Heat-generating Porous Medium Research Articles

Effect of electric field on the onset of Jeffery fluid convection in a heat-generating porous medium layer

Effect of electric field on the onset of Jeffery fluid convection in a heat-generating porous medium layer

Natural convection in a horizontal annular sector containing heat-generating porous medium

PurposeThe purpose of this work is to propose the generalized integral transform technique (GITT) for the investigation of two-dimensional steady-state natural convection in a horizontal annular sector containing heat-generating porous medium.Design/methodology/approachGITT was used to investigate steady-state natural convection in a horizontal annular sector containing heat-generating porous medium. The governing equations in stream function formulation are integral transformed in the azimuthal direction, with the resulting system of nonlinear ordinary differential equations numerically solved by finite difference method. The GITT solutions are validated by comparison with fully numerical solutions by finite difference method, showing excellent agreement and convergence with low computational cost.FindingsThe effects of increasing Rayleigh number are more noticeable in stream function, whereas less significant for temperature. With decreasing annular sector angle from π to π/6, a reduction in the maximum temperature and stream function was noticed. While the two counter-rotating vortical structure is common for all annular sector angles investigated, the relative size of the two vortices varies with decreasing sector angle, with the vortex near the outer radius of the cavity becoming dominant. The annular sector angle affects strongly the maximum temperature and the partition of heat transfer on the inner and outer surfaces of the annular sector with heat-generating porous medium.Originality/valueThe strong effects of the annular sector angle on natural convection in annular sectors containing heat-generating porous medium are investigated for the first time. The proposed hybrid analytical–numerical approach can be applied in other convection problems in cylindrical or annular configurations, with or without porous medium. It shows potential for applications in practical convection problems in the nuclear and other industries.

Characteristics of thermal energy removal from heat-generating porous media considering liquid-vapour phase change

Heat-generating porous media is encountered in different industrial applications as well as natural processes - natural geysers, geothermal energy extraction, packed bed reactors, nuclear and thermal power plants etc. The present article discusses the characteristics of thermal energy removal from heat-generating porous media, considering phase change of the saturating fluid phases. The complex phenomena of multiphase flow through porous media, coupled with the associated heat and mass transfer processes, is modelled numerically and implemented in a general computational platform with the help of user-defined functions. The model is validated extensively with experimental data and utilised for analysing heat removal from a heat-generating porous bed submerged in a liquid pool. This is in contrast to the various specialised numerical codes that have been specifically developed for modelling these phenomena.The study analyses the fundamental impacts of bed porosity, particle size and bed configuration on heat transfer and multiphase flow mechanism in the heat-generating porous bed. Bed porosity and particle size are observed to influence both fluid transport and heat transfer mechanisms, while bed composition is observed to mainly affect the fluid transport process. These effects, as such, influence heat removal from the heat-generating porous bed, which is quantified in terms of the maximum temperature rise within the bed and the ultimate energy removal possible from the bed. The latter is represented in terms of dryout power density, which represents the minimum volumetric heat generation at which it becomes impossible to ensure adequate heat removal from the bed. Assessment of dryout power density, as such, is very important in the context of heat removal and safety of the related applications. Increase in particle size as well as porosity is observed to augment this limit. The influence of bed composition on this limit is observed to be determined by the interplay of two parameters bed height and interface area of the bed with the surrounding liquid pool.

Non-equilibrium natural convection in a differentially-heated nanofluid cavity partially filled with a porous medium

Purpose This study aims to numerically analyze natural convection of alumina-water nanofluid in a differentially-heated square cavity partially filled with a heat-generating porous medium. A single-phase nanofluid model with experimental correlations for the nanofluid viscosity and thermal conductivity has been considered for the description of the nanoparticles transport effect in the present study. Local thermal non-equilibrium approach for the porous layer with the Brinkman-extended Darcy model has been used. Design/methodology/approach Dimensionless governing equations formulated using stream function, vorticity and temperature have been solved by the finite difference method. The effects of the Rayleigh number, Ostrogradsky number, Nield number and nanoparticles volume fraction on nanofluid flow, heat and mass transfer have been analyzed. Findings It has been revealed that the dimensionless heat transfer coefficient at the fluid/solid matrix interface can be a very good control parameter for the convective flow and heat transfer intensity. The present results are original and new for the study of non-equilibrium natural convection in a differentially-heated nanofluid cavity partially filled with a porous medium. Originality/value The results of this paper are new and original with many practical applications of nanofluids in the modern industry.

Single domain integral transform analysis of natural convection in cavities partially filled with heat generating porous medium

An analysis of natural convection within a rectangular cavity partially filled with a heat-generating porous medium is carried out through the Generalized Integral Transform Technique (GITT), in which the laminar flow and energy equations are solved with automatic error control. A single domain reformulation strategy is adopted to rewrite the governing equations within the fluid and the porous medium as a single heterogeneous medium formulation, with spatially variable physical properties and source terms that account for the abrupt transition of the two regions. This fundamental study is motivated by the analysis of wet storage of spent nuclear fuel elements with passive cooling of the pool and physical conclusions are drawn from the hybrid numerical-analytical solution. Increases in the Rayleigh number with constant internal heat generation are found to lower the maximum temperature within the cavity. Moreover, decreasing the aspect ratio also has positive effects on the cooling of the cavity.

Reflooding with internal boiling of a heating model porous medium with mm-scale pores

This paper presents a pore-scale experimental study of the reflooding of a two-dimensional model porous medium. The objective is to better understand the reflooding mechanisms in play in the context of nuclear reactor safety. The hot debris bed that forms in a nuclear reactor following a loss of coolant accident is comparable to a heat-generating porous medium. Its cooling by water reflooding involves intense boiling mechanisms that must be modeled properly to assess mitigation procedures.The experimental study presented in this paper focuses on the phenomenology of reflooding of a model porous medium composed of a bank of mm-scale heating cylinders placed between two ceramic plates. A Fluorinert™ liquid, HFE-7000, is injected at a temperature close to saturation into the dry and superheated porous medium. Each cylinder of the test section is used both as a heating element and a temperature probe, which enables to track the evolution of the three different macroscopic zones identified during cooling of the system. The reflooding dynamics, in particular the cooling fronts velocities, are thus determined thanks to pore-scale thermal measurements together with direct visualizations. The influence of the injection flow rate and of the heating power are studied in a parametric way.

Numerical Simulation of Natural Convection in a Porous Cavity with Linearly Temperature Distributions Under the Local Thermal Nonequilibrium Condition

A numerical investigation of the natural convection heat transfer in a rectangular cavity filled with a heat-generating porous medium by adopting the local thermal nonequilibrium (LTNE) model is reported in this paper. The top and bottom walls of the enclosure are adiabatic, the left wall is linearly cooled, and the right wall is cooled by a linear or uniform temperature profile. The results show that the isotherms for the fluid and solid phases become similar with the increase of the interphase heat transfer coefficient H; the increasing heat transfer between the two phases brings their temperatures closer to each other and thus the solid and fluid phases are in a state of the thermal equilibrium at higher values of H. For case A, the interphase heat transfer coefficient has little influence on the heat transfer rate of the solid phase of the porous cavity and the heat transfer profile of the solid phase (Nusy) is symmetrical with respect to the center point of line Y = 0.5. For case B, the interphase heat transfer coefficient H has a significant effect on that at the right wall, and the total heat transfer of the heat-generating porous cavity is implemented by the right-side wall. The total heat transfer rate Q of case B is higher than that of case A at a high thermal conductivity ratio γ (γ = 1, 10).

Natural convection in a porous rectangular enclosure with sinusoidal temperature distributions on both side walls using a thermal non-equilibrium model

This study reports a numerical investigation of the natural convective flow and heat transfer in a rectangular cavity filled with a heat-generating porous medium by adopting the local thermal non-equilibrium model. The top and bottom walls of the enclosure are adiabatic and the left and right walls are partially heated and partially cooled by sinusoidal temperature profile. The results show that periodic variations with positive and negative values appear in the isotherms for fluid phase and solid phase, and the periodicity increases with the increase of N. The phase deviation has significant influence on fluid flow and heat transfer in the porous cavity. When N is large enough (N=32), patterns of streamlines, isotherms for fluid phase and solid phase display like that of uniform thermal boundary condition case, and the total heat transfer rate through the whole cavity is close to that resulted by uniform thermal boundary condition. The heat transfer of porous cavity can be enhanced by sinusoidal thermal boundary condition and the phase deviation has tiny effect on the heat transfer of cavity when N is large enough (N=32). The increase of inter-phase heat transfer coefficient leads to faster reduction of Q with the increase of periodicity parameter.

A Thermal Nonequilibrium Approach to Natural Convection in a Square Enclosure Due to the Partially Cooled Sidewalls of the Enclosure

This article presents a numerical investigation of steady non-Darcy natural convection heat transfer in a square cavity filled with a heat-generating porous medium with partial cooling using a local thermal nonequilibrium (LTNE) model. Five different partial cooling boundary conditions and the fully cooled boundary condition are investigated under LTNE and local thermal equilibrium (LTE). The cooling portions of the left and the right sidewalls of the cavity are maintained at temperature T 0 while the enclosure's top and bottom walls, as well as the inactive parts of its sidewalls, are kept insulated. The simulation results show that the placement order of wall cooling has a significant effect on the flow pattern and heat transfer rate. Compared with the fully cooled wall, the partially cooled wall of the cavity yielded a higher local Nusselt number for both fluid and solid phases. Under the same boundary conditions, the LTNE and LTE models can demonstrate significant differences in flow patterns and temperature fields. The total heat transfer rate increases with both Darcy number and Rayleigh number. Enhancement of interphase heat transfer coefficient (H) reduces the impact of Darcy number on the heat transfer rate of a porous cavity. Also, the total heat transfer rate of the porous medium decreases steadily with thermal conductivity ratio γ and interphase heat transfer coefficient H.

The effects of an outer flow on the unsteady free convection boundary layer near a stagnation point in a heat-generating porous medium

The effects of an outer flow on the unsteady free convection boundary layer near a stagnation point in a heat-generating porous medium

Numerical Investigation of Unsteady Natural Convection in an Inclined Square Enclosure With Heat-Generating Porous Medium

The unsteady laminar natural convection in an inclined square enclosure with heat-generating porous medium whose heat varies by a cosine function is investigated by a thermal equilibrium model and the Brinkman–Darcy–Forchheimer model numerically, with the four cooled walls of closure as isothermal. The numerical code based on the finite-volume method has been validated by reference data before it was adopted. Influence of dimensionless frequency and inclination angle on heat transfer characteristics in a square enclosure, such as flow distribution, isotherm, averaged Nusselt number on each wall, and time-averaged Nusselt number, are discussed, with specified value for Rayleigh number = 108, Darcy number = 10−4, Prandtl number = 7, porosity = 0.4, and specific heat ratio = 1. It is found that when the internal heat source varies by cosine, the Nusselt numbers of the four walls oscillate with the same frequency as the internal heat source; however, phase difference occurs. Moreover, frequency has little impact on time-averaged Nusselt number of the four walls, which is different from the phenomenon discovered in natural convection with suitable periodic varying wall temperature boundary condition. Moreover, inclination angle plays an important role in the heat transfer characteristics of the walls studied.

Unsteady free convective boundary-layer flow near a stagnation point in a heat-generating porous medium

The free convection boundary-layer flow near a stagnation point in a porous medium is considered when there is local heat generation at a rate proportional to (T − T ∞) p , (p ≥ 1), where T is the fluid temperature and T ∞ the ambient temperature. Two cases are treated, when the surface is thermally insulated and when heat is supplied at a constant (dimensionless) rate h s from the boundary. If h s = 0 the solution approaches a nontrivial steady state for time t large in which the local heating has a significant effect when p ≤ 2. For p > 2 the effects of the local heating become increasingly less important and the solution dies away, with the surface temperature being of O(t −1) for t large. When h s > 0 and there is heat input from the surface, the solution for p ≤ 2 again approaches a nontrivial steady state for t large and all h s . For p > 2 there is a critical value h s,crit (dependent on the exponent p) of h s such that the solution still approaches a nontrivial steady state if h s h s,crit a singularity develops in the solution at a finite time, the nature of which is analysed.

Convection in a Lid-Driven Heat-Generating Porous Cavity with Alternative Thermal Boundary Conditions

Mixed convection flow in a two-sided lid-driven cavity filled with heat-generating porous medium is numerically investigated. The top and bottom walls are moving in opposite directions at different temperatures, while the side vertical walls are considered adiabatic. The governing equations are solved using the finite-volume method with the SIMPLE algorithm. The numerical procedure adopted in this study yields a consistent performance over a wide range of parameters that were 10−4 ≤ Da ≤ 10−1 and 0 ≤ RaI ≤ 104. The effects of the parameters involved on the heat transfer characteristics are studied in detail. It is found that the variation of the average Nusselt number is non-linear for increasing values of the Darcy number with uniform or non-uniform heating condition.

Free convective boundary-layer flow in a heat-generating porous medium: similarity solutions

The free convection boundary-layer flow on a vertical surface in a porous medium with local heat generation proportional to (T – T∞)p, where T is the local temperature and T∞ is the ambient temperature, is considered when there are power-law variations in either the wall temperature or the wall heat flux which enables the equations to be reduced to similarity form. When the wall temperature is prescribed, solutions are found for p ≤ 2 and p ≥ pc (pc = 10.673) with a saddle-node bifurcation at p = pc and two solution branches for p > pc. When the wall heat flux is prescribed, solutions are found only for p < 2. The special case p = 2 is considered and the limiting forms as p → 2 and p → ∞ are obtained and compared with the solutions obtained from solving the similarity equations numerically

Free convection boundary layers on a vertical surface in a heat-generating porous medium

The natural convection boundary-layer flow on a solid vertical surface with heat generated within the boundary layer at a rate proportional to (T - T ∞ ) p (p ≥ 1) is considered. The surface is held at the ambient temperature T ∞ except near the leading edge where it is held at a temperature above ambient. The behaviour of the flow as it develops from the leading edge is examined and is seen to become independent of the initial heat input; however, it does depend strongly on the exponent p. For 1 ≤ p ≤ 2, the local heating eventually dominates at large distances and there is a convective flow driven by this mechanism. For p ≥ 4, the local heating does not have a significant effect, the fluid temperature remains relatively small throughout and the heat transfer dies out through a wall jet flow. For 2 < p < 4, the local heating has a significant effect at relatively small distances, with a thermal runaway developing at a finite distance along the surface.

Free Convection in a Wavy Cavity Filled with Heat-Generating Porous Media

Free Convection in a Wavy Cavity Filled with Heat-Generating Porous Media

A Non-Darcian Numerical Modeling in Domed Enclosures Filled With Heat-Generating Porous Media

ABSTRACT Numerical study of the natural-convection flow and heat transfer in a dome-shaped, heat-generating, porous enclosure is considered. The general conic equation for the top dome is used to consider various conical top sections such as circular, elliptical, parabolic, and hyperbolic. The individual effect of fluid Rayleigh, Darcy, and heat-generating parameters on flow patterns and heat transfer rates are analyzed and presented. The predicted results show that the heat-generating parameter has the most significant contribution toward the growth of bicellular core flow. Moreover, there is significant change in temperature distribution in comparison to rectangular enclosures, due to the existence of the domed-shape top adiabatic cover. The results also show that, regardless of Darcy and Rayleigh values, a flat adiabatic top cover tends to yield the highest value of Nusselt number, followed by circular, elliptical, parabolic, and hyperbolic top covers, respectively.

BUOYANT CONVECTION OF A POWER-LAW FLUID IN AN ENCLOSURE FILLED WITH HEAT-GENERATING POROUS MEDIA

A numerical study is performed of the buoyant convection in a rectangular enclosure. A heat-generating porous medium, saturated with a non-Newtonian fluid, fills the enclosure. The non-Newtonian fluid is assumed to follow the power-law rheological model. The flow is described by the Darcy equation for a porous medium. The vertical side walls of the enclosure are cooled at constant temperature T 0, and the horizontal walls are thermally insulated. The modified internal Rayleigh number Ra I* is large to render a boundary-layer-type flow. Comprehensive numerical solutions are acquired for the governing equations. Details of flow and thermal characteristics are portrayed for ranges of RaI* and the power-law index n. The behavior of the Nusselt number, based on the maximum temperature θmax in the enclosure, is delineated. By combining the numerical results, a correlation for the average Nusselt number is proposed. The validity of the assumption of local thermal equilibrium in the present configuration is discussed.

The effect of water density extremum on heat transfer within a cylinder containing a heat-generating porous media

A numerical model was used to investigate the effect of the density extremum of water in a cylinder containing a heat-generating porous media. The modeled vertical cylinder had an adiabatic bottom surface with isothermal sides and top. The density of water was varied with temperature, as was the heat generation rate, aspect ratio, and boundary temperature to reveal the affects upon heat transfer and maximum temperatures. Results of the explicit finite difference model using Darcy's formulation for the momentum equations indicate that the uniform internal heat generation rate and the surface area to volume ratio determine maximum temperatures and steady-state flow patterns. At very low heat generation rates, the boundary temperature does not significantly affect the location of the maximum velocity unless the boundary temperature is at the extremum temperature of 4°C. When larger internal heat generation rates are considered, and as the surface area to volume ratio decreases, the effect of boundary temperature becomes less significant. Because the density extremum of water is so near its melting point of 0°C, the effect of the maximum density is essentially negligible for boundary temperatures above the melting point of water.

Variable Property Effects on Convection in a Heat Generating Porous Medium

Convection heat transfer in a fluid-saturated porous medium has many applications, such as in oil and gas production, grain storage, and geothermal energy. A number of numerical studies have been carried out using Darcy's law to formulate the natural convection heat transfer mathematically in enclosures of internally heat-generating porous media. This paper uses Irmay's momentum equation for radial and axial equations that include inertia terms with models an internally heat-generating porous medium in a short, vertical circular cylinder (R = 2m, H = 4m). The cylinder side and top are isothermal and at the same temperature (T{sub {infinity}}). The bottom surface of the cylinder is adiabatic. The variations in density and viscosity with temperature and inertia are investigated. For slow flows, the effect of inertia would be expected to be small. For large temperature variations, the effects of variable dynamic viscosity and density are expected to be large. The density and the dynamic viscosity of air were represented by the relationships {rho} = {rho}{sub {infinity}} (1 {minus} (T {minus} T{sub {infinity}})/T) and v = v{sub {infinity}} (1 + 2(T {minus} T{sub {infinity}})/T{sub {infinity}}). These relationships for {rho} and v are accurate for air between 20 and 200C.