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.

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.

Heat transfer enhancement in microchannels using ribs and secondary flows

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Karthikeyan Paramanandam ◽  
Venkatachalapathy S. ◽  
Balamurugan Srinivasan
Keyword(s):  
Heat Transfer ◽  
Temperature Distribution ◽  
Heat Transfer Enhancement ◽  
Heat Transfer Rate ◽  
Transfer Rate ◽  
Secondary Flows ◽  
Transfer Enhancement ◽  
Heat Transfer Characteristics ◽  
Content Type ◽  
Flow And Heat Transfer

Purpose The purpose of this paper is to study the flow and heat transfer characteristics of microchannel heatsinks with ribs, cavities and secondary channels. The influence of length and width of the ribs on heat transfer enhancement, secondary flows, flow distribution and temperature distribution are examined at different Reynolds numbers. The effectiveness of each heatsink is evaluated using the performance factor. Design/methodology/approach A three-dimensional solid-fluid conjugate heat transfer numerical model is used to study the flow and heat transfer characteristics in microchannels. One symmetrical channel is adopted for the simulation to reduce the computational cost and time. Flow inside the channels is assumed to be single-phase and laminar. The governing equations are solved using finite volume method. Findings The numerical results are analyzed in terms of average Nusselt number ratio, average base temperature, friction factor ratio, pressure variation inside the channel, temperature distribution, velocity distribution inside the channel, mass flow rate distribution inside the secondary channels and performance factor of each microchannels. Results indicate that impact of rib width is higher in enhancing the heat transfer when compared with its length but with a penalty on the pressure drop. The combined effects of secondary channels, ribs and cavities helps to lower the temperature of the microchannel heat sink and enhances the heat transfer rate. Practical implications The fabrication of microchannels are complex, but recent advancements in the additive manufacturing techniques makes the fabrication of the design considered in this numerical study feasible. Originality/value The proposed microchannel heatsink can be used in practical applications to reduce the thermal resistance, and it augments the heat transfer rate when compared with the baseline design.

Non-axisymmetric Homann stagnation point flow and heat transfer past a stretching/shrinking sheet using hybrid nanofluid

2020 ◽  
Vol 30 (10) ◽  
pp. 4583-4606 ◽  
Author(s):  
Najiyah Safwa Khashi’ie ◽  
Norihan Md Arifin ◽  
Ioan Pop ◽  
Roslinda Nazar ◽  
Ezad Hafidz Hafidzuddin ◽  
...  
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Strain Rate ◽  
Stagnation Point ◽  
Heat Transfer Rate ◽  
Transfer Rate ◽  
Hybrid Nanofluid ◽  
Ambient Fluid ◽  
Content Type ◽  
Flow And Heat Transfer

Purpose This paper aims to scrutinize the analysis of non-axisymmetric Homann stagnation point flow and heat transfer of hybrid Cu-Al2O3/water nanofluid over a stretching/shrinking flat plate. Design/methodology/approach The similarity transformation which fulfils the continuity equation is opted to transform the coupled momentum and energy equations into the nonlinear ordinary differential equations. Numerical solutions which are elucidated in the tables and graphs are obtained using the bvp4c solver. Findings Non-unique solutions (first and second) are feasible for both stretching and shrinking cases within the specific values of the parameters. First solution is the physical/real solution based on the execution of stability analysis. An upsurge of the ratio of the ambient fluid strain rate to the plate strain rate can delay the boundary layer separation, whereas a boost of the ratio of the ambient fluid shear rate to the plate strain rate only accelerates the separation of boundary layer. The heat transfer rate of hybrid nanofluid is greater for the stretching case than the shrinking case. However, for the shrinking case, the heat transfer rate intensifies with the increment of the copper (Cu) nanoparticles volume fraction, whereas a contrary result is found for the stretching case. Originality/value The present numerical results are original and new. It can contribute to other researchers on electing the relevant parameters to optimize the heat transfer process in the modern industry, and the right parameters to generate non-unique solution so that no misjudgment on flow and heat transfer features.

scholarly journals Numerical Simulation of the Flow and Heat Transfer in an Electric Steel Tempering Furnace

Energies ◽  
2020 ◽  
Vol 13 (14) ◽  
pp. 3655 ◽  
Author(s):  
Iván D. Palacio-Caro ◽  
Pedro N. Alvarado-Torres ◽  
Luis F. Cardona-Sepúlveda
Keyword(s):  
Heat Transfer ◽  
Heat Transfer Rate ◽  
Thermal Efficiency ◽  
Transfer Rate ◽  
Tempering Temperature ◽  
External Temperature ◽  
Rotating Speed ◽  
Flow And Heat Transfer ◽  
Temperature Homogeneity ◽  
Flow Mixing

Heat treatments, such as steel tempering, are temperature-controlled processes. It allows ferrous steel to stabilize its structure after the heat treatment and quenching stages. The tempering temperature also determines the hardness of the steel, preferably to its optimum working strength. In a tempering furnace, a heat-resistant fan is commonly employed to generate moderate gas circulation to obtain adequate temperature homogeneity and heat transfer. Nevertheless, there is a tradeoff because the overall thermal efficiency is expected to reduce because of the high rotating speed of the fan. Therefore, this study numerically investigates the thermal efficiency changes of an electric tempering furnace due to changes in the rotating speed of the fan and the effects on temperature homogeneity and the heat transfer rate to the load. Heat losses through the walls were calculated from the external temperature measurement of the furnace. Four different speeds were simulated: 720, 990, 1350, and 1800 rpm. Thermal homogeneity was improved at higher rotating speeds; this is because the recirculation zone caused by the fan improved the flow mixing and the heat transfer. However, it was found that the thermal efficiency of the tempering furnace decreased as the rotating speed values increased. Therefore, these characteristics should be modulated to obtain a profit when controlling the rotating speed. For example, although thermal efficiency decreases by 20% when the rotating speed is doubled, the heat transfer rate to load is increased by up to 50%, which can be beneficial in decreasing the process of tempering times.

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.

scholarly journals Effect of Reynolds Number and Property Variation on Fluid Flow and Heat Transfer in the Entrance Region of a Turbine Blade Internal-Cooling Channel

2005 ◽  
Vol 2005 (1) ◽  
pp. 36-44 ◽  
Author(s):  
R. Ben-Mansour ◽  
L. Al-Hadhrami
Keyword(s):  
Heat Transfer ◽  
Reynolds Number ◽  
Mass Flow Rate ◽  
Heat Transfer Rate ◽  
Turbine Blade ◽  
Flow Rate ◽  
Transfer Rate ◽  
Internal Cooling ◽  
Cooling Channel ◽  
Flow And Heat Transfer

Internal cooling is one of the effective techniques to cool turbine blades from inside. This internal cooling is achieved by pumping a relatively cold fluid through the internal-cooling channels. These channels are fed through short channels placed at the root of the turbine blade, usually called entrance region channels. The entrance region at the root of the turbine blade usually has a different geometry than the internal-cooling channel of the blade. This study investigates numerically the fluid flow and heat transfer in one-pass smooth isothermally heated channel using the RNGk−εmodel. The effect of Reynolds number on the flow and heat transfer characteristics has been studied for two mass flow rate ratios (1/1and1/2) for the same cooling channel. The Reynolds number was varied between10 000and50 000. The study has shown that the cooling channel goes through hydrodynamic and thermal development which necessitates a detailed flow and heat transfer study to evaluate the pressure drop and heat transfer rates. For the case of unbalanced mass flow rate ratio, a maximum difference of8.9% in the heat transfer rate between the top and bottom surfaces occurs atRe=10 000while the total heat transfer rate from both surfaces is the same for the balanced mass flow rate case. The effect of temperature-dependent property variation showed a small change in the heat transfer rates when all properties were allowed to vary with temperature. However, individual effects can be significant such as the effect of density variation, which resulted in as much as9.6% reduction in the heat transfer rate.

scholarly journals Mathematical Modeling of Fluid Flow and Heat Transfer in Petroleum Industries and Geothermal Applications

Energies ◽  
2020 ◽  
Vol 13 (6) ◽  
pp. 1344
Author(s):  
Mehrdad Massoudi
Keyword(s):  
Mathematical Modeling ◽  
Heat Transfer ◽  
Porous Media ◽  
Fluid Flow ◽  
Heat Exchanger ◽  
Ground Heat Exchanger ◽  
Special Issue ◽  
Flow And Heat Transfer ◽  
Convection In Porous Media

This Special Issue of Energies is dedicated to all aspects of fluid flow and heat transfer in geothermal applications, including the ground heat exchanger, conduction, and convection in porous media [...]

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