Heat Transfer in Packed Bed Elliptic-Cylindrical Reactor: The Geometry Effect

2019 ◽  
Vol 391 ◽  
pp. 54-59 ◽  
Author(s):  
R. Moura da Silva ◽  
A. Santos Pereira ◽  
A.G. Barbosa de Lima ◽  
Morgana Vasconcellos Araújo ◽  
R.S. Santos
Keyword(s):  
Heat Transfer ◽  
Aspect Ratio ◽  
Temperature Profile ◽  
Fixed Bed ◽  
Three Dimensional ◽  
Packed Bed ◽  
Dimensionless Temperature ◽  
Variable Porosity ◽  
Cylindrical Reactor ◽  
Half Axis

This work aims to develop a transient three-dimensional mathematical model to predict the temperature distribution in a fixed-bed elliptical cylindrical reactor to different geometric aspect ratio (L2/L1=1.5, 2.0 and 3.0). The model considers variable thermo-physical properties, a flat temperature profile at the fluid inlet, as well as a variable porosity model. The governing equation is solved using the finite volume method, coupled with WUDS interpolation scheme and fully implicit method. Results of the temperature profile along the reactor are presented and discussed at different times. As results, it was found that the maximum rate of heat transfer within the reactor occurs near the minor half-axis region of the ellipse (cross-section area of the reactor) and it intensifies over time and that the dimensionless temperature profile is practically unchanged with the aspect ratio.

Heat Transfer in Fixed Bed Elliptic Cylindrical Reactor via Two-Phase Model

2020 ◽  
Vol 400 ◽  
pp. 45-50
Author(s):  
Antonildo Santos Pereira ◽  
Rodrigo Moura da Silva ◽  
Maria Conceição Nóbrega Machado ◽  
Luan Pedro Melo Azerêdo ◽  
Anderson Ferreira Vilela ◽  
...  
Keyword(s):  
Heat Transfer ◽  
Solid Phase ◽  
Homogeneous Model ◽  
Fixed Bed ◽  
Fluid Phase ◽  
Packed Bed ◽  
Two Phase ◽  
Heterogeneous Model ◽  
Fully Implicit ◽  
Cylindrical Reactor

The study of heat transfer in fixed bed tubular reactors of heated or cooled walls has presented great interest by the academy and industry. The adequate and safe design of such equipment requires the use of reliable and realistic mathematical. Unfortunately several studies are restrict to homogeneous model applied to circular and elliptic cylindrical reactors. Then, the objective of this work was to predict heat transfer in packed-bed elliptic cylindrical reactor, by using a proposed heterogeneous model. The mathematical model is composed for one solid phase and another fluid phase, in which the balance equation for each constituent is applied separately. The finite volume method was utilized to solve the partial differential equations using the WUDS scheme for interpolation of the convective and diffusive terms, and the fully implicit formulation. Results of the temperature distribution of the fluid and solid phases along the reactor are presented and analyzed. It was verified that the highest temperature gradients of the phases are located close to the wall and inlet of the reactor.

Steady State Model for Heat Transfer in a Packed Bed Reactor of Elliptic Cylindrical Shape

2008 ◽  
Vol 6 (1) ◽  
Author(s):  
Laércio G. Oliveira ◽  
Ramdayal Swarnakar ◽  
Antonio G. B. de Lima
Keyword(s):  
Heat Transfer ◽  
Steady State ◽  
Fixed Bed ◽  
Packed Bed ◽  
Numerical Results ◽  
Packed Bed Reactor ◽  
Fixed Bed Reactor ◽  
Dimensionless Temperature ◽  
Cylindrical Shape ◽  
Temperature Profiles

The fixed-bed reactors of circular cylindrical geometry with heated or cooled walls are frequently used to carry out heterogeneous reactions of solid-gas type in engineering applications. The design of a fixed bed reactor requires an extensive knowledge of heat transfer characteristics within the packed bed. In this sense, this work presents a three-dimensional mathematical model to predict the heat transfer inside a fixed bed elliptical cylinder heat exchanger. The model considers uniform velocity and temperature profiles of the fluid phase at the entrance of the reactor, and constant thermo-physical properties. The surface of the equipment convective boundary condition is assumed to be constant. The energy equation, written in the elliptical cylindrical coordinates, was discretized using a finite-volume method considering a fully implicit formulation, and WUDS interpolation scheme. Numerical results of the dimensionless temperature profiles inside the packed bed reactor at a steady state are presented and temperature distribution is interpreted. To validate the model, numerical results obtained for the circular cylinder are compared with analytical results from literature and a good agreement was obtained.

Heat Transfer inside Elliptic Cylindrical Reactor: Effect of Bed Porosity

2013 ◽  
Vol 336 ◽  
pp. 97-102
Author(s):  
A.A. Silva Filho ◽  
J.P. Silva de Almeida ◽  
Antônio Gilson Barbosa de Lima
Keyword(s):  
Heat Transfer ◽  
Fixed Bed ◽  
Three Dimensional ◽  
Axial Direction ◽  
Cylindrical Geometry ◽  
Heat Diffusion ◽  
Fixed Bed Reactor ◽  
Three Dimensional Model ◽  
Variable Porosity ◽  
Steady State Heat Transfer

The study of heat transfer phenomenon in porous media by fluids percolated in the axial direction has been of interest to many researchers in various branches of science and technology. Applications are directed to different process such as filtration, distillation, absorption and adsorption in columns, drying and catalytic reactions in fixed beds. The literature has presented several solutions of the heat diffusion / convection equation in fixed bed reactors, but these studies are limited to a cylindrical geometry. In this sense, this work aim to present a pseudo-homogeneous three-dimensional model to describe the steady-state heat transfer within a fixed bed reactor with elliptic cylindrical geometry by considering variable porosity. The energy equation written in elliptical cylindrical coordinates and applied to the porous medium (particulate system) is discretized numerically using the finite volume method. Results of the temperature distribution within the bed are presented analyzed. It was verified that with increased porosity heat transfer inside the reactor tends to be more intense and thus, lower temperature gradients are found in all cross section of the reactor.

Numerical Simulation Of A Microchannel For Microelectronic Cooling

2012 ◽  
Author(s):  
Wai Hing Wong ◽  
Normah Mohd. Ghazali
Keyword(s):  
Heat Transfer ◽  
Numerical Simulation ◽  
Heat Flux ◽  
Aspect Ratio ◽  
Three Dimensional ◽  
Large Temperature ◽  
Rectangular Microchannel ◽  
Numerical Work ◽  
Solid Region ◽  
Wall Interaction

Kertas kerja ini membincangkan simulasi berangka ke atas sinki haba saluran mikro dalam penyejukan alatan mikroelektronik. Model Dinamik Bendalir Berkomputer (CFD) tiga dimensi dibina menggunakan pakej komersil, FLUENT, untuk mengkaji fenomenon aliran bendalir dan pemindahan haba konjugat di dalam suatu sinki haba segi empat yang diperbuat daripada silikon. Model ditentusahkan dengan keputusan daripada uji kaji dan pengkajian berangka yang lepas untuk lingkungan nombor Reynolds kurang daripada 400 berdasarkan diameter hidraulik 86 mm. Kajian ini mengambil kira kesan kelikatan bendalir yang bersandaran dengan suhu dan keadaan aliran pra–membangun dari segi hidrodinamik dan haba. Model memberi maklumat tentang taburan suhu dan fluks haba yang terperinci di dalam sinki haba saluran mikro. Kecerunan suhu yang tinggi dicatat pada kawasan pepejal berdekatan dengan sumber. Fluks haba paling tinggi didapati pada dinding tepi saluran mikro diikuti oleh dinding atas dan bawah. Purata pekali pemindahan haba yang lebih tinggi bagi silikon menjadikan ia bahan binaan sinki haba saluran mikro yang lebih baik berbanding dengan kuprum dan aluminium. Peningkatan nisbah aspek saluran mikro yang bersegi empat memberi kecekapan penyejukan yang lebih tinggi kerana kelebaran saluran yang berkurangan memberi kecerunan halaju yang lebih tinggi dalam saluran. Nisbah aspek yang optimum yang diperoleh adalah dalam lingkungan 3.7 – 4.1. Kata kunci: Saluran mikro, CFD, FLUENT, simulasi berangka, penyejukan mikroelektron The paper discusses the numerical simulation of a micro–channel heat sink in microelectronics cooling. A three–dimensional Computational Fluid Dynamics (CFD) model was built using the commercial package, FLUENT, to investigate the conjugate fluid flow and heat transfer phenomena in a silicon–based rectangular microchannel heatsink. The model was validated with past experimental and numerical work for Reynolds numbers less than 400 based on a hydraulic diameter of 86 mm. The investigation was conducted with consideration of temperaturedependent viscosity and developing flow, both hydrodynamically and thermally. The model provided detailed temperature and heat flux distributions in the microchannel heatsink. The results indicate a large temperature gradient in the solid region near the heat source. The highest heat flux is found at the side walls of the microchannel, followed by top wall and bottom wall due to the wall interaction effects. Silicon is proven to be a better microchannel heatsink material compared to copper and aluminum, indicated by a higher average heat transfer. A higher aspect ratio in a rectangular microchannel gives higher cooling capability due to high velocity gradient around the channel when channel width decreases. Optimum aspect ratio obtained is in the range of 3.7 – 4.1. Key words: Microchannel, CFD, FLUENT, numerical simulation, microeletronics cooling

Thermohydrodynamic Performance Evaluation of Recharging, Interrupted and Simple Microchannels: A Comparative Study

2019 ◽  
Vol 142 (1) ◽  
Author(s):  
Sangram Kumar Samal ◽  
Manoj Kumar Moharana
Keyword(s):  
Heat Transfer ◽  
Aspect Ratio ◽  
Three Dimensional ◽  
High Heat ◽  
Heat Sinks ◽  
High Heat Flux ◽  
Transverse Wall ◽  
Performance Factor ◽  
Channel Aspect Ratio ◽  
Small Channels

Abstract In this study, a three-dimensional numerical investigation on the thermohydrodynamic performance of a recently proposed recharging microchannel (RMC) is carried out. In this design, a straight microchannel is split into more than one smaller length channels (having individual inlet and outlet) placed end to end. This design enhances overall heat transfer and maintains temperature uniformity across the substrate length. The comparison of fluid flow and heat transfer performance of RMC, interrupted microchannel (IMC) and straight microchannel (SMC) with the same hydraulic diameter and substrate length are presented to explore the effect of geometrical configuration on heat transfer enhancement. The parametric variations include the number of channels (n), transverse wall length (Ltw), channel aspect ratio (α), and flow Reynolds number. The results reveal that recharging microchannel shows better thermal performance compared to simple and interrupted microchannel with a maximum performance factor of 1.80. The results also indicate that the performance factor of RMC increases with an increase in the number of small channels, transverse wall length, and channel aspect ratio. The outcome of this study indicates the possible use of recharging microchannel heat sinks for high heat flux removal applications such as electronic cooling.

An Experimental Investigation of Heat Transfer in Variable Porosity Media

1985 ◽  
Vol 107 (3) ◽  
pp. 642-647 ◽  
Author(s):  
K. Vafai ◽  
R. L. Alkire ◽  
C. L. Tien
Keyword(s):  
Heat Transfer ◽  
Experimental Investigation ◽  
Packed Bed ◽  
Volume Averaging ◽  
Experimental Results ◽  
Variable Porosity ◽  
Local Volume Averaging ◽  
Convection In Porous Media ◽  
Impermeable Boundary ◽  
Good Agreement

This paper presents an experimental investigation on the effects of a solid impermeable boundary and variable porosity on forced convection in porous media. Emphasis is placed on the channeling effects on heat transfer in packed beds. The local volume-averaging technique is used to establish the governing equations and a numerical scheme is developed which incorporates the boundary and variable porosity effects on heat transfer. The experimental results for the heat flux at the boundary are presented as a function of the pertinent variables in a packed bed. The Nusselt number is found to increase almost linearly with an increase in the Reynolds number based on the pore diameter. The experimental results are found to be in good agreement with the theoretical results which account for the variable porosity effects. A comparison between the numerical and the experimental results demonstrates the importance of boundary and variable porosity effects on heat transfer in variable porosity media.

scholarly journals Solvability of the Brinkman-Forchheimer-Darcy Equation

2017 ◽  
Vol 2017 ◽  
pp. 1-10 ◽  
Author(s):  
Piotr Skrzypacz ◽  
Dongming Wei
Keyword(s):  
Fixed Bed ◽  
Packed Bed ◽  
Reynolds Numbers ◽  
Fixed Bed Reactor ◽  
Small Data ◽  
Convective Flows ◽  
Finite Element Approximations ◽  
Darcy Equation ◽  
Variable Porosity ◽  
Porous Medium Flow

The nonlinear Brinkman-Forchheimer-Darcy equation is used to model some porous medium flow in chemical reactors of packed bed type. The results concerning the existence and uniqueness of a weak solution are presented for nonlinear convective flows in medium with variable porosity and for small data. Furthermore, the finite element approximations to the flow profiles in the fixed bed reactor are presented for several Reynolds numbers at the non-Darcy’s range.

Role of Three-Dimensional Swirl in Forced Convection Heat Transfer Enhancement in Wavy-Plate-Fin Channels

2022 ◽  
Author(s):  
Dantong Shi ◽  
Kuan-Ting Lin ◽  
Milind A. Jog ◽  
Raj M. Manglik
Keyword(s):  
Heat Transfer ◽  
Aspect Ratio ◽  
Forced Convection ◽  
Three Dimensional ◽  
Local Heat Transfer ◽  
Swirl Flow ◽  
Channel Height ◽  
Wave Trough ◽  
Spacing Ratio ◽  
Fin Spacing

Abstract The influence of swirl flow on enhanced forced convection in wavy-plate-fin cores has been investigated. Three-dimensional computational simulations were carried out for steady-state, periodically developed flow of air (Pr ~ 0.71) with channel walls subject to constant-uniform temperature and flow rates in the range 50 = Re = 4000. The recirculation that develops in the wall troughs and grows to an axial helix is scaled by the Swirl number Sw. As Sw increases, tornado-shaped vortices appear in the wave trough region mid-channel height, then extend longitudinally to encompass majority of the flow channel. As shown by the local wall-shear and heat transfer coefficient variations, the boundary-layer thinning upstream of the wave peak assists to intensify the momentum and heat transfer. However, the flow recirculation in wave trough impedes the local heat transfer at low Sw due to flow stagnation but promotes it at high Sw because of swirl-augmented fluid mixing. Swirling flows also create pressure drag that contributes substantively to the overall pressure loss. Its proportion grows as Sw, corrugation severity, and fin spacing increases to as much as 80% of the total pressure drop. The fin-wall curvature-induced secondary circulation nevertheless produces significantly enhanced convection, and more so in flows with higher Sw. It is quantified by Ff (or j), which is seen to increase log-linearly as fin corrugation aspect ratio and/or fin spacing ratio increases; the influence of cross-section aspect ratio is found to be marginal.

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