Transient Convection Research Articles

Input Uncertainty and Implication for Modeling Generic and High-Fidelity Transient Convection Problems

Transient processes and uncertainty propagation impacting the transient temperature variation profile for a plate heated from the top and convection cooled at the bottom surface are investigated. The model dimensionless input parameters, such as the Biot number Bi and dimensionless initial conditions, are formulated describing physical properties of the plate and ambient medium with subsequent impact on the dimensionless temperature variation. As is shown, in the case of small Bi, dimensionless relaxation time of the temperature variation toward its steady state is proportional to and can be very large. For large Bi, the temperature variation usually passes through a peak before reaching its stationary profile. Stochastic nature of the dimensionless temperature variation is explored. As is found, the amplitude of its stochastic spread depends, in general, on the mean values of the dimensionless inputs at a fixed standard deviation. As is also shown, dimensionless time evolution of the uncertainty amplitude depends crucially on standard deviations of the dimensionless input parameters; it may increase or decrease with time, or stay small over time. Finally, uncertainty propagation in a high-fidelity model of a copper block, used in an experimental setup, is compared with the developed generic plate model.

Ceres’ Broad‐Scale Surface Geomorphology Largely Due To Asymmetric Internal Convection

AbstractWhile we now know much about the volatile‐rich world of Ceres from the Dawn mission, the deep interior remains something of an enigma, shrouded by a crust composed of water ice, carbonates, phyllosilicates, salts and clathrate hydrates. While smaller than most active moons or planets, Ceres has many features commonly associated with active, icy bodies including: hydrothermal, cryovolcanic, and tectonic features. Yet on active icy moons tidal heating is a significant component of the thermal budget; it is unclear whether radiogenic heating alone would be sufficient to supply the heat necessary for Ceres' interior to undergo solid‐state convection. Here we show that transient asymmetric convection develops as the temperature within the body rises from heat generated by the decay of long‐lived radionuclides (e.g., U, Th, K). The onset of transient asymmetric convection may reconcile a number of puzzling features on Ceres including: the missing large craters, Hanami Planum—the region of thickened crust, the gravity and crustal thickness, and the lithospheric stress state represented by the Samhain Catenae. Hemispheric‐scale instabilities may also be important in the evolution of small bodies with small cores throughout the solar system, including the small icy moons of Saturn and Uranus as well as Kuiper belt objects.

Unified scale laws for transient convective boundary layers: From flat to curved boundary layers

Transient natural convection boundary layer flow is studied at Pr>1 and the curvature effect is specifically and fundamentally explored. Important scale laws, i.e. boundary layer thickness \ensuremath{\delta}t and characteristic velocity ${u}_{z}$ of the transient and steady states and the cut-off time ${t}_{s}$ of the initial growth, are proposed and validated. We find that for cylinder radius much larger than the boundary layer thickness, the present scaling relations reduce to those of the classic flat boundary layer. The most curved boundary layer we examine is 26 times thicker than the cylinder radius. We show that the present scaling set is accurate for all flow conditions bounded by the two limiting scenarios.

Analytical Solution to Transient Convection–Diffusion Equation for Reaction at Rotating Disk Electrode Using Novel Hybrid Integral Balance-Collocation Method

Analytical Solution to Transient Convection–Diffusion Equation for Reaction at Rotating Disk Electrode Using Novel Hybrid Integral Balance-Collocation Method

Numerical investigation on transient third-grade magnetized nanofluid flow and radiative convection heat transfer from a stationary/moving cylinder: nanomaterial and nanoparticle shape effects

In this study, a mathematical model is developed for analyzing the time-dependent magneto-convective flow and heat transfer characteristics of an electrically conducting (functional) third-grade Reiner-Rivlin non-Newtonian nanofluid from a moving or stationary hot cylinder in the presence of magnetic field and thermal radiation. A well-tested convergent Crank–Nicolson type finite difference algorithm is employed to solve the transformed, nonlinear boundary value problem. The Tiwari-Das nanofluid volume fraction model is adopted for nanoscale effects and the Rosseland algebraic flux model for radiative heat flux effects. It has been shown that the shape of nanoparticles remarkably contributes to the enhancement of heat transfer. Several metallic nanoparticle types such as Al2O3, Cu, and TiO2 are examined. It is found from the investigation that the viscoelastic nanofluid with TiO2 nanoparticles results in more heat transfer than the other nanoparticles. Lower velocity and higher temperature values are computed at transient conditions with a higher third-grade fluid parameter for the flow of nanofluid (Al2O3-SA). The plots of transient friction and heat transfer coefficients are visualized at the surface of a hot cylinder. The tabulated heat transfer coefficient is comparatively more for the moving cylinder than the stationary cylinder. Detailed validation of results of the numerical scheme with previous studies is included. The simulations find applications in coating deposition (enrobing) of magnetic nanomaterial at high temperatures, functional nanomaterial synthesis, etc.

A semi-Lagrangian meshfree Galerkin method for convection-dominated partial differential equations

A new numerical method, which is based on the coupling between semi-Lagrangian (SL) method and element free Galerkin (EFG) method, is developed for convection–diffusion partial differential equations with dominated convection terms. It is the first time that the SL method combined with the EFG method to solve the transient convection–diffusion equations. This combination has been more effective than expected. Compared with the existing SL methods, the proposed method shows several new advantages. Firstly, it takes full advantages of meshfree methods, therefore, the implementation difficulties of the SL method in backward tracing and departure point interpolation are greatly reduced. As interpolating the function values to a departure point, complex searching algorithm is not needed to determine which grid cell contains the departure point, and higher order interpolation is not essential to ensure the global accuracy. Meanwhile, in addition to having good stability and allowing the use of large time-step sizes, the new method realizes the continuous transition from convection–diffusion equation to pure convection equation and provides a uniform numerical format for these two kinds of equations. A problem with available analytical solution is solved to analyze the convergence behavior of the proposed method. It is demonstrated that the method can achieve the optimal convergence rate. Subsequently, the method is applied to solve the 1D and 2D Burgers’ equations. The results show that the proposed method can indeed obtain surprisingly good results for the Burgers’ equations in the very challenging convection-dominated and pure convection cases. These results are better than almost all the ones we have seen in literature. The good performance of this method in solving the challenging Burgers’ equations makes us believe that it will be a very promising method for solving convection-dominated problems.

Implicit-explicit multistep formulations for finite element discretisations using continuous interior penalty

We consider a finite element method with symmetric stabilisation for the discretisation of the transient convection–diffusion equation. For the time-discretisation we consider either the second order backwards differentiation formula or the Crank–Nicolson method. Both the convection term and the associated stabilisation are treated explicitly using an extrapolated approximate solution. We prove stability of the method and the τ2 + hp+½ error estimates for the L2-norm under either the standard hyperbolic CFL condition, when piecewise affine (p = 1) approximation is used, or in the case of finite element approximation of order p ≥ 1, a stronger, so-called 4/3-CFL, i.e. τ ≤ Ch4/3. The theory is illustrated with some numerical examples.

Surrogate Modeling of Transient Convection Heat Transfer Using Conditional Generative Adversarial Networks

Surrogate Modeling of Transient Convection Heat Transfer Using Conditional Generative Adversarial Networks

Heat transfer past rotationally oscillating circular cylinder heated with time‐periodic pulsating temperature in a uniform flow

AbstractThe transient forced convection heat transfer from an impulsively started rotationally oscillating circular cylinder, heated with time‐periodic pulsating temperature in a two‐dimensional uniform, laminar and viscous flow of Newtonian, incompressible, constant property fluid is investigated in this paper. The two‐dimensional Navier‐Stokes and energy equations are solved using a higher‐order compact (HOC) finite difference scheme on non‐uniform polar grids. Computational code for solving the problem is written in C programming language and is validated against existing research works. The flow and heat transfer characteristics are mainly influenced by the amplitude of time‐periodic pulsating temperature (), period of time‐periodic pulsating temperature (), Prandtl number (), Reynolds number (), and cylinder oscillation parameters i.e. maximum rotational rate (), frequency ratio (). The numerical computations are done for the range of parameter values , , , , and . The backward heat transfer is observed for certain values of the amplitude of time‐periodic pulsating temperature and the amount of backward heat transfer enhances with increasing amplitude of temperature. High period value () of pulsating temperature is found to reduce the amount of heat convection downstream. The influence of pulsating temperature is discussed for an increase or decrease in heat transfer rate relative to the constant cylinder‐temperature case.

Dynamic Europa ocean shows transient Taylor columns and convection driven by ice melting and salinity

The deep (~100 km) ocean of Europa, Jupiter’s moon, covered by a thick icy shell, is one of the most probable places in the solar system to find extraterrestrial life. Yet, its ocean dynamics and its interaction with the ice cover have received little attention. Previous studies suggested that Europa’s ocean is turbulent using a global model and taking into account non-hydrostatic effects and the full Coriolis force. Here we add critical elements, including consistent top and bottom heating boundary conditions and the effects of icy shell melting and freezing on ocean salinity. We find weak stratification that is dominated by salinity variations. The ocean exhibits strong transient convection, eddies, and zonal jets. Transient motions organize in Taylor columns parallel to Europa’s axis of rotation, are static inside of the tangent cylinder and propagate equatorward outside the cylinder. The meridional oceanic heat transport is intense enough to result in a nearly uniform ice thickness, that is expected to be observable in future missions.

Onset of transient convection in a porous medium with an embedded low-permeability layer

Deep saline aquifers used for CO2 sequestration are commonly made of sedimentary formations consisting of several layers of distinguishable permeability. In this work, the effect of a non-monotonic, vertically varying permeability profile on the onset of convective instability is studied theoretically using linear stability analyses. The onset time depends on the interaction between the permeability profile and the location of the concentration perturbation peak beyond which the concentration of CO2 decays. A thin low-permeability layer can either accelerate or delay the onset time of the convective instability depending on the nature of the permeability variation – whether the permeability transition is smooth or layered, the Rayleigh number (Ra), and the location of the permeability change (a^) relative to the perturbation peak (a^c*), which scales as a^c*≈14Ra−1 for homogeneous systems. However, the low permeable layer has no effect on the onset time when it is near the lower boundary of a medium with sufficiently large Ra (a^c*≪a^). This nontrivial dependence highlights the implication of ignoring geological features of a small spatial extent, indicating the importance of a detailed characterization of CO2 storage sites.

Transient nonlinear Rayleigh–Bénard convection with single-mode initiation

Transient nonlinear convection in a finite Prandtl number fluid heated uniformly from below is studied analytically and numerically. We consider the simple geometry of a square cavity with normal-mode compatible boundary conditions. By design, only the marginal state of convection onset contributes to the initial condition for the two-dimensional supercritical convection. The thermal amplitude and the flow amplitude are taken as two independent initial conditions. There are two ways of initiation: (i) soft start with a very small initial amplitude, leading to early exponential growth. (ii) Kick-started transient convection with relatively large initial amplitudes, by which we perform a small-time expansion for benchmarking. Seemingly complicated transient flow occurs with a kick-start where the initial spin and the initial buoyancy torque are in conflict. However, the intricate spiraling flow decays after a couple of reversals of flow directions, and a steady convection settles. This is due to the strict antisymmetry of the temperature perturbation around the mid-point of the cavity, in combination with the symmetry of the flow field.

Parameter Variability in Viscous Convection

For the optimal design of cooling and heating devices, the properties of the included fluids are crucial. The temperature dependence of viscosity deserves attention, as changes can be one order of magnitude or more. Here we examine the influence on convective motions by simulating a heating and cooling experiment with a vertical cylinder by finite element computational fluid dynamics (CFD) models. Such an experimental setup in which flow patterns are determined by transient viscous convection has not been simulated before. Evaluating the general behavior of the experiment in 2D, we find a dynamic phase after and before phases with moderate changes. Flow patterns in the dynamic phase change significantly with the temperature range of the experiment. We compare the outcome of the numerical models with results from laboratory experiments, finding major discrepancies concerning the flow patterns in the dynamic phase. 3D modeling shows weaker dynamics but does not show good timing with the experiment. The study depicts the importance of parameter dependencies for convective motions and demonstrates the capabilities and limitations of models to reproduce details of viscous convection.

Development of the Substorm as a Manifestation of Convection Transient

AbstractWe reproduced the substorm by global simulation and analyzed the development of convection, shear, the dynamo, and the field‐aligned current (FAC) at the final stage of the growth phase. From these investigations, we show that the substorm is a manifestation of reconfiguration in global flow dynamics. Ionospheric convection can be understood from two aspects. One understanding is as the potential field generated by the FAC, and the other is as the projection of magnetospheric convection. In order for the two to coincide, the FAC must be transmitted together with the motion. As a consequence, the resulting convection must be continuous from the magnetosphere to the ionosphere. We see this connection from the drawing of shear to recognize that the substorm is the projection process of transient convection. In the growth phase, convective shear that causes the quiet arc and the Harang reversal (HR) occurs on the open/closed boundary along the surface of the plasma sheet with a continuous flow structure from the magnetosphere to the ionosphere. The onset starts from a more local flow that is induced by the near‐earth neutral line (NENL). A narrow shear commences from the NENL in the mid‐tail and extends to the ionosphere to replace growth phase shear. Along a closed magnetic field line connected to the NENL, direct penetration flow, squeezing flow, the near‐earth dynamo, release of the HR, and the onset FAC occur successively and consequently cause the ground onset. Such onset mechanism is quite different from the model adopting the current wedge.

Prandtl Number Effects on the Entropy Generation During the Transient Mixed Convection in a Square Cavity Heated from Below

This numerical study considers the mixed convection, heat transfer and the entropy generation within a square cavity partially heated from below with moving cooled vertical sidewalls. All the other horizontal sides of the cavity are assumed adiabatic. The governing equations, in stream function–vorticity form, are discretized and solved using the finite difference method. Numerical simulations are carried out, by varying the Richardson number, to show the impact of the Prandtl number on the thermal, flow fields, and more particularly on the entropy generation. Three working fluid, generally used in practice, namely mercury (Pr = 0.0251), air (Pr = 0.7296) and water (Pr = 6.263) are investigated and compared. Predicted streamlines, isotherms, entropy generation, as well as average Nusselt numbers are presented. The obtained results reveal that the impact of the Prandtl number is relatively significant both on the heat transfer performance and on the entropy generation. The average Nusselt number increase with increasing Prandtl number. Its value varies thereabouts from 3.7 to 3.8 for mercury, from 5.5 to 13 for air and, from 12.5 to 15 for water. In addition, it is found that the total average entropy generation is significantly higher in the case of mercury (Pr«1) and water (Pr»1) than in the case of air (Pr~1). Its value varies approximately from 700 to 1100 W/m3 K for mercury, from 200 to 500 W/m3 K for water and, from 0.03 to 5 W/m3 K for air.

Corrigendum

Nawal Ferroudj, Hasan Koten, Sacia Kachi, Saadoun Boudebous "Prandtl Number Effects on the Entropy Generation During the Transient Mixed Convection in a Square Cavity Heated from Below", 65(4), pp. 310–325, 2021. (in this issue)https://doi.org/10.3311/PPme.17563When the above article was first published online Fig. 16 was incorrect. This has now been corrected in the online version. The correct version of Fig. 16 is published in this paper.

Dufour Effect on Transient MHD Double Convection Flow of Fractionalized Second-Grade Fluid with Caputo–Fabrizio Derivative

This article presents the problem, in which we study the unsteady double convection flow of a magnetohydrodynamics (MHD) differential-type fluid flow in the presence of heat source, Newtonian heating, and Dufour effect over an infinite vertical plate with fractional mass diffusion and thermal transports. The constitutive equations for the mass flux and thermal flux are modeled for noninteger-order derivative Caputo–Fabrizio (CF) with nonsingular kernel, respectively. The Laplace transform and Laplace inversion numerical algorithms are used to derive the analytical and semianalytical solutions for the dimensionless concentration, temperature, and velocity fields. Expressions for the skin friction and rates of heat and mass transfer from the plate to fluid with noninteger and integer orders, respectively, are also determined. Furthermore, the influence of flow parameters and fractional parameters α and β on the concentration, temperature, and velocity fields are tabularly and graphically underlined and discussed. Furthermore, a comparison between second-grade and viscous fluids for noninteger and integer is also depicted. It is observed that integer-order fluids have greater velocities than noninteger-order fluids. This shows how the fractional parameters affect the fluid flow.

Heat transfer characterisation of impinging flame jet over a wedge

• It is an experimental-cum-analytical study on impinging jet over a wedge-shaped object. • Transient temperature is analysed using analytical inverse heat conduction technique. • Forward model is based on Green’s Function Approach. • The solution procedure is suitable to analyse transient convection and radiation heat losses. • The flame jet heating effect improves as the wedge angle is increased from 90° to 120°. This paper aims to estimate two unknown parameters - Nusselt number and effectiveness – analytically and study the heat transfer characteristics of impinging flame jet over a wedge-shaped structure similar to a missile deflector plate. Experimentally obtained raw transient temperature history at the non-impinging face of a 4-mm-thick test object made of stainless steel is the only input data. An analytical Inverse Heat Conduction Technique based on Green's Function Approach is employed to estimate both parameters simultaneously. Multiple experimental cases are considered in this work by varying methane-air gas mixture Reynolds number (800, 1000, 1200, and 1500), non-dimensional nozzle tip to test object distance (2, 4, and 6), and wedge-angle (90° and 120°). The observations concerning heat transfer characteristics of the impinging flame jet are discussed in detail. The flame jet's heating effect has been observed to improve as the wedge angle is increased from 90° to 120°. Uncertainty of the estimated parameters is evaluated using the Monte Carlo technique.

Analysis of transient mixed convection in a horizontal channel partially heated from below

The heat convection phenomenon has been investigated numerically (mathematically) for a channel located horizontally and partially heated at a uniform heat flux with forced and free heat convection. The investigated horizontal channel with a fluid inlet and the enclosure was exposed to the heat source from the bottom while the channel upper side was kept with a constant temperature equal to fluid outlet temperature. Transient, laminar, incompressible and mixed convective flow is assumed within the channel. Therefore, the flow field is estimated using Navier Stokes equations, which involves the Boussinesq approximation. While the temperature field is calculated using the standard energy model, where, Re, Pr, Ri are Reynolds number, Prandtl number, and Richardson number, respectively. Reynolds number (Re) was changed during the test from 1 to 50 (1, 10, 25, and 50) for each case study, Richardson (Ri) number was changed during the test from 1 to 25 (1, 5, 10, 15, 20, and, 25). The average Nusselt number (Nuav) increases exponentially with the Reynold number for each Richardson number and the local Nusselt number (NuI) rises in the heating point. Then gradually stabilized until reaching the endpoint of the channel while the local Nusselt number increases with a decrease in the Reynolds number over there. In addition, the streamlines and isotherms patterns in case of the very low value of the Reynolds number indicate very low convective heat transfer with all values of Richardson number. Furthermore, near the heat source, the fluid flow rate rise increases the convection heat transfer that clarified the Nusselt number behavior with Reynolds number indicating that maximum Nu No. are 6, 12, 27 and 31 for Re No. 1, 10, 25 and 50, respectively

Numerical investigation of transient mixed convection of nanofluid in a cavity with non-Darcy porous inner block and rotating cylinders with harmonic motion

Mixed convection of nanofluid in a 2D square enclosure with a porous block in its center and four rotating cylinders, which are forced by a simple harmonic function, was studied numerically. The porous zone was studied by considering the Forchheimer–Brinkman-extended Darcy model. Effects of various parameters including Darcy number (10–5 ≤ Da ≤ 10–2), porosity (0.2 ≤ ɛ ≤ 0.7), Richardson number (0.1 ≤ Ri ≤ 10), and volume fraction of nanoparticles (0 ≤ ϕ ≤ 0.03), on heat transfer, entropy generation, PEC, velocity, streamline and isotherm contours were demonstrated. The results show that decreasing the Darcy number as well as reducing the Richardson number leads to an increase in the average Nusselt number. However, porosity changes had no decisive effect on heat transfer. Maximize the volume fraction of copper nanoparticles in the base fluid enhanced heat transfer. In the case of the high permeability of the porous medium, the impact of the harmonic rotation of the cylinders on the flow patterns became more pronounced.