-dependent semilinear convection–diffusion equations, where the hyperbolic part of the state equation is first treated by directional derivatives and then discretized by backward difference, the semilinear term is dealt with interpolation coefficient finite elements technique. A priori error estimates for the control, state and co-state variables are derived. Theoretic results are confirmed by a numerical example.

Thermocapillary-driven coherent structures by low-Stokes-number particles and their morphology in high-aspect-ratio liquid bridges

Thermocapillary-driven coherent structures by low-Stokes-number particles are experimentally investigated. Time-dependent convection is induced in a tall or high-aspect-ratio half-zone liquid bridge. We successfully realize coherent structures, which seem rigidly rotating by following the traveling-wave-type convection of mHTW=1 in azimuthal wave number due to so-called hydrothermal-wave instability. The Poincaré sections at different heights of a single particle forming the coherent structure are obtained in the rotating frame of reference by preparing a thin light sheet. Projected distribution of the multiple particles forming the coherent structure are also depicted to examine the correlation with the Poincaré points. The stability of the coherent structures is discussed by tracking the particles exhibiting turnover motion in the liquid bridge.

Numerical computing of Soret and linear radiative effects on MHD Casson fluid flow toward a vertical surface through a porous medium: Finite element analysis

In this work, we investigate the time-dependent MHD free convection of Casson fluid across a vertical semi-infinite plate fitted inside a permeable medium, along with viscous dissipation, radiation absorption, and Soret effect by using several non-dimensional variables. The characteristics of a variety of elements influencing the flow phenomenon are examined using the Casson fluid model. The governing dimensional partial differential equations are transformed into an ordinary differential equation set by introducing the similarity variables. The reduced model is numerically solved via the Galerkin finite element method. The non-dimensional equations with suitable boundary conditions can be mathematically simplified using the efficient Galerkin finite element approach. The restrictions are shown numerically and graphically, and their effects on temperature, velocity, species concentration, and rate coefficients are all shown. This study is to present the influence of radiation absorption along with viscous dissipation on the heat transfer phenomenon. For different flow parameter estimations, graphs are generated for various flow profiles as well as skin friction coefficients. The Nusselt (Nu) and Sherwood (Sh) quantities are also demonstrated via graphs.

Numerical Study of Non-Newtonian Fluid in a Cavity with Corrugated Bottom Wall Using Buongiorno’s Mathematical Model

A 2-dimensional computational analysis is carried out for a time dependent double diffusive mixed convection flow using non-Newtonian nanofluid. A square-shaped cavity with a corrugated bottom wall is taken with higher temperature and concentration on the top wall. The physical model under consideration is represented by a set of governing equations and solved using the Galerkin weighted residual method based on Finite Element Analysis. Solutions are done for 4 controlling parameters such as Richardson number (Ri = 0.1 - 15), Lewis number (Le = 0.5 - 3), and thermophoresis parameter (Nt = 0.2 - 0.9), and Brownian motion parameter (Nb = 0.2 - 1.0) at different values of τ. For the aforementioned parameters, heat and mass transfer rates, temperature distributions, velocity distributions, and mass distributions in terms of isotherm, streamlines, and iso-concentration are graphically presented. It has been observed that for higher values of Ri, both Nuav and Shav increased while Le decreased for higher values of Nt at any fixed time. It is worth noting that the considered parameter exhibits consistent behavior after a while. HIGHLIGHTS The numerical analysis of non-Newtonian nanofluid with a corrugated bottom wall and a sliding upward wall is performed using Buongiorno's mathematical model The effect of the Richardson number, Lewis number, Brownian motion, and thermophoresis parameters on different dimensionless time periods is addressed The heat and mass transfer rate is increased as the Richardson number, Lewis number, Brownian motion, and thermophoresis parameters increase in value GRAPHICAL ABSTRACT

Uniform stability of the SUPG method for the evolutionary convection–diffusion–reaction equation

To solve the evolutionary convection-diffusion-reaction equation, the implicit Euler method and the streamline upwind Petrov Galerkin (SUPG) method are used for time discretization and space discretization respectively in this paper. Uniform stability is obtained with respect to the temporal and spatial discretization parameters. A new projection is introduced for the stability analysis instead of the common idea of material derivative. The analysis does not require a strict relation between time step and space step, which is usually needed by derivations based on the technique of material derivative. Furthermore, it can handle the case of time-dependent convection and reaction coefficients.

Numerical investigation of the effect of surface viscosity on droplet breakup and relaxation under axisymmetric extensional flow

In this study, we perform boundary-integral simulations to investigate the role of interfacial viscosity in the deformation and breakup of a single droplet suspended in an axisymmetric extensional flow under the Stokes flow regime. We model the insoluble surfactant monolayer using the Boussinesq–Scriven constitutive relationship for a Newtonian interface. We compare the deformation and breakup results from our boundary-element simulations with results from small deformation perturbation theories. We observe that the surface shear/dilational viscosity increases/decreases the critical capillary number beyond which the droplet becomes unstable and breaks apart by reducing/increasing the droplet deformation at a given capillary number compared with a clean droplet. We present the relative importance of surface shear and dilational viscosity on droplet stability based on their measured values reported in experimental studies on surfactants, lipid bilayers and proteins. In the second half of the paper, we incorporate the effect of surfactant transport by solving the time-dependent convection–diffusion equation and consider a nonlinear equation of state (Langmuir adsorption isotherm) to correlate the interfacial tension with the changes in surfactant concentration. We explore the coupled influence of pressure-dependent surface viscosity and Marangoni stresses on droplet deformation and breakup. In the case of a droplet with pressure-dependent surface shear viscosity, we find that a droplet with pressure-thinning/thickening surfactant is less/more deformed than a droplet with pressure-independent surfactant. We conclude by discussing the combined impact of surface viscosity and surfactant transport on the relaxation of an initially extended droplet in a quiescent external fluid.

Energy transfer mechanism during ethanol evaporation with external tangential temperature gradient under low pressure environment

For the purpose of revealing the energy-transfer process during ethanol evaporation under low pressure environment, experimental measurement and numerical simulation are adopted for ethanol evaporation at different liquid depths and external radial temperature differences in annular pools. The results show that two thermocapillary vortexes appear below the liquid–vapor interface. Most of the latent heat of vaporization is from the liquid phase, but little from the gas phase. With the increase of liquid layer depth, the steady axisymmetric flow will transform into three-dimensional time-dependent convection. The mechanism of flow instability should be attributed to the variation lag of velocity behind the variation of flow resistance. The critical vapor pressure of flow destabilization depends on radial temperature difference and liquid layer depth. Furthermore, the magnitude of temperature discontinuity across the liquid–vapor interface is the largest near the hot inner cylinder. With the increase of the liquid layer depth, the temperature discontinuity decreases.

An assessment of solvers for algebraically stabilized discretizations of convection–diffusion–reaction equations

Abstract We consider flux-corrected finite element discretizations of 3D convection-dominated transport problems and assess the computational efficiency of algorithms based on such approximations. The methods under investigation include flux-corrected transport schemes and monolithic limiters. We discretize in space using a continuous Galerkin method and ℙ1 or ℚ1 finite elements. Time integration is performed using the Crank–Nicolson method or an explicit strong stability preserving Runge–Kutta method. Nonlinear systems are solved using a fixed-point iteration method, which requires solution of large linear systems at each iteration or time step. The great variety of options in the choice of discretization methods and solver components calls for a dedicated comparative study of existing approaches. To perform such a study, we define new 3D test problems for time dependent and stationary convection–diffusion–reaction equations. The results of our numerical experiments illustrate how the limiting technique, time discretization and solver impact on the overall performance.

Numerical Model of the Railway Brake Disk for the Temperature and Axial Thermal Stress Analyses

Abstract Increases in travel speeds and traffic density in railway sector impose challenges on the modern disk-pad brake systems such as higher temperatures and stresses resulting in cracks/hot spots and a degraded system performance. The prediction of disk thermal behavior under challenging conditions has become an important engineering issue. In this study, a model is developed using the finite difference method with realistic time-dependent boundary conditions and different experimental convection correlations with non-uniform time-step size features. A previous numerical/experimental study on the thermal behavior of railway disk brake is partly adopted and enhanced. The results of the developed model agree well with the results of the previous study. A practical prediction method for thermal stresses in the disk is applied using the axial temperature distributions at several time instants from locations with highest temperature. Apart from that, same configuration of the disk with the pad is modeled in simcenter star-ccm+ which is a well-validated commercial computational fluid dynamics software to compare the results and computation times with that of the developed model. Using this model, an investigation has been conducted on the effect of temperature-dependent material properties on thermal behavior of the disk. The developed numerical model can simulate the conditions experienced by a railway disk in a relatively new standard (EN 14535-3) considering the transient thermal behavior and axial thermal stress distribution with relatively low computational time and reasonable accuracy. Also, in this study, valuable insights are obtained on the effect of variable thermal properties of the disk and convection correlations on the disk thermal behavior.

A stabilizer free spatial weak Galerkin finite element methods for time-dependent convection-diffusion equations

In this paper, we propose a stabilizer free spatial weak Galerkin (SFSWG) finite element method for solving time-dependent convection diffusion equations based on weak form Eq. (4). SFSWG method in spatial direction and Euler difference operator Eq. (37) in temporal direction are used. The main reason for using the SFSWG method is because of its simple formulation that makes this algorithm more efficient and its implementation easier. The optimal rates of convergence of 𝒪⁢(hk) and 𝒪⁢(hk+1) in a discrete H1 and L2 norms, respectively, are obtained under certain conditions if polynomial spaces (Pk⁢(K),Pk⁢(e),[Pj⁢(K)]2) are used in the SFSWG finite element method. Numerical experiments are performed to verify the effectiveness and accuracy of the SFSWG method.

Time-dependent mixed convection flow of Ag–MgO/water hybrid nanofluid over a moving vertical cone with rough surface

Time-dependent mixed convection flow of Ag–MgO/water hybrid nanofluid over a moving vertical cone with rough surface

A fast method for solving time-dependent nonlinear convection diffusion problems

<abstract><p>In this paper, a fast scheme for solving unsteady nonlinear convection diffusion problems is proposed and analyzed. At each step, we firstly isolate a nonlinear convection subproblem and a linear diffusion subproblem from the original problem by utilizing operator splitting. By Taylor expansion, we explicitly transform the nonlinear convection one into a linear problem with artificial inflow boundary conditions associated with the nonlinear flux. Then a multistep technique is provided to relax the possible stability requirement, which is due to the explicit processing of the convection problem. Since the self-adjointness and coerciveness of diffusion subproblems, there are so many preconditioned iterative solvers to get them solved with high efficiency at each time step. When using the finite element method to discretize all the resulting subproblems, the major stiffness matrices are same at each step, that is the reason why the unsteady nonlinear systems can be computed extremely fast with the present method. Finally, in order to validate the effectiveness of the present scheme, several numerical examples including the Burgers type and Buckley-Leverett type equations, are chosen as the numerical study.</p></abstract>

Could the Réunion plume have thinned the Indian craton?

AbstractThick and highly viscous roots are the key to cratonic survival. Nevertheless, cratonic roots can be destroyed under certain geological scenarios. Eruption of mantle plumes underneath cratons can reduce root viscosity and thus make them more prone to deformation by mantle convection. It has been proposed that the Indian craton could have been thinned due to eruption of the Réunion plume underneath it at ca. 65 Ma. In this study, we constructed spherical time-dependent forward mantle convection models to investigate whether the Réunion plume eruption could have reduced the Indian craton thickness. Along with testing the effect of different strengths of craton and its surrounding asthenosphere, we examined the effect of temperature-dependent viscosity on craton deformation. Our results show that the plume-induced thermomechanical erosion could have reduced the Indian craton thickness by as much as ~130 km in the presence of temperature-dependent viscosity. We also find that the plume material could have lubricated the lithosphere-asthenosphere boundary region beneath the Indian plate. This could be a potential reason for acceleration of the Indian plate since 65 Ma.

Forced convection heat transfer from a plate stack embedded in a homogeneous porous medium

The current paper examines some novel and interesting aspects of the mathematical modelling of fluid flow and forced convection heat transfer from a plate stack embedded in a homogeneous porous media. Time-dependent forced convection heat transfer from some cylinders embedded in groundwater are explored numerically using finite difference methods. An algorithm was developed about rectangular heated solid objects with the same size placed in an in-line arrangement in homogeneous porous media. Central and one-sided finite difference formulae are used to discretize the domain. Applying the mathematical model, continuity, momentum, and energy equations are solved by the finite difference methods. Generally, analytical solutions are not possible for such problems, so most of the work is done numerically. The numerical results for the two-dimensional velocity potential and stream function have been calculated and the resulting fluid and temperature contours are represented graphically for various values of the parameters involved (e.g. length of the entrance, the fluid flow rates, coefficient of thermal diffusion and advection in the observed long-time plume behaviour, effect of time and temperature on heat transfer, etc.). It is observed that fluid and heat fluxes and fluid velocity depend upon the size, shape, burial depth, position of heated objects, and positions of the entrance and exit of the homogeneous porous media. Moreover, the hydraulic conductivity of the porous medium affects the pressure drops, fluid velocity as well as the heat transfer rates.

Finite volume element approximation for time dependent convection diffusion reaction equations with memory

Error estimates for element schemes for time-dependent for convection-diffusion-reaction equations with memory are derived and stated. For the spatially discrete scheme, optimal order error estimates in L2 , H1 , and W1,p norms for 2 ≤ p < ∞, are obtained. In this paper, we also study the lumped mass modification. Based on the Crank-Nicolson method, a time discretization scheme is discussed and related error estimates are derived.

Asteroseismology of RRab variable star EZ Cnc from K2 photometry and LAMOST spectroscopy

ABSTRACT EZ Cnc, or EPIC 212182292, is a non-Blažko RRab variable star located in the field of K2 Campaign 16. Its atmospheric parameters (Teff, log g, [M/H]) and radial velocities are measured from the 55 high-quality LAMOST medium-resolution spectra. The fundamental frequency of pulsation is derived as f = 1.8323(17) d−1 from the K2 light curves. The amplitude ratios R21 = 0.5115(15), 0.490(8), R31 = 0.3249(20), 0.279(7) and Fourier phase differences φ21 = 2.7550(20), 2.764(16), φ31 = 5.7194(25), 5.719(31) are determined from the Fourier decomposition of K2 light curve and LAMOST radial velocity curve, respectively. Through the constraints of the parameters, four optimal models are obtained in a time-dependent turbulent convection model survey for EPIC 212182292. The parameters of EPIC 212182292 are derived as M = 0.48 ± 0.03 M⊙, L = 42 ± 2 L⊙, Teff = 6846 ± 50 K, log g = 2.79 ± 0.01 dex, and Z = 0.006 ± 0.002, respectively. The precisely determined parameters for RRab variable stars like EPIC 212180092 might help to better understand the period–luminosity relationship of RR Lyrae stars.

Simulation of the onset of convection in a porous medium layer saturated by a couple-stress nanofluid

Linear and nonlinear stability analyses for the onset of time-dependent convection in a horizontal layer of a porous medium saturated by a couple-stress non-Newtonian nanofluid, intercalated between two thermally insulated plates, are presented. Brinkman and Maxwell–Garnett formulations are adopted for nanoscale effects. A modified Darcy formulation that includes the time derivative term is used for the momentum equation. The nanofluid is assumed to be dilute and this enables the porous medium to be treated as a weakly heterogeneous medium with variation of thermal conductivity and viscosity, in the vertical direction. The general transport equations are solved with a Galerkin-type weighted residuals method. A perturbation method is deployed for the linear stability analysis and a Runge–Kutta–Gill quadrature scheme for the nonlinear analysis. The critical Rayleigh number, wave numbers for the stationary and oscillatory modes, and frequency of oscillations are obtained analytically using linear theory, and the nonlinear analysis is executed with minimal representation of the truncated Fourier series involving only two terms. The effect of various parameters on the stationary and oscillatory convection behavior is visualized. The effect of couple-stress parameter on the stationary and oscillatory convections is also shown graphically. It is found that the couple-stress parameter has a stabilizing effect on both the stationary and oscillatory convections. Transient Nusselt number and Sherwood number exhibit an oscillatory nature when time is small. However, at very large values of time, both Nusselt number and Sherwood number values approach their steady-state values. The study is relevant to the dynamics of biopolymers in solution in microfluidic devices and rheological nanoparticle methods in petroleum recovery.