Mixed Convection In Porous Medium Research Articles

Darcy–Carreau–Yasuda rheological model and onset of inelastic non-Newtonian mixed convection in porous media

An extension of Carreau and Carreau–Yasuda rheological models to porous media is proposed to study the onset of mixed convection of both pseudoplastic fluids (PF) and dilatant fluids (DF) in a porous layer heated from below in the presence of a horizontal throughflow. In comparison with Newtonian fluids, three more dimensionless parameters are introduced, namely, the Darcy–Weissenberg number Wi, the power–law index n, and the Yasuda parameter a. Temporal stability analysis of the basic state showed that in the absence of a throughflow (Wi = 0), the critical Rayleigh number and the critical wavenumber at the onset of convection are the same as for Newtonian fluids, namely, Rac=4π2 and kc=π, respectively. When the throughflow is added (Wi > 0), it is found that moving transverse rolls (stationary longitudinal rolls) are the dominant mode of the instability for PF (for DF). Furthermore, depending on Wi, two regimes of instability were identified. In the weakly non-Newtonian regime (i.e., Wi<Wit≈1), a destabilizing effect is observed for PF, while the reverse occurs for DF. These effects are more intense by reducing (increasing) the index n for PF (for DF). In this regime, a significant qualitative difference is found between the Darcy–Carreau model and the power–law model. However, in the strongly non-Newtonian regime, the two models lead to similar results. A mechanical energy budget analysis is performed to understand the physical effects of the interaction between the basic throughflow and the disturbances. It is also shown that the intrinsic macroscale properties of the porous medium may play a key role in the stabilizing/destabilizing effect. Finally, a comparison is made between the present theoretical predictions and recent mixed convection experiments in a Hele–Shaw cell.

Forced flow structure and mixed convection in a ventilated porous enclosure with a local contaminant source

In this paper forced flow structure and mixed convection in a ventilated porous enclosure with a local contaminant source centrally positioned on the floor have been investigated numerically. The physical model for the momentum conservation equation makes use of the Darcy-Brinkman equation, which allows the no-slip boundary condition on a solid wall to be satisfied. The set of coupled equations is solved via the SIMPLE algorithm. Comparisons with previously published work are performed and found to be in excellent agreement. An extensive series of numerical simulations is conducted in the range of, 200 ≤ Re ≤ 10,000, 0.02 ≤ Re · Da ≤ 20 and, 0.01⩽f=(Grs·Da2)/(Re·Da)⩽1000 where Re is the Reynolds number, Da is the Darcy number, Grs is the solutal Grashof number and f is derived from the discretized V equation and represents the relative magnitude between the effective solutal buoyancy and the effective external force. Streamlines are produced to illustrate the forced flow structure transition from eddy-free motion to multi-eddy pattern and Re · Da ≥ 0.2 is the critical condition of eddy emergence. The analysis of overall Sherwood number and iso-concentrations indicate that the parameter f is appropriate to be regarded as the criterion of mixed convection in porous medium.

A pore scale analysis for determination of interfacial convective heat transfer coefficient for thin periodic porous media under mixed convection

Purpose The purpose of this study is to determine interfacial convective heat transfer coefficient numerically, for a porous media consisting of square blocks in inline arrangement under mixed convection heat transfer. Design/methodology/approach The continuity, momentum and energy equations are solved in dimensionless form for a representative elementary volume of porous media, numerically. The velocity and temperature fields for different values of porosity, Ri and Re numbers are obtained. The study is performed for the range of Ri number from 0.01 to 10, Re number from 100 to 500 and porosity value from 0.51 to 0.96. Based on the obtained results, the value of the interfacial convective heat transfer coefficient is calculated by using volume average method. Findings It was found that at low porosities (such as 0.51), the interfacial Nusselt number does not considerably change with Ri and Re numbers. However, for porous media with high Ri number and porosity (such as 10 and 0.51, respectively), secondary flows occur in the middle of the channel between rods improving heat transfer between solid and fluid, considerably. It is shown that the available correlations of interfacial heat transfer coefficient suggested for forced convection can be used for mixed convection for the porous media with low porosity (such as 0.51) or for the flow with low Ri number (such as 0.01). Originality/value To the best of the authors’ knowledge, there is no study on determination of interfacial convective heat transfer coefficient for mixed convection in porous media in literature. The present study might be the first study providing an accurate idea on the range of this important parameter, which will be useful particularly for researchers who study on mixed convection heat transfer in porous media, macroscopically.

Dual Solutions for Opposing Mixed Convection in Porous Media

The problem of steady mixed convection boundary layer flow on a cooled vertical permeable circular cylinder embedded in a fluid-saturated porous medium is studied. Here, we evaluate the flow and heat transfer characteristics numerically for various values of the governing parameters and demonstrate the existence of dual solutions beyond a critical point.

Application of transient experimental techniques for developing a heat transfer correlation for mixed convection in porous medium

An approach based on transient heat transfer experiments combined with numerical optimization procedures is studied to develop a heat transfer correlation for mixed convection heat transfer in a vertical duct filled with metallic porous structures. The heat source of the vertical duct is a near isothermal plate which during cooling is treated as a lumped heat capacity model. The temperature–time history, during the cooling of the plate, is measured using K-type (36AWG) thermocouples connected to a PC-based data acquisition system. A numerically computed temperature–time history of the plate is then compared with the experimentally known temperature–time history to estimate the residual. The minimization of sum of the squares of the residual is done using a hybrid numerical optimization technique, i.e. a combination of Genetic Algorithm and the Levenberg–Marquardt method, in order to obtain the coefficient and the exponents of the pertinent non-dimensional parameters in the Nusselt number correlation. The consistency of the present approach is further substantiated by comparing the Nusselt number values predicted using the proposed correlation and that evaluated from the steady-state experiments.

The spatiotemporal instability on mixed convection in porous media

The absolute and convective instability on mixed convection in porous media is examined, and the phase transition from the oscillatory wave motion to the stationary vortex one is observed. Based on linear and weakly nonlinear analyses, the critical conditions to mark the onset of traveling transverse rolls are analytically obtained for small Peclet numbers. The flow change from transverse wave to longitudinal vortex is reproduced by numerical simulation. These criteria made good agreement with the available experiment data.

Nonlinear global modes in inhomogeneous mixed convection flows in porous media

The aim of this work is to investigate the fully nonlinear dynamics of mixed convection in porous media heated non-uniformly from below and through which an axial flow is maintained. Depending on the choice of the imposed inhomogeneous temperature profile, two cases prove to be of interest: the base flow displays an absolute instability region either detached from the inlet or attached to it. Results from a combined direct numerical simulations and linear stability approach have revealed that in the first case, the nonlinear solution is a steep nonlinear global mode, with a sharp stationary front located at a marginally absolutely unstable station. In the second configuration, the scaling laws for the establishment of a nonlinear global mode quenched by the inlet are found to agree perfectly with the theory. It is also found that in both configurations, the global frequency of synchronized oscillations corresponds to the local absolute frequency determined by linear criterion, even far from the threshold of global instability.

Transient mixed convective heat transfer with melting effect from the vertical plate in a liquid saturated porous medium

This paper aims to numerically analyze the melting effect on transient mixed convective heat transfer from a vertical plate in a liquid saturated porous medium. The Darcy’s flow with the Boussinesq approximation and energy equations for this study is transformed into the non-dimensional equations by using pseudo-similarity coordinate ( ζ) and dimensionless time ( ξ). The resulting the boundary value problem is solved by the method of lines (MOLs) with central finite difference and Newton’s iteration to completely obtain the solutions for the whole transient mixed convective heat transfer from transient heat conduction to steady mixed convection in porous medium with melting effect in the presence of aiding and opposing external flows. As shown in the results, it is both found that the rate of dynamic heat transfer is reduced with increasing melting strength and the response time from transient heat conduction to steady mixed convection in porous medium for aiding external flow is shorter than that for opposing external flow in the presence of melting effect. Additionally, the melting effect may be reduced with increasing mixed convective strength Gr/ Re 1/2 during transient mixed convective heat transfer in porous medium with aiding external flow.

A study of the liquid evaporation with Darcian resistance effect on mixed convection in porous media

A problem of the evaporation of liquid with Darcian resistance effect on mixed convection flow over a vertical plate in an isotropic porous medium has been studied. Two flow models, aiding and opposing flows, are considered. The boundary layer equations are integrated numerically to obtain the non-similar solutions for the velocity, temperature and concentration distributions for several values of the Darcian resistance and buoyancy force parameters. The results show that the evaporation of liquid on the wall increases when the buoyancy force Ra K / Pe x is gradually increased and the overall heat transfer rate will be pronounced when the Darcian resistance ζ is very small.

Mixed convection in porous media between vertical concentric cylinders

Mixed convection in porous media between vertical concentric cylinders

Mixed convection in porous media between vertical concentric cylinders

In this paper,dimensionless parameters Gr**/Rep and H/dp, which govern the mixed convection in a vertical annulus filled with porous media, are deduced through dimensional analysis,and the criteria for mixed convection is estabilished thereby.The mixed calculated results for detecting the non-Darcy effects are discussed.The predicted results agree well with the experiments.

Mixed convection in porous media between vertical concentric cylinders

In this paper, the dimensionless parameters Gr ** /Re p and H/dp that govern mixed convection in a vertical annulus filled with porous media, are deduced through dimensional analysis, and the criteria for mixed convection is established thereby. The calculated results for detecting the non-Darcian effects are discussed. The predictions agree with the experiments.

Evolution of oscillatory and chaotic flows in mixed convection in porous media in the non-Darcy regime

The problem of buoyancy-induced flow in gas- or liquid-saturated porous media is of great interest in various applications ranging from geothermal engineering to underground nuclear waste disposal. In many cases, the effect of forced and free convection may be significant. Previous studies in this regard were mainly done using the Darcy of Brinkman model. In the case of fluid flow under high temperature or pressure gradient, however, the flow regime is dictated by a Forchheimer, [P. H. Forchheimer, Z. Cer. Dt. Ing. 45, 1731–1788 (1901)] type equation. This paper investigates the time evolution of multicellular flows in a fluid-saturated porous medium in the case of mixed convection. Numerical results show the presence of periodic, quasi-periodic and chaotic behavior for increasingly high Grashof numbers.

Universal formulations and comprehensive correlations for non-Darcy natural convection and mixed convection in porous media

Universal similarity equations of non-Darcy mixed convection along an isothermal vertical plate and a uniform-flux horizontal plate in porous media are obtained by introducing proper transformation variables. Very accurate similarity solutions and comprehensive correlation equations of the local Nusselt numbers are presented over the entire range of flow inertia including the Darcy and non-Darcy regimes for any mixed convection intensity from the pure forced convection limit to the pure natural convection limit. The finite-difference solution and correlation of the local Nusselt number for any extent of flow inertia are also presented for natural convection along a vertical plate with uniform wall heat flux.

Melting with mixed convection flow from horizontal flat plate embedded in a porous medium

The problem of melting from a flat plate embedded in a porous medium is studied. The main focus is to determine the effect of mixed convection flow in the liquid phase on the melting phenomenon. It is discussed of the numerical considerations of boundary conditions and coupling between the governing equations through buyoyancy and melting parameters. Computations have been made for assisting flow over a horizontal flat plate at zero incident, and for stagnation point flow about a horizontal impermeable surface. It is found that the parameter governing mixed convection in porous media is % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaeOuaiaabg% gacaqGVaGaaeikaiaabkfacaqGLbGaaeiuaiaabkhacaqGPaWaaWba% aSqabeaacaqGZaGaae4laiaabkdaaaaaaa!3F7E!\[{\text{Ra/(RePr)}}^{{\text{3/2}}} \]. The effects of buoyance and melting parameters variations on heat transfer characteristics about a heated horizontal surfaces are examined. The melting phenomenon decreases the local Nusselt number at the solid-liquid interface.

Combined convection from an isothermal horizontal rod buried in a porous medium

Abstract This paper reports the results of a numerical investigation of mixed convection heat transfer from a horizontal rod of circular cross-section that is embedded in a porous medium. The rod temperature is first assumed to be the same as that of the medium and then suddenly increased to a higher constant value. The steady-state problem has been solved by the method of series truncation in combination with a finite-difference scheme for the two flow configurations of parallel and counter-flow regimes. The flow and thermal fields as well as the variations of the average and local heat transfer rates with a wide range of Reynolds number, Grashof number and buoyancy parameter have been examined in detail for a Prandtl number of 0.7. One of the interesting features found is the occurrence of a recirculating flow zone near the upper half surface of the rod in the case of the counter-flow regime. The numerical method and the results presented fill in a gap in the literature on one of the most fundamental problems in the field of mixed convection in porous media.