Convection Problem Research Articles

Effects of flow direction and thermal short-circuiting on the performance of coaxial ground heat exchangers

The effects of flow direction and thermal short-circuiting on the performance of coaxial ground heat exchangers are studied by finite-element simulations, performed through COMSOL Multiphysics 3.4 (©Comsol, Inc.). The real 2-D axisymmetric unsteady heat conduction and convection problem is considered. The distribution of the fluid bulk temperature in the inner circular tube is determined by means of the “weak boundary form” boundary condition available in COMSOL Multiphysics; the laminar convective heat transfer in the outer annular passage is simulated directly. Two Coaxial Ground Heat Exchangers (CGHEs) with the same length but different cross sections are examined; moreover, two values of the ground thermal conductivity, as well as two materials for the inner tube wall are considered. The results point out that the annulus-in flow direction (fluid inlet in the outer annular passage) is more efficient than the center-in flow direction (fluid inlet in the inner circular tube) and that the effect of short circuiting is not very important, if the annulus-in flow direction is employed. Indeed, with this inlet configuration the energy loss for thermal short-circuiting is less than 1% for time intervals longer than 1 hour.

Efficient passive GDQLL scrutinization of an advanced steady EMHD mixed convective nanofluid flow problem via Wakif–Buongiorno approach and generalized transport laws

Owing to the practical importance of nanofluids and their adjustable thermal capabilities, this study intends to develop a robust generalized differential quadrature local linearization (GDQLL) algorithm for examining realistically the heat and mass aspects of electrically conducting nanofluids during their non-Darcian laminar motion nearby a convectively heating vertical surface of an active electromagnetic actuator (i.e., Riga plate). By invoking Wakif–Buongiorno model and Oberbeck–Boussinesq approximations along with other generalized transport laws (i.e., Cattaneo–Christov and non-Fick’s laws) and Grinberg’s concept, a set of gigantic partial differential equations is stated appropriately in the sense of the boundary layer approximations for describing exhaustively the present EMHD mixed convective nonhomogeneous flow under the passive control strategy of nanoparticles within the nanofluidic medium. Operationally, the dimensionless differential forms of the governing boundary equations are derived properly by introducing reasonable mathematical adjustments into the preliminary formulation. In this case, the differential complexity of the leading differential structure is reduced to a nonlinear coupled system of ordinary differential equations, whose discrete numerical solutions are computed perfectly via a well-structured GDQLL algorithm. As foremost outcomes, it is demonstrated that the nanofluid motion and its surface thermal enhancement rate can be reinforced significantly through the thermal strengthening in the convective heating and mixed convective process as well as via the electromagnetic improvement in the driven aspect of Lorentz’s forces.

Experimental correlation of natural convection in low Rayleigh atmospheres for vertical plates and comparison between CFD and lumped parameter analysis

This paper offers a comprehensive exploration of thermal analysis for space systems operating in low Rayleigh atmospheres, with a primary focus on enhancing the accuracy and reliability of convective heat transfer modeling. The study centers around an analysis of a vertical heated plate experiment, where a lumped parameter model is employed to encompass conductive, radiative, and convective heat transfer mechanisms. To advance the accuracy of convective heat transfer coefficient calculations, this paper introduces a novel approach involving the utilization of Nusselt number correlations. These correlations are developed through an analytical solution derived from the Navier-Stokes equations, tailored specifically for the internal natural convection problem. This approach treats convection as a heat exchange process between the heated plate and the surrounding air, thereby improving the precision of modeling internal convection within a lumped parameter framework. A specific correlation (González-Bárcena et al.) is obtained for the proposed problem, derived from experimental tests conducted in a thermal vacuum chamber, under varying pressure conditions to control the Rayleigh number. Additionally, the findings are validated using Computational Fluid Dynamics (CFD) tools to calculate the velocity and temperature fields within the cavity. The González-Bárcena et al. correlation significantly enhances temperature predictions, demonstrating an improvement of up to 10∘C when compared to conventional literature correlations. The methodology presented in this paper holds promise for extension to more complex experiments in low Rayleigh atmospheres, including those conducted in the Earth's stratosphere or on the Martian surface, thereby contributing to the advancement of thermal analysis in challenging space environments.

Double diffusive convection in bidispersive porous media with couple stresses effect and relatively large macropores

In this study, we have investigated the problem of double-diffusive convection in a porous medium that exhibits bidispersive characteristics and is influenced by couple stresses. The model employed considers the Darcy theory in the micropores, while utilizing the Brinkman theory in the macropores. The system encompasses two competing effects: a temperature gradient that induces instability and a salt gradient that enhances system stability. The study involved conducting analyses of linear instability and nonlinear stability. The eigenvalue systems obtained from both the linear and nonlinear theories were solved using the Chebyshev collocation method. To ensure the accuracy of this numerical method, the results were cross-validated by comparing them with the analytical solution of the eigenvalue system derived from the linear instability theory. Notably, the Chebyshev collocation method exhibited high accuracy even in the presence of high-order derivatives arising from the couple stresses term. Finally, numerical computations were performed to determine and extensively discuss the linear instability thresholds and global nonlinear thresholds. The findings contribute valuable insights into the behavior of the system under investigation. The results show that the stability thresholds of bidisperse flow in porous media are lower than those of single-phase flow. Moreover, the results confirm the stabilizing effect of the Brinkman parameter, couple stresses parameter, and permeability ratio parameter. It has also noted the stabilizing effect of the concentration Rayleigh number if the layer is salted below and the destabilizing effect if the layer is salted above.

Study of chaos in the Darcy–Bénard convection problem with Robin boundary condition on the upper surface

Possibility of chaos is studied in Darcy–Bénard convection using the Dirichlet and the Robin boundary condition at the lower and upper boundaries, respectively. Comparison is made with the results of Dirichlet (classical-Darcy–Bénard convection, CDBC) and Neumann boundary condition (Barletta–Darcy–Bénard convection, BDBC). It is found that the cell size at onset is bigger in the case of BDBC compared to the generalized-Darcy–Bénard convection (GDBC) and much bigger compared to CDBC. The critical-Darcy–Rayleigh number of BDBC is found to be the least and that of CDBC is the largest. Nonlinear-stability-analysis is performed leading to the scaled-generalized-Vadasz–Lorenz model (SGVLM). In deriving this model, help is sought from a local-nonlinear-stability-analysis that yields the form of the convective-mode. The SGVLM is shown to be dissipative and conservative, with its bounded solution trapped within an ellipsoid. Onset of chaos and its characteristics are studied using the Hopf–Rayleigh-number, the Lorenz-butterfly-diagram, and the plot of the amplitude of the convective-mode vs the control-parameter, R, which is the eigenvalue. Chaos sets in earlier in CDBC and much later in BDBC when compared to that in GDBC. Beyond the onset of chaos is seen a sequence of chaotic and periodic motions, with the latter sometimes being present for an extended period.

Thermal convection with a Cattaneo heat flux model

The problem of thermal convection in a layer of viscous incompressible fluid is analysed. The heat flux law is taken to be one of Cattaneo type. The time derivative of the heat flux is allowed to be a material derivative, or a general objective derivative. It is shown that only one objective derivative leads to results consistent with what one expects in real life. This objective derivative leads to a Cattaneo–Christov theory, and the results for linear instability theory are in agreement with those for a material derivative. It is further shown that none of the theories allow a standard nonlinear, energy stability analysis. A further heat flux due to P.M. Mariano is added and then an analysis is performed for stationary convection, oscillatory convection, and fully nonlinear theory. For the material derivative case, the analysis proceeds and global nonlinear stability is achieved. For Cattaneo–Christov theory, it appears necessary to add a regularization term in the equation for the heat flux, and even then the analysis only works in two space dimensions, and is conditional upon the size of the initial data. For the three-dimensional situation, it is shown how a nonlinear stability analysis may be achieved with a Navier–Stokes–Voigt fluid rather than a Navier–Stokes one.

Central discontinuous Galerkin finite element method for the time-fractional convection equation in two space dimensions

In this study, an efficient approach for solving the two-dimensional time-fractional convection problem with a non-smooth solution in the temporal direction is proposed. The solution exhibits weakly regular at the initial time, so the L1 formula on the nonuniform meshes is applied to discretizing the Caputo derivative. In the spatial direction, the central discontinuous Galerkin (CDG) method involving two approximate solutions defined on overlapping elements is used. The fully discrete scheme is proven to be numerically stable, and the optimal convergence result is attained. A few numerical experiments are conducted to confirm the theoretical conclusions.

Analysis of geometric uncertainties in 3D thermo-fluid problems solved by RBF-FD meshless method

The tolerances of production processes can lead to uncertainties in the behaviour and in the features of the manufactured products. From the point of view of the design of engineering components it is therefore of valuable practical interest to be able to quantify such uncertainties as well as the expected, i.e., averaged, performances. Such uncertainty quantification is carried out in this work by means of the Non-Intrusive Polynomial Chaos (PC) method in order to estimate the propagation of geometrical uncertainties of the boundaries, i.e., when the boundaries are described by stochastic variables. Existing deterministic solvers can be used with the PC method because of its non-intrusive formulation, allowing an accurate and practical prediction of the random response through a simple set of deterministic response simulations. The Radial Basis Function Finite Differences (RBF-FD) method is employed as a black box solver for the computation of the required set of responses defined over deterministic boundaries. The RBF-FD method belongs to the class of meshless methods which do not require a computational mesh/grid, therefore its main capability is to easily deal with practical problems defined over complex-shaped domains. The geometrical flexibility of the RBF-FD method is even more advantageous when coupled to the Non-Intrusive PC method for uncertainty quantification since different deterministic solutions over different geometries are required. The applicability of the proposed approach to practical problems is presented through the prediction of geometric uncertainty effects for a steady-state forced convection problem in a 3D complex-shaped domain.

Updated Lagrangian Particle Hydrodynamics (ULPH) Modeling of Natural Convection Problems

Updated Lagrangian Particle Hydrodynamics (ULPH) Modeling of Natural Convection Problems

Sensitivity analysis for a thermohydrodynamic model: Uncertainty analysis and parameter estimation

This paper proposes an efficient computational strategy to deal with uncertainty propagation problems for the Navier–Stokes equations coupled with a temperature equation based on a sensitivity analysis technique model. Sensitivity analysis allows one to investigate how the model response in a point is affected by a change in the boundary conditions on the temperature, the heat capacity, the thermal conductivity, and the thermal diffusivity under the hypothesis of a small variance of the input parameters. The variance can be estimated with just one simulation of the state and as many simulations of the sensitivity as there are uncertain parameters. We focused on the benchmark problem of natural convection in a square cavity, also known as the de Vahl Davis problem. Various areas of the domain were analysed to determine the relative influence of each parameter on temperature and velocity. We use the open-source code TrioCFD to simulate the state equations and a specific module is developed for the sensitivity equations.

Combination of Karhunen-Loève and intrusive polynomial chaos for uncertainty quantification of thermomagnetic convection problem with stochastic boundary condition

Uncertainty propagation analysis plays a crucial role in understanding the impact of variations in initial condition, boundary condition, and fluid physical properties on simulation results for thermomagnetic convection heat transfer problems. To effectively analyze the uncertainty problem of thermomagnetic convection caused by random temperature fluctuations, a novel and comprehensive computational framework based on intrusive polynomial chaos approach was proposed in this paper. Our proposed approach aims to represent random temperature boundaries using Karhunen-Loève expansion (KLE) and stochastic output response using polynomial chaos expansion (PCE). In addition, we use spectral projection method to transform the stochastic control equation into a group of deterministic control equations. We obtained the uncertainty characteristics of the stochastic output response by solving each polynomial chaos basis. Compared with Monte Carlo simulation (MCS), our approach accurately and efficiently predicts the uncertainty characteristics of thermomagnetic convection problems under stochastic temperature boundary conditions while significantly reducing computational resources.

Effect of Gravity Modulation on the Onset of Heat Transfer by Buoyancy Induced Convection in Boussinesq- Stokes Suspension with Temperature

The current paper considers the Boussinesq-Stokes suspensions and the temperature-dependent viscosity with the influence of gravity modulation to analyze a weak non-linear stability problem of Rayleigh Benard magnetoconvection. In the study of convective instability problems, the impact of time-periodic body force also known as gravity modulation or g-gitter is essential. In the problem of gravity modulation, the gravity field has two components: one is the constant part and another an externally imposed time periodic part, which can be produced by oscillating the fluid layer. The effect of varying frequency of gravitational oscillation on convection is examined. The truncated form of the Fourier series is used in the non-linear analysis. The effects of numerous factors on the onset of convection have been discussed in this paper. The thermal Nusselt number is computed and shown for slow time periods using non-linear theory. The impacts of gravity modulation frequency and amplitude have been investigated in order to study heat transport in the system, as well as other aspects that exist in the problem.

Результаты моделирования смешанной конвекции для оценки целесообразности использования тепловых пушек в обогреве сварочного поста локомотивного депо

Purpose: Numerical investigation of mixed convection processes to assess the feasibility of using jet heaters for local heating in locomotive depot welding stations with a mechanical localized ventilation system. Methods: The research has been conducted using the finite difference method in the COMSOL Multiphysics software, with the problem of mixed convection formulated and the calculation domain reduced to a two-dimensional plane. Results: Temperature fields and velocity maps have been obtained for the workstations under various conditions and positions of the jet heater. The analysis of the results has allowed us to propose options for using jet heaters and their installation locations, as well as to refine the impact of their impact on the microclimate of the workstation. The conditions under which the use of jet heaters is both practical and safe have been determined. Practical significance: The results obtained during the study can be used for the organization or optimization of local heating systems for welding stations in locomotive depots, as well as for similar workplace arrangements.

A Nitsche‐based cut finite element solver for two‐phase Stefan problems

AbstractWe present a cut finite element method based on ghost penalty stabilization technique for solving two‐phase Stefan problems. The essential interfacial constraints are weakly enforced using the symmetric variant of Nitsche's method. To track the interface efficiently, the level‐set technique is employed and the front location is updated at each time step by solving a transport equation. Because this is a convection problem, we utilize the continuous interior penalty method to stabilize the finite element formulation. According to the Stefan condition, the normal velocity of the interface is proportional to the jump in the interfacial flux. To accurately approximate this quantity, we use a recent post‐processing technique that combines a ghost penalty regularization and the domain integral method on cut elements. We validate our algorithm with several numerical examples that demonstrate optimal convergence.

Modeling of heat transfer at local convection over a vertical throughflow in a two-layered air-heat generating porous system

Convective heat transfer in an air layer partially filled with a heat-generating granular porous medium is studied. There is a slow seepage of air through the layer in the vertical direction with a constant velocity. Equal temperatures are maintained at the outer solid permeable boundaries, and the heat source strength is constant within the porous sublayer and is proportional to the solid volume fraction. The permanent heat generation within the porous sublayer, combined with the vertical throughflow, causes a nonlinear thermal profile which is conducive for convection to occur. The Boussinesq approximation and Darcy's law are used to describe this convection. Numerical solution of the nonlinear convective problem is obtained on the basis of Newton's method. In the limiting case, the numerical data for the onset of convection are compared with the results of the earlier paper of the authors, where a linear stability theory and a method for constructing of the fundamental system of partial solution vectors have been applied, and with the data by other authors. The stationary regimes of local convection, which occurs in an “air – heat-generating porous medium-air” system over the basic vertical throughflow, and its effect on the heat transfer from the porous air sublayer with the growth of supercriticality are studied. It is shown that, depending on the velocity of the basic throughflow (the Peclet number), convection excitation can be both soft (due to supercritical pitchfork bifurcation) and hard (when the loss of stability of the basic throughflow is accompanied by subcritical pitchfork bifurcation that gives rise to an unstable secondary convective regime). This secondary regime is replaced by a stable tertiary convective regime with increasing supercriticality. It has been found that the total heat transfer rate for the upward basic throughflow exceeds that for the downward basic throughflow significantly, and that local convection at any direction of this throughflow increases the heat transfer rate in the system. An increase in the Nusselt number with the growth of supercriticality is recorded. However, a noticeable contribution of local convection to the total heat transfer is observed only when all values of the Pecklet number are negative and its positive values are lower than 2.

Effect of variable viscosity, porous walls and mixed thermal boundary condition on the onset of Rayleigh-Bénard convective instability

In this paper, we have studied the criteria for the onset of instability in the Rayleigh-Bénard convection problem, by considering a fluid layer confined between two infinitely extended rough boundaries, which are subjected to mixed-type thermal boundary conditions, physically representing the imperfectly conducting boundaries. The rough boundaries are assumed to be shallow porous layers with different pore size, properties, and permeabilities. Mathematically, it is given by the Saffman type boundary condition. Therefore, we have two generalized forms of boundary conditions, one for the flow field and the other for the thermal field. The two limiting cases of the mixed-type thermal boundary condition correspond to a perfectly conducting boundary and to a perfectly insulating boundary, whereas the two limiting cases of the hydrodynamic boundary condition correspond to a no-slip condition and to a free-surface condition, depending upon the limiting values of the parameters involved in these two generalized boundary conditions. The linear and nonlinear energy stability analyses are performed, and the existence of the region of subcritical instability is checked. Through the principle of exchange of stability analysis, it is found that the instability occurs only in the stationary mode. The adiabatic boundary condition is found to be more restrictive than the isothermal boundary condition. Under given conditions, the instability is observed to be occurring in the infinite wavelength mode for the case of adiabatic boundaries. In the present work, the effect of temperature and pressure dependent viscosity on the stability of the system has been shown and found to be of destabilizing nature. However, the roughness of the boundaries is found to be of stabilizing nature.

Sharp Instability Estimates for Bidisperse Convection with Local Thermal Non-equilibrium

We analyse a theory for thermal convection in a Darcy porous material where the skeletal structure is one with macropores, but also cracks or fissures, giving rise to a series of micropores. This is thus thermal convection in a bidisperse, or double porosity, porous body. The theory allows for non-equilibrium thermal conditions in that the temperature of the solid skeleton is allowed to be different from that of the fluid in the macro- or micropores. The model does, however, allow for independent velocities and pressures of the fluid in the macro- and micropores. The threshold for linear instability is shown to be the same as that for global nonlinear stability. This is a key result because it shows that one may employ linearized theory to ensure that the key physics of the thermal convection problem has been captured. It is important to realize that this has not been shown for other theories of bidisperse media where the temperatures in the macro- and micropores may be different. An analytical expression is obtained for the critical Rayleigh number and numerical results are presented employing realistic parameters for the physical values which arise.Article HighlightsA two-temperature regime for a bidisperse Darcy porous medium is proposed to study the thermal convection problem.The optimal result of coincidence between the linear instability and nonlinear stability critical thresholds is proven.Numerical analysis enhances that the scaled heat transfer coefficient between the fluid and solid and the porosity-weighted conductivity ratio stabilize the problem significantly.

Mathematical Modeling of Collisional Heat Generation and Convective Heat Transfer Problem for Single Spherical Body in Oscillating Boundaries

The application of high-energy ball milling in the field of advanced materials processing, such as mechanochemical alloying and ammonia synthesis, has been gaining increasing attention beyond its traditional use in material crushing. It is important to recognize the role of thermodynamics in high-energy processes, including heat generation from collisions, as well as ongoing investigations into grinding ball behavior. This study aims to develop a mathematical model for the numerical analysis of a spherical ball in a shaker mill, taking into account its dynamics, contact mechanics, thermodynamics, and heat transfer. The complexity of the problem for mathematical modeling is reduced by limiting the motion to one-dimensional translation and representing the vibration of the vial wall in a shaker mill as rigid boundaries that move in a linear fashion. A nonlinear viscoelastic contact model is employed to construct a heat generation model. An equation of internal energy evolution is derived that incorporates a velocity-dependent heat convection model. In coupled field modeling, equations of motion for high-energy impact phenomena are derived from energy-based Hamiltonian mechanics rather than vector-based Newtonian mechanics. The numerical integration of the governing equations is performed at the system level to analyze the general heating characteristics during collisions and the effect of various operational parameters, such as the oscillation frequency and amplitude of the vial. The results of the numerical analysis provide essential performance metrics, including steady-state temperature and time constant for the characteristics of temperature evolution for a high-energy shaker milling process with a computation accuracy of 0.1%. The novelty of this modeling study is that it is the first to obtain such a high accuracy numerical solution for the temperature evolution associated with a shaker mill process.

The Elder Problem with Reactive Infiltration Effects

The occurrence of buoyancy-driven flow and reactive solute transport in a fluid-saturated porous medium can be induced by either natural processes or human activities. Typical examples include the groundwater salinization in carbonate-rock aquifers and the acid treatment of oil wells in petroleum drilling industry. In this paper, the classical Elder problem of buoyancy-driven convection in two-dimensional porous media is extended to include the local chemical interactions between the solute in the pore liquid (e.g. salt such as NaCl or acids such as HCl and HCl/HF mixtures) and the solid space of the porous medium (e.g. minerals such as calcite and dolomite). Effects of the geochemical processes on the flow and mass transport are investigated. For the reactive, strongly solute-driven case in the regime dominated by the diffusive mass transport, a decrease in the net solute concentration is found as compared to the non-reactive case. This decrease is pronounced at higher values of the Damköhler number when the solute reaction rate becomes larger than the solute diffusion rate. Furthermore, the flow structure is affected by products generated by the chemical reaction when the Rayleigh number for the products is sufficiently high. In that case, numerical simulations show the formation of diluted fluid tongues exhibiting damped periodic oscillations about a nonzero mean. The results are obtained using the pseudospectral numerical method, verified against the analytical solution for the non-reactive, purely diffusive case.

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.