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E Zanchini - One of the best experts on this subject based on the ideXlab platform.
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forced convection in the Thermal Entrance Region of a circular duct with slug flow and viscous dissipation
International Journal of Heat and Mass Transfer, 1997Co-Authors: A. Barletta, E ZanchiniAbstract:Abstract Slug flow forced convection in a circular duct is studied. The effect of viscous dissipation is analysed in the Thermal Entrance Region. The temperature field and the local Nusselt number are determined analytically for any prescribed axial distribution of wall heat flux. Three examples are considered: a uniform wall heat flux, a linearly varying wall heat flux and an exponentially varying wall heat flux. In the case of a uniform wall heat flux, it is shown that viscous dissipation reduces the value of the local Nusselt number in the whole duct. In the case of a linearly or exponentially increasing wall heat flux, viscous dissipation affects the local Nusselt number only in the Thermal Entrance Region and becomes negligible in the fully developed Region.
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Thermal Entrance Region for laminar forced convection in a circular tube with a power law wall heat flux
International Journal of Heat and Mass Transfer, 1996Co-Authors: A. Barletta, E ZanchiniAbstract:Laminar forced convection in a circular tube is investigated with a boundary condition of prescribed axially varying wall heat flux, under the assumptions of hydrodynamically developed flow and of negligible axial conduction and viscous dissipation in the fluid. A condition on the asymptotic behaviour of the axial distribution of wall heat flux is established which is fulfilled by power-law varying axial distributions and which guarantees the existence of a Thermally developed regime. It is proved that for all the axial distributions which fulfil this condition the asymptotic value reached by the local Nusselt number is 48/11, i.e. the same which holds for a uniform wall heat flux. For some power-law varying axial distributions of wall heat flux, a finite difference determination of the Thermal Entrance Region is performed. In every numerical solution, the local Nusselt number tends asymptotically to 48/11.
A. Barletta - One of the best experts on this subject based on the ideXlab platform.
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Effects of Brownian Diffusion and Thermophoresis on the Laminar Forced Convection of a Nanofluid in a Channel
Journal of Heat Transfer, 2013Co-Authors: Eugenia Rossi Di Schio, Michele Celli, A. BarlettaAbstract:A steady laminar forced convection in a parallel–plane channel using nanofluids is studied. The flow is assumed to be fully developed, and described through the Hagen–Poiseuille profile. A boundary temperature varying with the longitudinal coordinate in the Thermal Entrance Region is prescribed. Two sample cases are investigated in detail: a linearly changing wall temperature, and a sinusoidally changing wall temperature. A study of the Thermal behavior of the nanofluid is performed by solving numerically the fully–elliptic coupled equations. The numerical solution is obtained by a Galerkin finite element method implemented through the software package Comsol Multiphysics (© Comsol, Inc.). With reference to both the wall temperature distributions prescribed along the Thermal Entrance Region, the governing equations have been solved separately both for the fully developed Region and for the Thermal Entrance Region. The analysis shows that if a linearly varying boundary temperature is assumed, for physically interesting values of the Péclet number the concentration field depends very weakly on the temperature distribution. On the other hand, in case of a longitudinally periodic boundary temperature, nonhomogeneities in the nanoparticle concentration distribution arise, which are wrongly neglected whenever the homogeneous model is employed.
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Periodic Forced Convection in a Darcy Metallic Foam: The LTNE Model
Volume 7: Fluids and Heat Transfer Parts A B C and D, 2012Co-Authors: Eugenia Rossi Di Schio, A. BarlettaAbstract:The present paper studies the Thermal Entrance Region in a concentric annular duct filled by a fluid saturated porous metallic foam, with reference to steady forced convection and to a Thermal boundary condition given by a wall temperature longitudinally varying with a sinusoidal law. The effect of viscous dissipation in the fluid is taken into account, and a two-temperature model is employed in order to evaluate separately the local fluid and solid matrix temperatures. The governing equations in the Thermal Entrance Region are solved numerically by the method of lines. The Nusselt numer and its mean value in an axial period is evaluated, with reference both to the inner and the outer boundary.Copyright © 2012 by ASME
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Thermal Nonequilibrium and Viscous Dissipation in the Thermal Entrance Region of a Darcy Flow With Streamwise Periodic Boundary Conditions
Journal of Heat Transfer, 2011Co-Authors: A. Barletta, E. Rossi Di Schio, L. SelmiAbstract:The Thermal Entrance Region in a plane-parallel channel filled by a fluid saturated porous medium is investigated with reference to steady forced convection and to a Thermal boundary condition given by a wall temperature longitudinally varying with a sinusoidal law. The effect of viscous dissipation in the fluid is taken into account, and a two-temperature model is employed in order to evaluate separately the local fluid and solid matrix temperatures. The asymptotic temperature distributions are determined analytically. The governing equations in the Thermal Entrance Region are solved numerically by a finite element method and by the method of lines.
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forced convection in the Thermal Entrance Region of a circular duct with slug flow and viscous dissipation
International Journal of Heat and Mass Transfer, 1997Co-Authors: A. Barletta, E ZanchiniAbstract:Abstract Slug flow forced convection in a circular duct is studied. The effect of viscous dissipation is analysed in the Thermal Entrance Region. The temperature field and the local Nusselt number are determined analytically for any prescribed axial distribution of wall heat flux. Three examples are considered: a uniform wall heat flux, a linearly varying wall heat flux and an exponentially varying wall heat flux. In the case of a uniform wall heat flux, it is shown that viscous dissipation reduces the value of the local Nusselt number in the whole duct. In the case of a linearly or exponentially increasing wall heat flux, viscous dissipation affects the local Nusselt number only in the Thermal Entrance Region and becomes negligible in the fully developed Region.
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Thermal Entrance Region for laminar forced convection in a circular tube with a power law wall heat flux
International Journal of Heat and Mass Transfer, 1996Co-Authors: A. Barletta, E ZanchiniAbstract:Laminar forced convection in a circular tube is investigated with a boundary condition of prescribed axially varying wall heat flux, under the assumptions of hydrodynamically developed flow and of negligible axial conduction and viscous dissipation in the fluid. A condition on the asymptotic behaviour of the axial distribution of wall heat flux is established which is fulfilled by power-law varying axial distributions and which guarantees the existence of a Thermally developed regime. It is proved that for all the axial distributions which fulfil this condition the asymptotic value reached by the local Nusselt number is 48/11, i.e. the same which holds for a uniform wall heat flux. For some power-law varying axial distributions of wall heat flux, a finite difference determination of the Thermal Entrance Region is performed. In every numerical solution, the local Nusselt number tends asymptotically to 48/11.
Almila G. Yazicioglu - One of the best experts on this subject based on the ideXlab platform.
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A numerical study of single-phase convective heat transfer in microtubes for slip flow
International Journal of Thermal Sciences, 2007Co-Authors: Wei Sun, Sadik Kakac, Almila G. YaziciogluAbstract:The steady-state convective heat transfer for laminar, two-dimensional, incompressible rarefied gas flow in the Thermal Entrance Region of a tube under constant wall temperature, constant wall heat flux, and linear variation of wall temperature boundary conditions are investigated by the finite-volume finite difference scheme with slip flow and temperature jump conditions. Viscous heating is also included, and the solutions are compared with theoretical results where viscous heating has been neglected. For these three boundary conditions for a given Brinkman number, viscous effects are presented in the Thermal Entrance Region along the channel. The effects of Knudsen and Brinkman numbers on Nusselt number are presented in graphical and tabular forms in the Thermal Entrance Region and under fully developed conditions.
F.c. Chou - One of the best experts on this subject based on the ideXlab platform.
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Combined buoyancy effects of Thermal and mass diffusion on laminar forced convection in the Thermal Entrance Region of horizontal square channels
The Canadian Journal of Chemical Engineering, 2009Co-Authors: J. N. Lin, F.c. Chou, Wei-mon Yan, P.y. TzengAbstract:Heat and mass transfer in laminar mixed convection in the Thermal Entrance Region of horizontal square channels is investigated by using the vorticity-velocity formulation of the Naiver-Stokes equations. The numerical results, including the developments of temperature and concentration contours, Nuz and friction coefficient ratios, fRe / (fRe)0, are presented for an air-water system. The effects of bottom wall temperature and the relative humidity on the momentum, heat and mass transfer in the flow are examined in detail. Results show that the influences of the evaporation of the water vapor along the wetted wall on the heat and mass transfer and the ratio fRe / (fRe)0 are rather substantial. On a etudie le transfert de chaleur et de matiere en convection laminaire mixte dans la Region d'entree thermique de canaux horizontaux de section carree au moyen de la formulation vitesse-vorticite des equations de Navier-Stokes. On presente les resultats numeriques, en particulier le developpement des isovaleurs de temperatures et de concentrations, la valeur de Nuz, les rapports des coefficients de friction, fRe / (fRe)0, pour un systeme air-eau. Les effets de la temperature de paroi de fond et de l'humidite relative sur le transfert de quantite de mouvement, de chaleur et de matiere dans l'ecoulement sont examines en detail. Les resultats montrent que les effets de l'evaporation de la vapeur d'eau le long de la paroi humide sur le transfert de chaleur et de matiere et le rapport fRe / (fRe)0 sont assez importants.
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Convective instability of heat and mass transfer for laminar forced convection in the Thermal Entrance Region of horizontal rectangular channels
International Journal of Heat and Fluid Flow, 1992Co-Authors: J.n. Lin, F.c. Chou, P.y. Tzeng, Wei-mon YanAbstract:Abstract A numerical analysis is performed to investigate the onset of convective instability and latent heat transfer, in connection with the vaporization of a liquid-water film, for laminar forced convection in the Thermal Entrance Region of horizontal rectangular ducts. Major dimensionless groups identified are aspect ratio γ, effective Rayleigh number Ra + , Prandtl number Pr, and Schmidt number Sc. The effects of the changes of bottom wall temperature T w , relative humidity of air φ, γ, and Ra + on the local Nusselt number Nu z . Sherwood number Sh z , and the onset point of convective instability are examined in detail. To understand the effects of the selection of different criteria on the onset point, two typical definitions are chosen: a 2 percent departure of Nu z from that of Graetz theory and the local minimum Nu z . Results show that the onset point, under the effects of the combined buoyancy forces of Thermal and mass diffusion, is rather advanced compared with that under the effect of Thermal buoyancy force only. Results also show that the convective instability is affected by changes of φ and T w for fixed γ. Additionally, the influence of water evaporation along the wetted wall on the laminar mixed convection heat transfer in this study is also presented.
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Effect of wall heat conduction on laminar mixed convection in the Thermal Entrance Region of horizontal rectangular channels
Wärme - und Stoffübertragung, 1991Co-Authors: F.c. Chou, W. Y. LienAbstract:This paper presents a numerical study of the effect of peripheral wall heat conduction on laminar mixed convection in the Thermal Entrance Region of horizontal rectangular channels. In addition to the Rayleigh number Ra and the channel aspect ratio (width-to-height) γ, the wall heat conduction parameter K = k _ w t /( k _ f D _ e ) plays an important role in heat transfer. A numerical method of solution utilizing the vorticity-velocity formulation is developed to solve the system of governing partial differential equations coupled with the boundary condition equation considering peripheral wall heat conduction. Local friction factor ratio and Nusselt number variations are shown for Pr =0.7, Ra =10^4, 3×10^4, and 10^5, γ=0.2, 0.5, 1, 2 and 5, K =0.01, 0.1 and 1. The effect of peripheral wall heat conduction on Nusselt number is found to be significant when the value of γ is less than 1. The asymptotic solutions for z →∞ are compared with the existing numerical results and good agreement is indicated. Diese Arbeit zeigt eine numerische Studie über den Einfluß der Wärmeleitung an der Wandoberfläche auf die laminare Mischkonvektion in der thermischen Eintrittszone von horizontalen, rechteckigen Kanälen. Neben der Rayleighzahl Ra und dem Kanalverhältnis γ von Breite zu Höhe, spielt der Wärmeleitungsparameter K = k _ w t /( k _ f D _ e ) eine wichtige Rolle im Wärmetransport. Ein numerisches Verfahren der Lösungsauswertung der Wirbel-Geschwindigkeits-Gleichung ist entwickelt worden, um bestehende Differenzial-Gleichungssysteme zu lösen, die als Randbedingung gekoppelt sind die Wärmeleitung der Wandoberfläche berücksichtigen. Das lokale Reibungsfaktorverhältnis und Nusseltzahlvariationen sind für Pr =0,7, Ra =10^4, 3×10^4 und 10^5 und γ=0,2, 0,5, 1, 2 und 5 und K =0,01, 0,1 und 1 aufgezeigt. Der Einfluß der Wärmeleitung an der Wandoberfläche auf die Nusseltzahl ist als sehr bedeutend angesehen worden, wenn der Wert von γ kleiner als 1 ist. Die asymptotischen Lösungen für z → ∞ sind mit den vorhandenen numerischen Ergebnissen verglichen worden und dabei wurde eine gute Übereinstimmung festgestellt.
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Theoretical prediction of the onset of Thermal instability in the Thermal Entrance Region of horizontal rectangular channels
International Journal of Heat and Fluid Flow, 1991Co-Authors: J.n. Lin, F.c. Chou, P.y. TzengAbstract:Abstract A numerical analysis was performed to study the onset of Thermal instability in the Thermal Entrance Region of horizontal rectangular ducts. Three kinds of surface Thermal boundary conditions are considered. In the analysis, three dimensionless groups, namely, Rayleigh number Ra, aspect ratio γ, and Prandtl number Pr appear. Their corresponding influences on the local Nusselt number distributions and the onset of Thermal instability are investigated. The predicted results, based on the criterion of 2% deviation of the local Nusselt number from that of Graetz theory, are in agreement with the published experimental data. Results show that the Thermal instability is only slightly affected by the change of γ under fixed Pr for the Thermal condition of case 1 (the bottom wall is heated while the top wall is closed and the side walls are adiabatic) and of case 2 (heated from below while the other walls are insulated), while for the isoThermal channels (case 3), the effects of different γ on the instability become significant. Another criterion, based on the location of the minimum local Nusselt number, is also considered in order to investigate the effects of the selection of different criteria on the prediction of the onset of Thermal instability.
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Effect of wall heat conduction on laminar mixed convection in the Thermal Entrance Region of horizontal rectangular channels
Wärme- und Stoffübertragung, 1991Co-Authors: F.c. Chou, W. Y. LienAbstract:This paper presents a numerical study of the effect of peripheral wall heat conduction on laminar mixed convection in the Thermal Entrance Region of horizontal rectangular channels. In addition to the Rayleigh numberRa and the channel aspect ratio (width-to-height) γ, the wall heat conduction parameterK=k w t/(k f D e ) plays an important role in heat transfer. A numerical method of solution utilizing the vorticity-velocity formulation is developed to solve the system of governing partial differential equations coupled with the boundary condition equation considering peripheral wall heat conduction. Local friction factor ratio and Nusselt number variations are shown forPr=0.7,Ra=104, 3×104, and 105, γ=0.2, 0.5, 1, 2 and 5,K=0.01, 0.1 and 1. The effect of peripheral wall heat conduction on Nusselt number is found to be significant when the value of γ is less than 1. The asymptotic solutions forz→∞ are compared with the existing numerical results and good agreement is indicated.
Bernhard Weigand - One of the best experts on this subject based on the ideXlab platform.
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axial heat conduction effects in the Thermal Entrance Region for flows in concentric annular ducts correlations for the local bulk temperature and the nusselt number at the outer wall
International Journal of Heat and Mass Transfer, 2016Co-Authors: M Axtmann, Magnus Heier, Wail El Hilali, Bernhard WeigandAbstract:Abstract Streamwise heat conduction in the flow can affect the heat transfer in ducts. This is mainly relevant for flows with small Prandtl numbers or in micro-channels. In both situations the Peclet number is small, so axial heat conduction in the fluid cannot be neglected. In literature analytical solutions of this so called extended Graetz problem are well documented. In the present paper correlations are developed for the local bulk-temperature and the local Nusselt number at the outer wall in the Thermal Entrance Region of concentric annular ducts. Correlations are given for laminar and turbulent fully-developed flow and different Thermal boundary conditions. The correlations also consider the effect of different ratios of the inner radius to the outer radius of the annular ducts.
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heat transfer in laminar and turbulent flows in the Thermal Entrance Region of concentric annuli axial heat conduction effects in the fluid
Heat and Mass Transfer, 1997Co-Authors: Bernhard Weigand, M. Wolf, H. BeerAbstract:The present analytical study investigates the influence of axial heat conduction within the flow on the heat transfer in the Thermal Entrance Region of a concentric annular duct with laminar and turbulent internal flow. The solution is based on a decomposition of the elliptic energy equation into a pair of first order partial differential equations. By using a new defined vector norm it is possible to obtain a selfadjoint eigenvalue problem for the extended Graetz problem even though the original convective diffusion operator is non-selfadjoint. The obtained exact analytical solutions for the Graetz problem with axial heat conduction are as simple to compute as the related solutions of the parabolic problem.
