DOCSLIB.ORG

Effect of Brinkman Number and Magnetic Field on Laminar Convection in a Vertical Plate Channel

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Effect of Brinkman Number and Magnetic Field on Laminar Convection in a Vertical Plate Channel Science World Journal Vol 12(No 4) 2017 www.scienceworldjournal.org ISSN 1597-6343 EFFECT OF BRINKMAN NUMBER AND MAGNETIC FIELD ON LAMINAR CONVECTION IN A VERTICAL PLATE CHANNEL 1* 2 3 Joseph Kpop Moses ; Peter Ayuba and Abubakar S. Magaji Full Length Research Article 1, 2, 3 Department of Mathematical Sciences, Kaduna State University – Nigeria. *Corresponding Author’s e-mail address: [email protected] ABSTRACT Gav et al (1992) showed experimentally for mixed convection that The effect of Brinkman number and magnetic field on laminar the increasing buoyancy parameter will make the reversal flow convection in a vertical plate channel with uniform and wider and deeper taking into consideration the effects of viscous asymmetric temperatures has been studied. The dimensionless dissipation. Barletta (1998) demonstrated that in the case of form of momentum and energy balanced equations has been upward flow reversal decreases with viscous dissipation. solved using one term perturbation series solution. The solution of However, in the case of downward flow, the flow reversal the dimensionless velocity u and temperature θ were obtained. increases with viscous dissipation. He also calculated criteria for The numerical values of the skin friction and the Nusselt number the onset of flow reversal for both directions of flow, but without were obtained and tabulated. It was found that the effect of taking viscous dissipation into account. magnetic parameter enhances the effect of flow velocity by Barletta (1999) investigated the fully developed and laminar suppressing the turbulence while Brinkman number has convection in a parallel – plate channel by taking into account accelerating effect on the temperature profile. both viscous dissipation and buoyancy. Uniform and asymmetric temperatures are prescribed at the channel walls. The velocity Keywords: MHD, Laminar, Convection, vertical channel, field is considered as parallel. A perturbation method is employed Brinkman number to solve the momentum balance equation and energy balance equation. A comparison between the velocity and temperature NOMENCLATURES profiles in the case of laminar forced convection with viscous ν - Kinematic viscosity dissipation is performed in order to point out the effect of 훼 - Thermal conductivity buoyancy. The case of convective boundary conditions is also 휇- Dynamic viscosity discussed. 푇푏 - Bulk temperature Daniel et.al. (2010) investigated the fully developed and laminar 푈푚 − Mean velocity convection in a vertical parallel plate channel by taking into ∆푇 - Temperature difference account both viscous dissipation and buoyancy. Uniform and 푀 표푟 퐻푎 − magnetic parameter asymmetric temperatures are prescribed at the channel walls. 퐺푟 -Grashof number The velocity field is considered as parallel. A perturbation method 푅푒 -Reynolds number is employed to solve the momentum balance equation and the - Acceleration due to gravity, energy balance equation. A comparison with the velocity and 퐵푟 - Brinkman number temperature profiles in the case of laminar forced convection with various dissipation is performed in order to point out the effect the INTRODUCTION effect of buoyancy. The case of convective boundary condition is The study of magnetohydrodynamic (MHD) flows with viscous also discussed. dissipation and buoyancy effects has many importance in Joseph et.al. (2013) studied the MHD forced convection in a industrial, technological and geothermal applications such as horizontal double – passage with uniform wall heat flux by taking temperature plasmas, cooling of nuclear reactors, liquid metals into account the effect of magnetic parameter. They assumed the etc. A comprehensive review of the study of MHD flows in flow of the fluid to be laminar, two – dimensional, steady and fully relations to the applications to the above areas has been made by developed. The fluid is incompressible and the physical properties several authors. are constants. Dileep and Rashin (2012) investigated the fully Mixed convection in a vertical parallel – plate channel with developed magntohydrodynamic mixed convection in a vertical uniform wall temperatures has been studied by Tao (1960). channel, partially filled with clear fluid and partially, filled with a Javerci (1975) dealt with the effects of viscous dissipation and fluid – saturated porous medium is by taking into account viscous Joule heating on the fully developed MHD flow with heat transfer and ohmic dissipations. Alim, et al (2007) investigated the in a channel. The exact solution of the energy equation was pressure work and viscous dissipation effects on MHD natural derived for constant heat flux with small magnetic Reynolds convection along a sphere. The laminar natural convection flow number. Sparrow et al (1984) observed experimentally flow from a sphere immersed in a viscous incompressible fluid in the reversal in pure convection in a one – sided heated vertical presence of magnetic field has been considered in this channel. The mixed convection in a vertical parallel – plate investigation. channel with asymmetric heating, where one plate is heated and Barik (2013) analyzed the free convection heat and mass transfer the other is adiabatic has been studied by Habchi and Acharya MHD flow in a vertical channel in the presence of chemical (1986). reaction. Ranuka et al (2009) studied the MHD effects of unsteady heat convective mass transfer flow past an infinite vertical porous plate with variable suction, where the plate’s Effect of Brinkman Number and Magnetic Field an Laminar Convection in a 58 Vertical Plate Channel Science World Journal Vol 12(No 4) 2017 www.scienceworldjournal.org ISSN 1597-6343 2 2 2 2 temperature oscillates with the same frequency as that of variable 푑 푇 ν 푑푈 푒퐵0 푈 훼 2 + ( ) + = 0 (2) suction velocity with soret effects. The governing equations are 푑푌 푐푝 푑푌 0푐푝 solved numerically by using implicit finite difference method. Where the acceleration due to gravity is g, ν is the kinematic 휇 Saleh and Hashim (2009) analysed flow reversal phenomena of viscosity which is defined by ν= , 푃 = 푝 + 휌푏푋 is the the fully – developed laminar combined free and forced MHD 푏 difference between the pressure p and the hydrostatic convection in a vertical plate – channel. The effect of viscous pressure P. 훼 is thermal conductivity and 휇 = 휌 휈 is the dissipation is taken into account. Tamia and Samad (2010) 푏 dynamic viscosity studied and analyzed the radiation and viscous dissipation effects Equations (2) and the boundary condition on푇, shows that 푃 on a steady two – dimensional magneto hydrodynamics free 휕푃 depends on 푋; 푇 depends only on 푌; 푇 is a constant; is convection flow along a stretching sheet with heat generation. 푏 휕푋 The non – linear partial differential equations governing the flow a constant. field under consideration have been transformed by a similarity The bulk temperature 푇푏 and the mean velocity 푈푚 (Barletta, transformation into a system of non – linear ordinary differential 1999) are given by. equations and then solved numerically by applying Nachtsheim – 1 퐿 1 퐿 Swigert shooting iteration technique together with sixth order and (3) 푇푏 = ∫0 푈푇푑푌 푈푚 = ∫0 푈푑푌 Runge – Kutta integration scheme. Resulting in non – 퐿푈푚 퐿 dimensional velocity, temperature and concentration profiles are The boundary conditions are: then presented graphically for different values of the parameters 푈(0) = 0 , 푇(0) = 푇0, of physical engineering interest. 푈(퐿) = 0 , 푇(퐿) = 푇0 (4) Idowu et.al (2013) investigated viscous dissipation and buoyancy Due to the symmetry of the problem, 푈 푎푛푑 푇 are symmetric effects on laminar convection with transpiration. Uniform and functions of 푌, so that they must fulfill the condition asymmetric temperatures are prescribed at the channel walls. 푈′(0) = 0, 푇′(0) = 0 (5) The velocity field is considered as parallel. A perturbation method Introducing the dimensionless quantities below 푈 푇−푇 푌 −퐿2 푑푃 is employed to solve the momentum balance equation and the 푢 = , 휃 = 푏 , 푦 = , 휆 = , 퐺푟 = energy balance equation. A comparison with the velocity and 푈푚 ∆푇 퐿 휇푈푚 푑푋 64퐿3훽∆푇 , temperature profiles in the case of laminar forced convection with 휈2 various dissipation is performed in order to point out the effect of 4퐿푈 퐺푟 휇푈2 푅푒 = 푚 , 퐸 = , 퐵푟 = 푚 buoyancy. The case of convective boundary condition is also 휈 푅푒 훼∆푇 discussed. Where the temperature difference ∆푇 is given by 2 Das et.al. (2015) studied the fully developed mixed convection 휇푈푚 ∆푇 = flow in a vertical channel filled with nanofluid in the presences of 푘 uniform transverse magnetic field. Anjali Devi and Ganga (2010) While the Grashof number 퐺푟 is always positive, the Reynolds studied the Viscous and Joule dissipation effects on MHD non – number 푅푒 and the parameter 퐸 can be either positive or linear flow and heat transfer past a stretching porous surface negative. In particular, in the case of upward flow (푈푚 > embedded in a porous medium under a transverse magnetic field. 0), both 푅푒 and 퐸 are positive, while, for downward flow(푈푚 < Patrulescu, et al (2010) investigated the steady mixed convection 0), these dimensionless parameters are negative. flow in a vertical channel for laminar and fully developed flow regime. In the modeling of heat transfer the viscous dissipation Therefore, as a consequence of the dimensional quantities term was also considered. Temperature on the right wall is together with the momentum balance equation (1), the energy assumed constant while a mixed boundary condition (Robin balance equation (2) and equations (3) – (5) yields; boundary condition) is considered on the left wall. 푑2푢 퐸휃 The mixed convection of Newtonian fluid between vertical parallel − 푀푢 = − + 휆 plates channel with MHD effect and variation in Brinkman number 푑푦2 16 2 2 has been studied by Alizadeh Rasul et.al. (2014). The effect of 푑 휃 2 푑푢 2 + 퐵푟푀푢 = −퐵푟 ( ) (6) MHD and Brinkman number on laminar mixed convection of 푑푦 푑푦 훽2퐿2 Newtonian fluid between vertical parallel plates channel was Where 푀 = 0 0 which is the magnetic parameter and 0휈 investigated by Salehi et.al (2013).
Load more

Recommended publications
  • Heating and Flow Computations of an Amorphous Polymer in the Liquefier of a Material Extrusion 3D Printer Franck Pigeonneau, D
    Heating and flow computations of an amorphous polymer in the liquefier of a material extrusion 3D printer Franck Pigeonneau, D. Xu, M. Vincent, J.-F. Agassant To cite this version: Franck Pigeonneau, D. Xu, M. Vincent, J.-F. Agassant. Heating and flow computations of an amor- phous polymer in the liquefier of a material extrusion 3D printer. Additive Manufacturing, Elsevier, 2019, pp.101001. 10.1016/j.addma.2019.101001. hal-02425219 HAL Id: hal-02425219 https://hal-mines-paristech.archives-ouvertes.fr/hal-02425219 Submitted on 30 Dec 2019 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. Heating and flow computations of an amorphous polymer in the liquefier of a material extrusion 3D printer F. Pigeonneau∗, D. Xu, M. Vincent, J.-F. Agassant MINES ParisTech, PSL Research University, CEMEF - Centre for material forming, CNRS UMR 7635, CS 10207, rue Claude Daunesse 06904 Sophia Antipolis Cedex, France Abstract The heating of a polymer in a liquefier of a material extrusion 3D printer is numeri- cally studied. The problem is investigated by solving the mass, momentum, and energy conservation equations. The polymer is taken as a generalized Newtonian fluid with a dynamical viscosity function of shear rate and temperature.
    [Show full text]
  • Constant-Wall-Temperature Nusselt Number in Micro and Nano-Channels1
    Constant-Wall-Temperature Nusselt Number in Micro and Nano-Channels1 We investigate the constant-wall-temperature convective heat-transfer characteristics of a model gaseous flow in two-dimensional micro and nano-channels under hydrodynamically Nicolas G. and thermally fully developed conditions. Our investigation covers both the slip-flow Hadjiconstantinou regime 0рKnр0.1, and most of the transition regime 0.1ϽKnр10, where Kn, the Knud- sen number, is defined as the ratio between the molecular mean free path and the channel Olga Simek height. We use slip-flow theory in the presence of axial heat conduction to calculate the Nusselt number in the range 0рKnр0.2, and a stochastic molecular simulation technique Mechanical Engineering Department, known as the direct simulation Monte Carlo (DSMC) to calculate the Nusselt number in Massachusetts Institute of Technology, the range 0.02ϽKnϽ2. Inclusion of the effects of axial heat conduction in the continuum Cambridge, MA 02139 model is necessary since small-scale internal flows are typically characterized by finite Peclet numbers. Our results show that the slip-flow prediction is in good agreement with the DSMC results for Knр0.1, but also remains a good approximation beyond its ex- pected range of applicability. We also show that the Nusselt number decreases monotoni- cally with increasing Knudsen number in the fully accommodating case, both in the slip-flow and transition regimes. In the slip-flow regime, axial heat conduction is found to increase the Nusselt number; this effect is largest at Knϭ0 and is of the order of 10 percent. Qualitatively similar results are obtained for slip-flow heat transfer in circular tubes.
    [Show full text]
  • Heat Transfer and Entropy in a Vertical Porous Plate Subjected to Suction Velocity and MHD
    entropy Article Heat Transfer and Entropy in a Vertical Porous Plate Subjected to Suction Velocity and MHD N. Ameer Ahammad 1 , Irfan Anjum Badruddin 2,* , Sarfaraz Kamangar 2, H.M.T. Khaleed 3, C. Ahamed Saleel 2 and Teuku Meurah Indra Mahlia 4,* 1 Department of Mathematics, Faculty of Science, University of Tabuk, Tabuk 71491, Saudi Arabia; [email protected] 2 Mechanical Engineering Department, College of Engineering, King Khalid University, Abha 61421, Saudi Arabia; [email protected] (S.K.); [email protected] (C.A.S.) 3 Department of Mechanical Engineering, Faculty of Engineering, Islamic University of Madinah, Madinah Munawwarra 42351, Saudi Arabia; [email protected] 4 Centre of Green Technology, Faculty of Engineering and Information Technology, University of Technology, Sydney, NSW 2007, Australia * Correspondence: [email protected] (I.A.B.); [email protected] (T.M.I.M.) Abstract: This article presents an investigation of heat transfer in a porous medium adjacent to a vertical plate. The porous medium is subjected to a magnetohydrodynamic effect and suction velocity. The governing equations are nondepersonalized and converted into ordinary differential equations. The resulting equations are solved with the help of the finite difference method. The impact of various parameters, such as the Prandtl number, Grashof number, permeability parameter, radiation parameter, Eckert number, viscous dissipation parameter, and magnetic parameter, on fluid flow characteristics inside the porous medium is discussed. Entropy generation in the medium is Citation: Ahammad, N.A.; analyzed with respect to various parameters, including the Brinkman number and Reynolds number. Badruddin, I.A.; Kamangar, S.; It is noted that the velocity profile decreases in magnitude with respect to the Prandtl number, but Khaleed, H.M.T.; Saleel, C.A.; Mahlia, increases with the radiation parameter.
    [Show full text]
  • 2D Temperature Analysis of Energy and Exergy Characteristics of Laminar Steady Flow Across a Square Cylinder Under Strong Blockage
    Entropy 2015, 17, 3124-3151; doi:10.3390/e17053124 OPEN ACCESS entropy ISSN 1099-4300 www.mdpi.com/journal/entropy Article 2D Temperature Analysis of Energy and Exergy Characteristics of Laminar Steady Flow across a Square Cylinder under Strong Blockage M. Ozgun Korukcu Department of Mechanical Engineering, University of Uludag, Gorukle, 16059 Bursa, Turkey; E-Mail: [email protected]; Tel.: +90-224-2941927; Fax: +90-224-2941903 Academic Editor: Marc A. Rosen Received: 10 March 2015 / Accepted: 7 May 2015 / Published: 12 May 2015 Abstract: Energy and exergy characteristics of a square cylinder (SC) in confined flow are investigated computationally by numerically handling the steady-state continuity, Navier-Stokes and energy equations in the Reynolds number range of Re = 10–50, where the blockage ratio (β = B/H) is kept constant at the high level of β = 0.8. Computations indicated for the upstream region that, the mean non-dimensional streamwise (u/Uo) and spanwise (v/Uo) velocities attain the values of u/Uo = 0.840→0.879 and v/Uo = 0.236→0.386 (Re = 10→50) on the front-surface of the SC, implying that Reynolds number and blockage have stronger impact on the spanwise momentum activity. It is determined that flows with high Reynolds number interact with the front-surface of the SC developing thinner thermal boundary layers and greater temperature gradients, which promotes the thermal entropy generation values as well. The strict guidance of the throat, not only resulted in the fully developed flow character, but also imposed additional cooling; such that the analysis pointed out the drop of duct wall (y = 0.025 m) non-dimensional temperature values (ζ) from ζ = 0.387→0.926 (Re = 10→50) at xth = 0 mm to ζ = 0.002→0.266 at xth = 40 mm.
    [Show full text]
  • Effects of Brinkman Number on Thermal-Driven Convective Spherical Dynamos
    March 2013 JASEM ISSN 1119-8362 Full-text Available Online at J. Appl. Sci. Environ. Manage. All rights reserved www.ajol.info and Vol. 17 (1) 139-151 www.bioline.org.br/ja Effects of Brinkman number on thermal-driven convective spherical Dynamos . *1M. I. NGWUEKE; T. M. ABBEY Theoretical Physics Group; Department of Physics, University of Port Harcourt, Port Harcourt, Nigeria. *Corresponding author (e-mail: [email protected]; Phone: 234-703-5891392, 234-803-3409479 ) KEYWORDS: Magnetic field generation, Thermal-driven convection, Brinkman number, Dynamo action, Fluid outer core ABSTRACT: Brinkman number effects on the thermal-driven convective spherical dynamos are studied analytically. The high temperature of the Earth’s inner core boundary is usually conducted by the viscous, electrically conducting fluid of the outer core to the core mantle boundary as the Earth cools. The problem considers conducting fluid motion in a rapidly rotating spherical shell. The consequence of this exponential dependence of viscosity on temperature is considered to be a thermal- driven convective phenomenon. A set of constitutive non-linear equations were then formulated in which the solutions for the flow variables were obtained by perturbation technique. The results illustrate enhancement of dynamo actions, demonstrating that magnetic field generation with time is possible. Moreover, the increased magnetic Prandtl number Pm with high Brinkman number shows dynamo actions for fixed Rayleigh and Taylor number values. The overall analyses succour our
    [Show full text]
  • Use of Dimensionless Numbers in Analyzing Melt Flow and Melt Cooling Processes
    USE OF DIMENSIONLESS NUMBERS IN ANALYZING MELT FLOW AND MELT COOLING PROCESSES NATTI S. RAO RANGANATH SHASTRI Plastics Solutions International CIATEO Ghent, NY 12075, USA San Luis Potosi, Mexiko Email: [email protected] Email:[email protected] ABSTRACT Dimensionless analysis is a powerful tool in analyzing the transient heat transfer and flow processes accompanying melt flow in an injection mold or cooling in blown film,to quote a couple of examples. However, because of the nature of non-Newtonian polymer melt flow the dimensionless numbers used to describe flow and heat transfer processes of Newtonian fluids have to be modified for polymer melts. This paper describes how an easily applicable equation for the cooling of melt in a spiral flow in injection molds has been derived on the basis of modified dimensionless numbers and verified by experiments. Analyzing the air gap dynamics in extrusion coating is another application of dimensional analysis. PREDICTING FLOW LENGTH IN INJECTION MOLDS Injection molding is widely used to make articles out of plastics for various applications. One of the criteria for the selection of the resin to make a given part is whether the melt is an easy flowing type or whether it exhibits a significantly viscous behavior. To determine the flowability of the polymer melt the spiral test, which consists of injecting the melt into a spiral shaped mold shown in Figure 1, is used. The length of the spiral serves as a measure of the ease of flow of the melt in the mold, and enables mold and part design suited to material flow.
    [Show full text]
  • Entropy 2006, 8, 188-199 Entropy ISSN 1099-4300 Full Paper
    Entropy 2006, 8, 188-199 entropy ISSN 1099-4300 www.mdpi.org/entropy/ Full Paper Thermodynamic Analysis of Gravity-driven Liquid Film along an Inclined Heated Plate with Hydromagnetic and Viscous Dissipation Effects Soraya Aïboud-Saouli 1, Salah Saouli 2,*, Noureddine Settou 2 and Nouredine Meza 2 1 Professional Training Institute, Saïd Otba, 30 000 Ouargla-Algeria, Tel: +21390891191, Fax: +21329716175, e-mail: [email protected] 2 Faculty of Sciences and Engineering Sciences, University of Ouargla, 30 000 Ouargla- Algeria, Tel: +21372842401, Fax: +21329711975, e-mail: [email protected] (S. Saouli) Received: 21 December 2005 / Accepted: 13 September 2006 / Published: 23 October 2006 Abstract: The purpose of this work is to investigate the entropy generation in a laminar, gravity-driven conducting liquid film with fully developed velocity flowing along an incline heated plate in the presence of a transverse magnetic field. The upper surface of the liquid film is considered free and adiabatic. The effect of heat generation by viscous dissipation is included in the analysis. The influence of the applied magnetic field and the viscous dissipation on velocity, temperature and entropy generation is examined. Keywords: Hydromagnetic effect, Inclined plate, liquid film, Thermodynamic analysis, Viscous dissipation Nomenclature A area, (m2) B magnetic induction, (Wb.m-2) 2 2 Br Brinkman number, µumCP λ∆T -1 -1 CP specific heat, (J.kg .K ) Ha Hartman number, Bδ σ µ NB entropy generation number, magnetic induction NC entropy generation, axial conduction
    [Show full text]
  • The Effect of MHD and Brinkman Number on Laminar Mixed Convection of Newtonian Fluid Between Vertical Parallel Plates Channel
    INTERNATIONAL JOURNAL OF GEOLOGY DOI: 10.46300/9105.2020.14.2 Volume 14, 2020 The effect of MHD and Brinkman number on laminar mixed convection of newtonian fluid between vertical parallel plates Channel Ebrahim Salehi Rasul alizadeh,Alireza darvish Department of Mechanical Engineering Department of Mechanical Engineering Iranian Construction Engineering Organization Quchan Branch Islamic Azad University Mashhad, Iran Quchan, Iran [email protected] [email protected] Abstract—This study investigates MHD and Brinkman equal wall temperatures. Barletta [7] have presented an number on mixed convection flow in a two parallel-plates vertical analytica analysis of fully developed mixed convection in channel with reference to laminar, thermal and hydrodynamical vertical channel include power-law fluid reference to unequal developing flow of Newtonian fluid. The boundaries are and uniform wall temperature boundary condition. Shohel considered to be isothermal with equal temperatures. The Mahmud et al [8] focused on analyze the first and second law governing equations are solved numerically. Also, their of thermodynamics characteristics of fully developed mixed dependence upon certain material parameters have been studied. convection flow in a channel in the presence of heat Velocity, temperature, pressure gradient and Nusselt number generation/absorption and transverse hydromagnetic effect profiles have also been presented. with isothermal boundary condition. Krishnan et al [9] experimentally and numerically studied the problem of steady
    [Show full text]
  • Journal of Non-Newtonian Fluid Mechanics a Generalized Brinkman
    J. Non-Newtonian Fluid Mech. 156 (2009) 202–206 Contents lists available at ScienceDirect Journal of Non-Newtonian Fluid Mechanics journal homepage: www.elsevier.com/locate/jnnfm Short communication A generalized Brinkman number for non-Newtonian duct flows P.M. Coelho a,∗, F.T. Pinho a,b a Centro de Estudos de Fenómenos de Transporte, DEMEGI, Faculdade de Engenharia da Universidade do Porto, Rua Dr. Roberto Frias, s/n, 4200-465 Porto, Portugal b Universidade do Minho, Largo do Pac¸ o, 4704-553 Braga, Portugal article info abstract Article history: When viscous dissipation effects are important in duct flows the Brinkman number is widely used to Received 23 April 2008 quantify the relationship between the heat generated by dissipation and the heat exchanged at the wall. Received in revised form 23 June 2008 For Newtonian laminar fully developed pipe flow the use of the classical expression for this dimensionless Accepted 3 July 2008 group is appropriate, but under different conditions it can lead to misleading conclusions, such as when comparing flows through different cross-section ducts, flow regimes and mainly non-Newtonian flows. Keywords: In this work a generalized Brinkman number is proposed, based on an energy balance for the power Viscous dissipation dissipated by friction, that allows proper quantification of viscous heating effects and reduces to the Convective heat transfer Generalized Brinkman number classical definition in laminar Newtonian pipe flow. The advantages of the new definition are shown and Duct flows expressions are given for generalized Brinkman numbers in the most common cases. © 2008 Elsevier B.V. All rights reserved.
    [Show full text]
  • Investigation of Heat Transfer in a Microchannel with Same Heat Capacity Rate
    Investigation of Heat Transfer in a Microchannel with Same Heat Capacity Rate Author Xu, Bin, Wong, Teck Neng, Nam-Trung, Nguyen Published 2019 Journal Title Heat and Mass Transfer Version Accepted Manuscript (AM) DOI https://doi.org/10.1007/s00231-018-2477-1 Copyright Statement © 2018 Springer-Verlag. This is an electronic version of an article published in Heat and Mass Transfer, Volume 55, Issue 3, pp 899–909. Heat and Mass Transfer is available online at: http:// link.springer.com/ with the open URL of your article. Downloaded from http://hdl.handle.net/10072/384874 Griffith Research Online https://research-repository.griffith.edu.au Investigation of Heat Transfer in a Microchannel with Same Heat Capacity Rate Bin Xu1,*, Teck Neng Wong2, Nam-Trung Nguyen3 1Research Center of Fluid Machinery Engineering and Technology, Jiangsu University, 301 Xuefu Road, Zhenjiang 212013 2School of Mechanical and Aerospace Engineering, Nanyang Technological University, 50 Nanyang Avenue, Singapore 639798 3Queensland Micro- and Nanotechnology Centre, Griffith University, 170 Kessels Road, Brisbane 4111, Australia Abstract In this paper, a new experimental setup was proposed to realize the constant-heat-flux boundary condition based on a counter flow microchannel heat exchanger with the same heat capacity rate of the hot and cold streams. This approach provides a constant fluid temperature gradient along the surfaces. An analytical two-dimensional model was developed to describe the heat transfer processes in the hot stream and the cold stream, respectively. In the experiments, DI-water was employed as the working fluid. Laser induced fluorescence (LIF) method was used to measure the fluid temperature field within the microchannel.
    [Show full text]
  • Effect of High-Prandtl Number on Microscale Flow and Heat Transfer
    Proceedings of the World Congress on Mechanical, Chemical, and Material Engineering (MCM 2015) Barcelona, Spain – July 20 - 21, 2015 Paper No. 319 Effect of High-Prandtl Number on Microscale Flow and Heat Transfer Ubade Kemerli, Damla Özgür, Ayşegül Öztürk, Kamil Kahveci Trakya University Mechanical Engineering Department, Trakya University, 22180, Edirne, TURKEY [email protected]; [email protected], [email protected]; [email protected] Abstract -The effect of high-Prandtl number on steady fully developed microscale flow and heat transfer between two parallel plates exposed to a constant heat flux is investigated analytically in this study. The Prandtl number over several orders of magnitude (5 < Pr <103) as well as different Knudsen number (0 < Kn <0.1) and different modified Brinkman number (-0.1 < Br <0.1) are considered. The momentum and energy equations are solved for first order boundaries of slip velocity and temperature jump. The influences of the Prandtl number, Knudsen number and Brinkman number on the temperature distribution and heat transfer characteristics are discussed. Keywords: Slip flow, parallel plate, microchannel, viscous dissipation 1. Introduction Fluid flow and heat transfer characteristics of microchannels have become the subject of intense research in recent years with the rapid developments in electronic industry. Many research has been conducted to understand the differences between micro and macro scale flows since microchannels are employed in many industrial applications such as micro-electric chip cooling, biochemical application, biomedical application, and microelectromechanical systems. Fluid flow and heat transfer characteristics in microchannels depend on the mean free path of the fluid and the characteristic length of the flow field.
    [Show full text]
  • Second Law Analysis of Viscoelastic Fluid Over a Stretching Sheet Subject to a Transverse Magnetic Field with Heat and Mass Transfer
    Entropy 2010, 12, 1867-1884; doi:10.3390/e12081867 OPEN ACCESS entropy ISSN 1099-4300 www.mdpi.com/journal/entropy Article Second Law Analysis of Viscoelastic Fluid over a Stretching Sheet Subject to a Transverse Magnetic Field with Heat and Mass Transfer Soraya Aïboud 1 and Salah Saouli 2,* 1 Department of Mechanical Engineering, Faculty of Sciences and Technology and Matter’s Sciences, University Kasdi Merbah, P.O. 511, Ouargla, 30 000, Algeria; E-Mail: aï[email protected] 2 Department of Process Engineering, Faculty of Sciences and Technology and Matter’s Sciences, University Kasdi Merbah, P.O. 511, Ouargla, 30 000, Algeria * Author to whom correspondence should be addressed; Tel.: +21329711714; Fax: +21329711714; E-Mail: [email protected]. Received: 26 June 2010 / Accepted: 25 July 2010 / Published: 28 July 2010 Abstract: This paper concerns the second law analysis of a viscoelastic fluid over a stretching sheet subject to a transverse magnetic field with heat and mass transfer. The velocity, temperature and concentration profiles are obtained analytically using Kummer’s functions. The effects of the magnetic and viscoelastic parameters on both the longitudianl and the transverse velocities are investigated. The influence of Prandt number, the magnetic parameter and the heat source/sink parameter on the temperature is analysed. The concentration and its variations with the Schmidt number and the magnetic parameter is presented as well. The velocity, the temperature and the concentration profiles are used to compute the entropy generation number. This number is graphed and studied as function of the magnetic parameter, the Prandtl number, The Schmidt number, the Reynolds number, the dimensionless group, the Hartmann number, the ratio of the dimensionless concentration difference to the dimensionless temperature difference and the constant parameter.
    [Show full text]