Convective behaviour of a uniformly Joule-heated liquid pool in a rectangular cavity

In the present paper, a study of magnetohydrodynamic (MHD) mixed convection around a heat conducting horizontal circular cylinder placed at the center of a rectangular cavity along with joule heating has been carried out. Steady state heat transfer by laminar mixed convection has been studied numerically by solving the equations of mass, momentum and energy to determine the fluid flow and heat transfer characteristics in the cavity as a function of Richardson number, Hartmann number and the cavity aspect ratio. The results are presented in the form of average Nusselt number at the heated surface; average fluid temperature in the cavity and temperature at the cylinder center for the range of Richardson number, Hartmann number and aspect ratio. The streamlines and isotherms are also presented. It is found that the streamlines, isotherms, average Nusselt number, average fluid temperature and dimensionless temperature at the cylinder center strongly depend on the Richardson number, Hartmann number and the cavity aspect ratio.Keywords: Mixed convection; Finite element method; Cylinder diameter; Lid-driven cavity; Hartmann number. © 2009 JSR Publications. ISSN: 2070-0237 (Print); 2070-0245 (Online). All rights reserved. DOI: 10.3329/jsr.v1i3.2597 J. Sci. Res. 1 (3), 461-472 (2009)

Technical Notes Relative permeabilities are used routinely in reservoir engineering, especially in numerical simulation, to describe multiphase flow through permeable media under the influence of 3D pressure fields and 1D gravitational body forces. Because gravitational body forces are directionally anisotropic (they point toward the center of the Earth) and pressure fields and body forces act differently on the fluids, relative permeabilities must depend on the direction of flow (i.e., be directionally anisotropic) even in homogeneous and isotropic reservoirs. In practice, the same relative permeabilities, usually measured in horizontal flows, are used to determine both horizontal and vertical flows. The one exception is when gravity drainage is considered or known to be important, such as in downward gas displacements, in which cases special care is taken to determine how vertical downward flows respond to the combined effects of both pressure gradients and gravitational body forces. The reason for the exceptional treatment is that relatively small oil saturations are often attained under gravity drainage; sometimes less than 0.1 pore volume, especially if film flow occurs. These conditions and results also may occur in high-permeability reservoirs undergoing gas displacement, such as thermal floods. And, of course, differences in relative permeability under vertical and horizontal flow at the same potential gradient and oil saturation mean that the oil relative permeability curves are directionally anisotropic. Directional anisotropy in relative permeability is not a mere matter of principle; it is a known and important phenomenon. Even though the anisotropic behavior described above when drainage is important is well known, and its implications regarding the directional anisotropy of relative permeabilities are apparent, we have been slow to embrace the concept that relative permeabilities are directionally anisotropic. Simply stated, relative permeabilities are not measured, used, and discussed as being directionally anisotropic. Let us emphasize that this discussion is not about the effective permeability anisotropy resulting from the anisotropies in the absolute permeability of a formation associated with small-scale heterogeneities attributable to its depositional and sedimentological environment. These effects are well known and accounted for by the industry, which routinely considers the ratio of vertical to horizontal absolute permeabilities to be generally less than one. We are arguing here for a more basic effect, that directional anisotropy in relative permeabilities is present even in a homogeneous and isotropic medium. That the directional anisotropy exists in principle does not mean it is universally important. But it is clearly important where gravity drainage is a dominant mechanism. Both industry and academia should inquire further into the full implications of the concept and of the pore-level phenomena associated with it. Specifically, it would seem important to have the option to use directionally anisotropic relative permeabilities in simulation models. To our knowledge, such capability is not generally available. Michael Prats, SPE Honorary Member Larry W. Lake, SPE Honorary Member

An integral treatment of combined body force and forced convection in laminar film condensation

Unsteady numerical simulation of flow and heat transfer in a uniformly Joule-heated rectangular pool

This study numerically explores the combined effects of flow modulation and Joule heating inside a hexagonal enclosure composed of seawater influenced by an external magnetic field. The cold upper wall of the cavity moves horizontally at a uniform speed, while a rotating thermally conductive circular cylinder is introduced as a flow modulation device to facilitate local vortices' formation. The numerical procedure is conducted utilizing the Galerkin finite element method to resolve the governing equations for both flow and thermal fields. The mixed convection phenomenon is modeled through the Richardson number (0.1 ≤ Ri ≤ 10), whereas the cylinder's rotation is devised by a variable speed ratio (−3 ≤ Ω ≤ 3). The effect of the magnetic field on the system's hydrodynamics is examined via the analysis of various Hartmann numbers (50 ≤ Ha ≤ 100) and Joule heating parameters (J). The model characteristics have been evaluated for streamlines and isotherms, Nusselt numbers, and average temperature. Outcomes demonstrate that the simultaneous influence of the rotating cylinder and the moving top wall dictates the hydrodynamics of the system, achieving up to 137% thermal enhancement. The system's heat transfer is enhanced by buoyancy force, although this effect diminishes with stronger magnetic fields, which stabilize the fluid flow while reducing thermal efficacy. The performance of the rotating flow modulator is the most effective in the forced convection region (0.1 ≤ Ri ≤ 0.4) under a moderately strong magnetic field (Ha = 70). This study presents a novel analysis of a thermo-electromagnetic system in a hexagonal seawater-filled enclosure, integrating rotating flow modulation, external magnetic field, and internal Joule heating. The findings derived from this work can be instrumental in designing marine cooling systems requiring effective heat transfer and flow stabilization.

Two-and-three-dimensional analysis of Joule and viscous heating effects on MHD nanofluid forced convection in microchannels

A comprehensive numerical analysis has been conducted to investigate unsteady natural convection (UNC), bifurcation behavior, and heat transfer (HT) in a rectangular enclosure containing thermally stratified air. The enclosure comprises a uniformly heated bottom wall, thermally stratified vertical sidewalls, and a cooled top wall. To assess thermal performance, square and rectangular cavities with identical boundary conditions and working fluid are considered. The finite volume method (FVM) is used to solve the governing equations over a wide range of Rayleigh numbers (Ra = 101 to 109) for air with a Prandtl number (Pr) of 0.71. Flow dynamics and thermal performance are analyzed using temperature time series (TTS), limit point–limit cycle behavior, average Nusselt number (Nuavg), average entropy generation (Savg), average Bejan number (Beavg), and the ecological coefficient of performance (ECOP). In the rectangular cavity, the transition from steady to chaotic flow exhibits three bifurcations: a pitchfork bifurcation at Ra = 3 × 104–4 × 104, a Hopf bifurcation at Ra = 3 × 106–4 × 106, and the onset of chaotic flow at Ra = 9 × 107–2 × 108. The comparative analysis indicates that Nuavg remains nearly identical for both cavities within Ra = 105 to 107. However, at Ra = 108, the HT rate in the rectangular cavity is 29.84% higher than that of the square cavity, while Savg and Beavg differ by 39.32% and 37.50%, respectively. Despite higher HT and Savg in the rectangular enclosure, the square cavity demonstrates superior overall thermal performance by 13.52% at Ra = 108. These results offer significant insights for optimizing cavity geometries in thermal system design based on energy efficiency and entropy considerations.

Soft-sediment deformation structures in the Miocene deposits in the Luoyanshan area of the Qaidam basin, China: Implications for paleogeomorphology

This paper presents a novel dual reciprocity formulation for elasticity problems with body forces in which the approximating functions are given in terms of augmented thin plate splines (ATPS). It is shown that the ATPS approximation is capable of correctly representing gravitational and centrifugal body forces, and provides superior accuracy for general load cases.

Second order slip micropolar MHD hybrid nanofluid flow over a stretching surface with uniform heat source and activation energy: Numerical computational approach

Hydromagnetic mixed convection in a triangular shed filled by nanofluid and equipped with rectangular heater and rotating cylinders

Fracture behavior of superconductor REBCO tapes with multiple edge cracks under electromagnetic force

Machine learning approach for predicting heat and mass transfer in Maxwell–Sutterby fluid flow over a Riga plate geometry via Levenberg–Marquardt backpropagation neural network algorithm: influence of joule heating and activation energy

This dissertation focuses on turbulent thermal convection, which occurs in a wide range of (geo)physical situations, like in the atmosphere, the oceans, the interior of stars or planets, and engineering applications, like metal casting or crystal growth processes. In this work, a special type of thermal convection, Rayleigh-Benard convection, is studied with and without an additional electromagnetic body force. Experiments are performed in a rectangular RB convection cell of aspect-ratio ?=4 filled with water. Particle image velocimetry (PIV), laser Doppler anemometry (LDA), and liquid crystal thermography (LCT) measurements are used to obtain velocity and temperature information. The first part of this dissertation describes an investigation of the large-scale circulation (LSC) in Rayleigh-Benard convection. In the second part, a study of the boundary layers in Rayleigh-Benard convection is described. The last part reports on the control and enhancement of the heat transfer in Rayleigh-Benard convection using an additional electromagnetic body force.

Liquid jet impingement is often used to cool heated surfaces encountered in various industrial applications. Such applications include cooling of electronic components and annealing of metals. Liquid jet impingement investigations primarily involve submerged jets and less commonly free liquid jets. Most of the studies done on both submerged jet impingement and free liquid jet impingement are done under terrestrial gravity conditions. There have been few studies on liquid jet impingement under non terrestrial conditions in zero or non zero gravitational force or of electrical body forces. These conditions are expected to result in significantly different flow patterns and heat transfer compared to terrestrial gravity.;The relatively uncommon forces like the electric Kelvin force could significantly affect the heat transfer and flow characteristics of an impinging liquid jet. As per one of the objectives of this research, an electrode arrangement was designed to obtain a uniform electric Kelvin body force acting in a direction opposite to the impinging jet. Another objective was to assess the effects of varying gravity on heat transfer to an impinging jet. Simulation results involving liquid jet impingement with different body forces are presented in this dissertation. These results were obtained with the aid of a commercial multiphysics code called CFD-ACE+.;The isothermal set of simulations included the electric Kelvin force as the source term, while in the non isothermal cases gravity was varied from 0 to 1.5 g in the increments of 0.5 g. The transient effects of the electric Kelvin force were observed in the isothermal simulations while in the non isothermal simulations it was found that for low velocities the heat transfer from an impinging liquid jet was enhanced as the gravitational force was increased.