Simulation of a Moving Porous Bed Reactor With a Two-Energy Equation Model

2010 ◽  
Author(s):  
Marcelo J. S. de Lemos ◽  
Ana C. Pivem
Keyword(s):  
Heat Transfer ◽  
Conduction Mechanism ◽  
Solid Phase ◽  
Porous Matrix ◽  
Momentum Equation ◽  
Equation Model ◽  
Porous Bed ◽  
Flow And Heat Transfer ◽  
Interface Heat Transfer ◽  
Interface Heat

Interface heat transfer in a moving porous bed is analyzed. This work proposes a set of transport equations for solving problems involving turbulent flow and heat transfer in a moving bed equipment. The device is modeled as a saturated porous matrix in which the solid phase moves with a steady imposed velocity. Additional drag terms appearing in the momentum equation, as well as interfacial heat transfer between phases, are assumed to be a function of the relative velocity between the fluid and solid phases. Results indicate that, as the phases attain velocities of equal order, heat transfer between solid and fluid occurs mainly by the conduction mechanism.

Mathematical Modeling of Flow and Heat Transfer in a Moving Bed Reactor

2008 ◽  
Author(s):  
Marcelo J. S. de Lemos
Keyword(s):  
Mathematical Modeling ◽  
Heat Transfer ◽  
Transfer Rate ◽  
Relative Velocity ◽  
Solid Phase ◽  
Porous Matrix ◽  
Momentum Equation ◽  
Moving Bed ◽  
Flow And Heat Transfer ◽  
Solid Phases

This paper shows a proposition of a set of transport equations and their boundary conditions for solving problems involving flow and heat transfer in a moving bed equipment. The reactor is seen as a porous matrix in which the solid phase is moving. Additional drag terms appearing the momentum equation are a function of the relative velocity between the fluid and solid phases. Turbulence equations are also influenced by the speed of the solid phase. Results show the decrease for turbulent kinetic energy as the solid speed approaches the fluid speed. Heat transfer rate between phases is also damped as the solid speed increases.

Simulation of Flow and Heat Transfer in a Moving Bed Reactor With Cross Flow

2008 ◽  
Author(s):  
Marcelo J. S. de Lemos
Keyword(s):  
Heat Transfer ◽  
Relative Velocity ◽  
Solid Phase ◽  
Cross Flow ◽  
Vertical Direction ◽  
Momentum Equation ◽  
Solid Matrix ◽  
Flow And Heat Transfer ◽  
Temperature Distributions ◽  
Solid Phases

Heat transfer in a porous reactor under cross flow is investigated. The reactor is modeled as a porous bed in which the solid phase is moving horizontally and the flow is forced into the bed in a vertical direction. Equations are time-and-volume averaged and the solid phase is considered to have a constant imposed velocity. Additional drag terms appearing the momentum equation are a function of the relative velocity between the fluid and solid phases. Turbulence equations are also affected by the speed of the solid matrix. Results show temperature distributions for several ratios of the solid to fluid speed.

Heat Transfer at an Evaporating Front in Porous Media

2009 ◽  
Author(s):  
V. K. Chaitanya Pakala ◽  
O. A. Plumb
Keyword(s):  
Heat Transfer ◽  
Porous Media ◽  
Coal Gasification ◽  
Solid Phase ◽  
Front Propagation ◽  
Porous Matrix ◽  
Equation Model ◽  
Local Thermal Equilibrium ◽  
Underground Coal Gasification ◽  
The One

Evaporating fronts propagate through porous media during drying processes, underground coal gasification, geothermal energy production from hot dry rock, and around nuclear waste repositories. Present work will focus on the one-dimensional heat transfer at the interface between vapor saturated porous matrix and water saturated porous region and evaluate the conditions for which various approximations yield an accurate representation of front velocity. An implicit finite difference scheme is utilized to simulate the propagation of an evaporating front in a porous medium saturated with water and undergoing the phase change process. The assumption of local thermal equilibrium (LTE) which results in a one-equation model and a simple two-equation model that does not assume LTE are examined by comparison with a quasi-analytic numerical model. We consider the case for low Reynolds number, hence Nusselt number is assumed constant. Results illustrate that the one-equation model does not yield accurate results even if the length scale for diffusion in the solid phase is relatively small. The one-equation model predicts faster front propagation than the two-equation model. It is illustrated that the one-equation model yields satisfactory results only when thermophysical properties characterized by the volume weighted ratio of thermal diffusivities is reduced to an order of magnitude less than those for the applications of interest. In addition, consistent with the established “rule of thumb”, for Biot < 0.1, the traditional two-equation model which makes the lumped capacitance assumption for the solid phase compares well with a two-equation model that more accurately predicts the time dependent diffusion in the solid phase using Duhamel’s theorem.

Passive Heat Transfer in Porous Enclosures Using a Two-Energy Equation Model

2012 ◽  
Author(s):  
Marcelo J. S. deLemos ◽  
Paulo H. S. Carvalho
Keyword(s):  
Heat Transfer ◽  
Energy Equation ◽  
Equation Model ◽  
Thermal Conductivity Ratio ◽  
Governing Equations ◽  
Flow And Heat Transfer ◽  
Energy Models ◽  
Different Temperatures ◽  
Volume Method ◽  
Generalized Coordinate

This paper presents computations for natural convection within a porous cavity filled with a fluid saturated permeable medium. The finite volume method in a generalized coordinate system is applied. The walls are maintained at constant but different temperatures, while the horizontal walls are kept insulated. Governing equations are written in terms of primitive variables and are recast into a general form. Flow and heat transfer characteristics are investigated for two energy models and distinct solid-to-fluid thermal conductivity ratio.

Free convection in a square porous cavity filled with a nanofluid using thermal non equilibrium and Buongiorno models

2016 ◽  
Vol 26 (3/4) ◽  
pp. 671-693 ◽  
Author(s):  
Ioan Pop ◽  
Mohammad Ghalambaz ◽  
Mikhail Sheremet
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Brownian Motion ◽  
Base Fluid ◽  
Average Nusselt Number ◽  
Solid Phase ◽  
Porous Matrix ◽  
Governing Equations ◽  
Content Type ◽  
Brownian Motion And Thermophoresis

Purpose – The purpose of this paper is to theoretically analysis the steady-state natural convection flow and heat transfer of nanofluids in a square enclosure filled with a porous medium saturated with a nanofluid considering local thermal non-equilibrium (LTNE) effects. Different local temperatures for the solid phase of the nanoparticles, the solid phase of porous matrix and the liquid phase of the base fluid are taken into account. Design/methodology/approach – The Buongiorno’s model, incorporating the Brownian motion and thermophoresis effects, is utilized to take into account the migration of nanoparticles. Using appropriate non-dimensional variables, the governing equations are transformed into the non-dimensional form, and the finite element method is utilized to solve the governing equations. Findings – The results show that the increase of buoyancy ratio parameter (Nr) decreases the magnitude of average Nusselt number. The increase of the nanoparticles-fluid interface heat transfer parameter (Nhp) increases the average Nusselt number for nanoparticles and decreases the average Nusselt number for the base fluid. The nanofluid and porous matrix with large values of modified thermal capacity ratios (γ p and γ s ) are of interest for heat transfer applications. Originality/value – The three phases of nanoparticles, base fluid and the porous matrix are in the LTNE. The effect of mass transfer of nanoparticles due to the Brownian motion and thermophoresis effects are also taken into account.

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