Convection Problem Research Articles

Double-diffusive convection in a porous layer subjected to an inclined temperature gradient incorporating Soret effect

In several commonly occurring natural convection phenomena, the system is subjected to non-uniform heating that causes an inclined thermal gradient. As a result, the natural convection problem deviates from the classical Rayleigh–Bénard problem, in which the thermal gradient has only a vertical component. In this study, we present linear and global stability analyses results concerning thermosolutal convection in a Newtonian fluid-saturated Darcy porous layer subjected to an inclined thermal gradient in the presence of the Soret effect (associated with thermophoresis). The thermal gradient is assumed to have horizontal and vertical components, resulting in the formulation having two thermal Rayleigh numbers as system parameters, viz. horizontal and vertical Rayleigh numbers. The horizontal thermal gradient gives rise to a Hadley-type circulation. This circulation can become unstable if the vertical thermal gradient attains a certain threshold. We focus on the effect of the Soret parameter on the system’s stability under non-uniform inclined heating. The analyses reveal that the solutal Darcy–Rayleigh number and Lewis number destabilise the system, while the Soret parameter has a non-monotonic effect on the system’s stability depending on the horizontal Rayleigh number. The energy stability bounds do not coincide with linear ones for the present problem; hence, subcritical instabilities are possible.

Viscoelastic effect on the triple diffusive oscillatory flow in a fluid-saturated porous layer

The combined heat and mass transfer, the so-called thermosolutal convective problem, has become an attractive field of research in many diversified areas. In this paper, for the first time, oscillatory flow analysis has been carried out for triple diffusive viscoelastic fluid flow in a porous medium. A comprehensive model is developed for the modified Darcy–Brinkman–Oldroyd-B fluid, porous medium, Boussinesq approximation, heat and mass transfer across a finite temperature and concentration difference in the chemical potential of two salts. Triple diffusive viscoelastic fluid flows through porous media have grown significantly as this situation occurs in more than a few applications such as improved oil recovery filtration, liquid complex molding, solidification of liquid crystals, cooling of metallic plate in a bath, exotic lubricants and colloidal solutions, polymer processing, chemical and bioengineering industries, among others. The governing coupled nonlinear partial differential equations with boundary constraints represent the modeled flow problem. In addition, these equations are converted into non-dimensional form by employing suitable non-dimensionalizing quantities. The impacts of the pertinent parameters and related dimensionless numbers on the dimensionless velocity, temperature, concentrations, shear stress, heat and mass transfer are examined for both suction and injection cases. It has been found that when the injection level on the heated plate is increased, the shear rate increases for each channel plate. Furthermore, we recognized that the viscoelastic parameters exhibit an opposite kind of behavior on the velocity, temperature, and concentrations fields.

Influence of magnetic field on MHD mixed convection in lid-driven cavity with heated wavy bottom surface

This study investigates the influence of a rectangular heat source on magnetohydrodynamic hybrid convection flow in a lid-driven cavity. The effects of various parameters, such as the heat source size, magnetic field strength, and heat absorption/generation, are analyzed. The results show that increasing the heat source size decreases the average Nusselt number along the heated wall. The average Nusselt number also decreases with higher magnetic field strength and heat generation, while it increases with heat absorption. The major finding is to apply an important technique the Galerkin weighted residual technique of the finite element (FE) method to solve the non-dimensional equations and the associated boundary conditions. The isotherms are used to show the temperature distribution in a domain. Streamline present the flow field in the enclosure. However, it is easy to realize the direction and intensity of the heat transfer particularly in convection problems which the path of heat flux is perpendicular and the isotherm due to convection effect. Thus, the purpose of this research is to study the results of mixed convection. The effects of location and height of the partitions are considered for the various Richardson numbers. Fluid flow field, thermal field and heat transfer are presented through the streamlines and isotherms, respectively. Results are substantiated relating to the published work.

An Example of an Exact Solution of a Nonstationary Problem of Two-Component Convection

An Example of an Exact Solution of a Nonstationary Problem of Two-Component Convection

Turbulent heat and mass lines in finite difference regime

AbstractFinite difference modelling of turbulent heat and mass flow visualization finds numerous applications in atmospheric flows/oceanic currents, wind turbines, thermal transfer in nuclear reactors, drag in oil pipelines, cooling of industrial machineries, and to investigate the complexity, dynamic and chaotic nature of the physical system. A turbulent phenomenon is effectively implemented in engineering, physics, earth sciences, bio‐engineering and medicine. Hence, motivated by the advantages of turbulence in various engineering fields, in the current article, a finite difference analysis is performed to demonstrate the k‐ε turbulence model‐based heat and mass lines visualization in boundary layer regime under turbulent buoyancy‐driven convective conditions along a cylinder. Turbulent flow characteristics are accurately explored by deploying the classical Newtonian flow model. Further, to accomplish a more sophisticated finite difference simulation, the effects of extra kinetic energy and its dissipation rate equations are considered. The produced Navier‐Stokes equations for time‐dependent turbulent heat and mass transmission are rendered to non‐dimensional by deploying suitable dimensionless numbers. The advanced coupled nonlinear turbulent unsteady buoyancy‐motivated vertical convection problem is then solved with a well‐sophisticated finite difference scheme such as Crank‐Nicolson technique using computational software. Authentication of current results with former solutions over a range of buoyancy number, Schmidt, and Prandtl parameters are presented. An extensive tabular and graphical discussion along with contours, heat and masslines visualization is included to enumerate the hydro‐dynamic, thermal and mass diffusion behaviour for the impact of emerged regulating numbers in the Prandtl regime. It is confirmed that, the accelerating turbulent buoyancy‐ratio number, maximizes the velocity, kinetic energy and dissipation rate at . Further, the numerical values of laminar thermal and mass diffusion rates are monotonically enhanced when compared to the turbulent values. Also, to verify the current findings, the authors compared the LRN k‐ε model turbulent results with the existing solutions and found good agreement. Further, the uniqueness and novelty of the current investigation is the exploration of heat and masslines in unsteady buoyancy‐driven convection regime under the influence of k‐ε turbulence model which extends the former studies and offers a more precise appraisal of the thermal and mass diffusion lines via the Crank‐Nicolson analysis.

CONVECTION OF A VISCOUS INCOMPRESSIBLE COOLANT IN A HORIZONTAL CYLINDRICAL PIPE HEATED FROM BELOW. AN ANALYTICAL SOLUTION

To intensify heat transfer processes in nuclear power, it is proposed to use natural convection in horizontal heat exchange tubes. In the article, the problem of convection of a viscous, incompressible fluid in a horizontal cylinder heated from below is analyzed analytically. The proposed analytical method is based upon the use of basic functions that satisfy the initial equation but do not satisfy the boundary conditions. The problem with boundary conditions with a sufficient degree of accuracy is solved by dividing the area of the square described around the cylinder into a large number of smaller element cells. This separation has made it possible to obtain analytical expressions of critical Rayleigh numbers for different positions of current lines in a horizontal cylinder with a viscous, incompressible fluid.

The reconstruction of flows from spatiotemporal data by autoencoders

Artificial neural networks have become essential tools in data science for uncovering insights from complex data. However, they are usually seen as black boxes. In this work we explore how an autoencoder processes complex spatiotemporal information. We analyze the topological structure of reconstructed flows in the latent space of an autoencoder for two distinct test cases. The first case involves a synthetic spatiotemporal pattern for the temperature field in a convective problem, illustrating a classic extended system that exhibits low-dimensional chaos. The second case focuses on an experimental recording of the labial oscillations responsible for sound production in an avian vocal organ, as an example of periodic dynamics in a biological system. We find that the state representation in its latent space can be topologically equivalent to the phase space of the problem. Autoencoders thus retain phase space representations of the data hidden in its latent layer.

On the convergence of a low order Lagrange finite element approach for natural convection problems

On the convergence of a low order Lagrange finite element approach for natural convection problems

Free Surface Motion of a Liquid Pool with Isothermal Sidewalls as a Benchmark for Marangoni Convection Problems

In single phase flows, benchmarks like the lid driven cavity have become recognized as fundamental tests for newly developed computational fluid dynamics, CFD, codes. For multiphase free surface flows with variable surface tension, the presently studied pool with isothermal sidewalls is suggested as it is the simplest domain where Marangoni effects can dominate. It was also chosen due to its strange sensitivity to the initial setup which is discussed at length from a chosen number of ‘scenarios’. It was found that the fluid interface can reverse deformation by a change in the top boundary condition, the liquid equation of state, and the gravity level. For the top boundary condition, this reversal is due to vapor expansion within the closed volume, creating an additional convection mechanism. Not only does the interface reverse, but the peak height changes by more than an order of magnitude at the same Marangoni number. When including gravity, the peak velocity can increase significantly, but it can also cause a decrease when done in combination with a change in the top wall boundary condition. Finally, thermal expansion of the liquid phase causes the peak velocity to be reduced, with additional reductions from the gravity and top wall condition. The differences in each scenario could lead to significant errors in analyzing a practical application of Marangoni flows. Therefore, it is important to demonstrate that a new CFD code can not only resolve Marangoni convection, but also has the capability to resolve the scenario most relevant to the application at hand.

Comprehensive assessment of the partially-saturated-cells framework for convective problems

We present a comprehensive investigation of Partially-Saturated-Cells method (PSC) for the simulations of incompressible thermal flows. The methodology comprises an additional collision operator introduced into the conventional simplified thermal lattice-Boltzmann (STLBM) method that offers a unified evolution equation for solid and fluid media present in the computational domain. It is a type of diffuse-interface immersed-boundary method that is dictated by the volume fraction of the solid medium and facilitates a smooth transition of boundary conditions at the solid-fluid interface. In this work, we devise a mechanism to evaluate local heat flux at the solid-fluid interface and present its congruity with several heat transfer problems. We also derive the recovery of the macroscopic energy equation from PSC's evolution equation through Chapman-Enskog multiscale expansion. Our investigation also reveals that the method is first-order accurate for moving body simulations irrespective of the straight or curved boundary. It is also Galilean invariant and demonstrates identical heat transfer characteristics in stationary and moving reference frames. A comprehensive analysis of the PSC algorithm is presented to enlighten its suitability for predicting thermo-hydrodynamic characteristics in free, forced, and mixed convection phenomena involving both stationary and moving boundary scenarios. To the best of our knowledge, these aspects pertaining to PSC methodology have not been discussed in the literature so far.

Learning an optimised stable Taylor-Galerkin convection scheme based on a local spectral model for the numerical error dynamics

We present a new spectral framework to design and optimise numerical methods for convection problems termed Local Transfer function Analysis (LTA), which improves the state-of-art model for error dynamics due to numerical discretisation. LTA converts the numerical discretisation into a network of transfer function blocks in the spectral space, where optimisation of the solution error becomes an impedance matching problem. In addition, a machine learning model based on the graph neural network is employed to learn the optimal coefficients of the transfer function leading to the matched impedance by examining both the local physical field and the local mesh topology. We demonstrate applications of this technique to design Taylor-Galerkin finite element numerical schemes for solving linear convection on irregular meshes in 1D. Using the LTA, we identify and constrain the neural network predictions to the numerically stable design space, thus improving the stability and generalisation of the optimal parameters that lead to a matched impedance.

Hyperreduced-order modeling of thermally coupled flows

This article presents a full and reduced-order methodology based on the finite element method that allows the characterization of convective-dominant conjugate heat transfer flows. Reduced-order modeling (ROM) allows the description of several degrees of freedom problems, referred to as full-order modeling (FOM), through a reduced-order surrogate representation based on a Petrov-Galerkin projection onto a reduced subspace. The FOM and ROM problems are stabilized through the Variational Multi-Scale (VMS) method, which ensures stability in dominant convective problems and allows equal interpolation spaces for the pressure, velocity, and temperature. The proposed methodology is validated solving natural heat convection in a differentially heated square cavity, considering air as the working fluid and Rayleigh numbers in the interval 104≤Ra≤108. In this problem, the benefit of using a ROM approximation for the three unknown fields, i.e., velocity, pressure, and temperature, is compared against ROM approximation only in the velocity and pressure fields and a FOM type approximation for temperature. The benefit of using mesh-based hyperreduction and its computational performance and precision are also analyzed. Subsequently, the method simulates a conjugate heat transfer problem that includes natural heat convection, allowing the inclusion of different rheologies between the working fluids. The results verify the precision and speed up of the calculations by more than three hundred times with respect to the time necessary to solve a full-order formulation, emerging it as a great potential tool in the resolution of thermally coupled flows.

Physics-informed graph convolutional neural network for modeling geometry-adaptive steady-state natural convection

This paper presents a novel deep learning-based surrogate model for steady-state natural convection problem with variable geometry. Traditional deep learning based surrogate models are more or less limited by the requirement for large amounts of training data, loss of accuracy due to pixelization of the original data, the low accurate prediction near the boundaries and low geometry adaptive capability. To overcome the above challenges, the proposed natural convection prediction framework is mainly composed of a physics-informed neural network (PINN) and a graph convolutional neural network (GCN), called natural convection prediction model based on physics-informed graph convolutional network (NCV-PIGN). The GCN serves as the prediction module, inferring and predicting natural convection phenomena by considering the interactions between unstructured nodes and their neighbor; the PINN incorporates the governing equations of natural convection into the loss function of the neural network, allowing the predictions from GCN to satisfy the constraints imposed by the physical laws. The advantages of this framework are twofold: the operation principles of the GCN better align with the development of the temperature field in real situations, and the embedding of physical information strengthens the model's understanding of the flow field, accurately describing the variations of temperature gradients at the boundary positions while reducing the model's reliance on training data. Finally, to validate the superiority of the NCV-PIGN, we analyze its geometric adaptability and accuracy of prediction using single and dual heat source cases. We compare the model's prediction results at different sampling point quantities and contrast them with those of purely data-driven models. The results demonstrate that the excellent geometric adaptability and prediction capability of the proposed model can be achieved with only 20 training data and once the fully trained the model can solve natural convection problems within 3 ms. The max and mean relative errors in predicting the temperature field are less than 2% and 0.4% for both single and dual heat source cases. Compared to the pure data-driven model, the proposed model has reduced the maximum error by 65.5% and the mean error by 72%. These results validate the effectiveness of the developed NCV-PIGN model, enabling better performance of the deep learning-based surrogate models for natural convection problems.

Numerical Investigation of Electrical Efficiency with the Application of Hybrid Nanofluids for Photovoltaic Thermal Systems Contained in a Cavity Channel

Photovoltaic thermal systems (PV/T) are devices used to collect both electrical and thermal energies from solar energy. By passing a coolant through flow channels that are connected to the PV/T systems, the temperature of the cells is reduced to enhance their electrical efficiency. Therefore, this study aims at investigating a photovoltaic thermal system via the transport of hybrid nanofluids based on Cu-Al2O3/water. We assume that the flow channel can be considered in two dimensions and is composed of the silicon panel, absorber, and flow channel. The flow channel consists of a cavity along the absorber with a fixed length and a certain height. This will be a combined conduction and convection problem, with conduction occurring on the top two layers of the silicon panel and absorber. Modeling and simulation problems are performed using COMSOL Multiphysics 5.6. The aspect ratio from inlet height to cavity height is defined by Ar, and the volume fraction of Al2O3 is taken double that of Cu. The cell efficiency is analyzed by performing a parametric study by altering the Reynold number (100–1000), inlet temperature (50°C–450°C), the volume fraction of copper (0.01%–10%), and the aspect ratio (0.5, 0.7, 0.9, and 1). It is found that increasing the inlet temperature and aspect ratio decreases the cell efficiency while increasing the Reynolds number and volume fraction increases it. The maximum efficiency of the cell, about 6%, is achieved when the inlet temperature is 50°C, the volume fraction of copper is 10%, Re = 1000, and Ar = 0.5. It was also concluded that when the volume fraction of copper is 0.1, the increase in Reynolds number from 100 to 1000 is improving the cell efficiency by 0.5%. On the other hand, when increasing the volume fraction of copper from minimum to maximum at Re = 1000, the cell efficiency is increasing by 0.3%.

Modeling Convective Heat Transfer of Air in a Data Center Using OpenFOAM

Achieving energy and cooling efficiency in data center convective air flow and heat transfer can be a challenging task. Among different numerical methods to work with such issues is the Finite Volume Method in Computational Fluid Dynamics. This work evaluates the performance of two such solvers provided by OpenFOAM® in solving this type of convective heat-transfer problem, namely BuoyantBoussinesqPimpleFOAM and BuoyantPimpleFOAM. This is done for two different flow configurations of significantly different Richardson number. To sufficiently resolve the flow, grid sizing effects are elucidated by way of the kernel density estimate. It determines the volume distribution of the temperature in the data center configuration. For the k-epsilon turbulence model used here, it was found that the compressible solver performs faster and requires less grid resolution for both flow configurations. This is attributed to the nature of the boundary conditions which are set such that the mass flow conservation per server rack and cooling unit is achieved. Transient solutions are found to provide better iterative convergence for cases that involves buoyancy, compressibility and flow separation. This is, in comparison to steady-state solutions where artificial numerical pressure drop is found, to depend on the momentum relaxation factors for the convective case with a higher Richardson number.

Brinkman–Bénard Convection with Rough Boundaries and Third-Type Thermal Boundary Conditions

The Brinkman–Bénard convection problem is chosen for investigation, along with very general boundary conditions. Using the Maclaurin series, in this paper, we show that it is possible to perform a relatively exact linear stability analysis, as well as a weakly nonlinear stability analysis, as normally performed in the case of a classical free isothermal/free isothermal boundary combination. Starting from a classical linear stability analysis, we ultimately study the chaos in such systems, all conducted with great accuracy. The principle of exchange of stabilities is proven, and the critical Rayleigh number, Rac, and the wave number, ac, are obtained in closed form. An asymptotic analysis is performed, to obtain Rac for the case of adiabatic boundaries, for which ac≃0. A seemingly minimal representation yields a generalized Lorenz model for the general boundary condition used. The symmetry in the three Lorenz equations, their dissipative nature, energy-conserving nature, and bounded solution are observed for the considered general boundary condition. Thus, one may infer that, to obtain the results of various related problems, they can be handled in an integrated manner, and results can be obtained with great accuracy. The effect of increasing the values of the Biot numbers and/or slip Darcy numbers is to increase, not only the value of the critical Rayleigh number, but also the critical wave number. Extreme values of zero and infinity, when assigned to the Biot number, yield the results of an adiabatic and an isothermal boundary, respectively. Likewise, these extreme values assigned to the slip Darcy number yield the effects of free and rigid boundary conditions, respectively. Intermediate values of the Biot and slip Darcy numbers bridge the gap between the extreme cases. The effects of the Biot and slip Darcy numbers on the Hopf–Rayleigh number are, however, opposite to each other. In view of the known analogy between Bénard convection and Taylor–Couette flow in the linear regime, it is imperative that the results of the latter problem, viz., Brinkman–Taylor–Couette flow, become as well known.

Diffuse interface-lattice Boltzmann modeling for heat and mass transfer with Neumann boundary condition in complex and evolving geometries

In this research, a diffuse interface-lattice Boltzmann method is developed to model heat and mass transfer problems with Neumann boundary condition in complex and evolving geometries. In this model, the physical domain with curved and moving boundaries is extended to a larger and regular domain based on the concept of fictitious domain. The Neumann boundary condition is incorporated into the jump conditions of field variable at the inner interface. Then a unified convection-diffusion equation of field variable with two singular source terms is built. Using the smoothing technique, a diffuse interface equation is obtained. Moreover, an energy method is presented to derive the diffuse interface equation in a special case. We utilized a multiple-relaxation-time lattice Boltzmann scheme to numerically solve the diffuse interface equation. A simple example with analytical solutions validates the numerical accuracy of the present model. Finally, several thermal convection and mass transport problems are also simulated. The numerical results denotes the validity of the proposed diffuse interface model.

Complexity measurements for the thermal convection in a viscoelastic fluid saturated porous medium

Measuring complexity statistical indicators is a key method to analyze and characterize dynamical systems. In this work, we perform a comparative analysis among the López-Ruiz, Mancini & Calbet complexity indicator and the largest Lyapunov exponent for the convection problem of a viscoelastic fluid in a porous medium with feedback control based in an Oldroyd carrier liquid through a four-dimensional generalized Lorenz system. With both indicators can be distinguished from chaotic to periodic states. We perform intensive numerical simulations with 4×106 in the space parameters, finding good agreement between them, such that difference is close to 2%. We have also detected that the computing time is much faster in the case of complexity indicator than for Lyapunov exponents. Finally, we have also studied the effect of the initial conditions in the coexistence states, encountering multistability.

Liquid chromatography on a centrifugal platform for separation and collection of water-soluble dyes

A reversed-phase chromatographic process is developed on a centrifugal platform to separate and collect water-soluble dyes from a mixture. A separation column filled with C18-reversed phase silica gel was used to separate the components from a mixture and the eluate was collected by a series of collecting chambers. The purified components can then be identified and extracted from the collecting chambers. The effects of the silica gel's particle size (7–10, 20–45, and 46–63 µm) and the platform's rotational speed (1000, 1500, 2000 RPM) on the separation and collection efficiency were investigated. Experimental results showed that dye separation could be well performed in the column with smaller-sized silica gels (7–10 µm) under a low rotational speed (1000 RPM). However, for the eluate collection, the high eluent flowrate and long processing time resulted in a convective band-broadening problem in the collecting chambers, which affected the recovery ratio of the dyes. Experimental results showed that the convective band broadening effect can be reduced by reducing the flowrate, shortening the collecting time, and switching the eluent to a different composition. The best recovery ratio of the dyes in the current design can be achieved by using the column with a powder size distribution of 46–63 µm and operating at the rotational speed of 1500 RPM. This platform can process a sample volume of 1 μL and the processing time is about 30 min. Since the only instrument used is a motor, the complete chromatographic process, from separation to fraction collection, can be carried out on a centrifugal platform at a low cost.

The application of upwind meshless approximation finite volume method to the convection dominated problems on the unstructured and deformed meshes

The primary objective of this research is to develop a finite volume method that can incorporate the most widely recognized upwind schemes using meshless techniques on an unstructured mesh. The recently developed Meshless Approximation Finite Volume Method (MAFVM) is expected to provide a solution to the convection–diffusion equation with an extremely high Pélect number, regardless of the type or quality of mesh, even when dealing with highly distorted meshes. By incorporating the local compactly supported radial basis functions differential quadrature method (LCRBFDQ), a meshless approximation technique, the field variables, flux, and gradient are directly approximated using information from neighboring scattered nodes. Building upon this concept, we propose two meshless approximation approaches for computing the flux and gradient within the framework of the finite volume method. Elliptic type problem on regular mesh is solved using the proposed MAFVM by different flux computation methods. Parameters for MAFVM that provide accurate and robust results are suggested. Next standard linear and second order upwind schemes as well as the well-known total variation diminishing (TVD) methods are integrated into the proposed MAFVM, using the developed flux calculation method to solve convection–diffusion problem with very high Pélect number on standard or highly deformed mesh. Accurate and robust results can be observed which show that the current MAFVM can provide an alternative and better way to deal with strong convection problem on meshes of arbitrary types by the proposed meshless flux computation methods.