On the Generalized Brinkman Number Definition and Its Importance for Bingham Fluids

2011 ◽  
Vol 133 (5) ◽  
Author(s):  
P. M. Coelho ◽  
J. C. Faria
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Viscous Dissipation ◽  
Pipe Flow ◽  
Graphical Representation ◽  
Bingham Fluid ◽  
Technical Note ◽  
Newtonian Fluids ◽  
Brinkman Number ◽  
Laminar Pipe Flow

In this technical note we discuss the importance of using a generalized Brinkman number definition for laminar pipe flow of a Bingham fluid, when viscous dissipation effects are relevant. We show that adapting the Brinkman number definition commonly used for Newtonian fluids directly to the more general class of non-Newtonian fluids does not calculate correctly the ratio between heat generated by viscous dissipation and heat transfer at the wall and leads to a distortion of the graphical representation of the Nusselt number, Nu, rendering difficult, if not impossible, the comparisons of the Nu behavior between different Brinkman numbers. The use of the proposed generalized Brinkman number removes these problems and simultaneously it has the merit of being independent of any reference apparent viscosities.

Thermal Viscous Dissipative Couette Flow in a Porous Medium Filled Microchannel

2016 ◽  
Author(s):  
Farrukh Mirza Baig ◽  
G. M. Chen ◽  
B. K. Lim
Keyword(s):  
Heat Transfer ◽  
Porous Medium ◽  
Nusselt Number ◽  
Couette Flow ◽  
Viscous Dissipation ◽  
Saturated Porous Medium ◽  
Local Thermal Equilibrium ◽  
Uniform Heat Flux ◽  
Brinkman Number ◽  
Essential Information

The increasing demand for high-performance electronic devices and surge in power density accentuates the need for heat transfer enhancement. In this study, a thermal viscous dissipative Coeutte flow in a micochannel filled with fluid saturated porous medium is looked into. The study explores the fluid flow and heat transfer phenomenon for a Coeutte flow in a microchannel as well as to establish the relationship between the heat convection coefficient and viscous dissipation. The moving boundary in this problem is subjected to uniform heat flux while the fixed plate is assumed adiabatic. In order to simplify the problem, we consider a fully developed flow and assume local thermal equilibrium in the analysis. An analytical Nusselt number expression is developed in terms of Brinkman number as a result of this study, thus providing essential information to predict accurately the thermal performance of a microchannel. The results obtained without viscous dissipation are in close agreement with published results whereas viscous dissipation has a more significant effect on Nusselt number for a porous medium with higher porous medium shape factor. The Nusselt number versus Brinkman number plot shows an asymptotic Brinkman number, indicating a change in sign of the temperature difference between the bulk mean temperature and the wall temperature. The effects of Reynolds number on the two dimensional temperature profile for a Couette flow in a microchannel are investigated. The temperature distribution of a microscale duct particularly along the axial direction is a strong function of viscous dissipation. The significance of viscous dissipation to a microscale duct as compared to a conventional scale duct is also discussed and compared in this study.

Semi-Analytical Solution of the Heat Transfer Including Viscous Dissipation in the Steady Flow of a Sisko Fluid in Cylindrical Tubes

2018 ◽  
Vol 140 (7) ◽  
Author(s):  
Sumanta Chaudhuri ◽  
Prasanta Kumar Das
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Fluid Flow ◽  
Analytical Solution ◽  
Viscous Dissipation ◽  
Cylindrical Tube ◽  
Least Square ◽  
Convective Term ◽  
Brinkman Number ◽  
Sisko Fluid

Hydrodynamically and thermally fully developed flow of a Sisko fluid through a cylindrical tube has been investigated considering the effect of viscous dissipation. The effect of the convective term in the energy equation has been taken into account, which was neglected in the earlier studies for Sisko fluid flow. This convective term can significantly affect the temperature distribution if the radius of the tube is relatively large. The equations governing the flow and heat transfer are solved by the least square method (LSM) for both heating and cooling of the fluid. The results of the LSM solution are compared with that of the closed form analytical solution of the Newtonian fluid flow case and are found to match exactly. The results indicate that Nusselt number decreases with the increase in Brinkman number and increases with the increase in the Sisko fluid parameter for the heating of the fluid. In case of cooling, Nusselt number increases with the increase in the Brinkman number asymptotically to a very large value, changes its sign, and then decreases with the increase in Brinkman number. With the increase in the non-Newtonian index, Nusselt number is observed to increase.

scholarly journals CONSTRUCTAL DESIGN OF FINS IN COOLED CAVITIES BY NON-NEWTONIAN FLUIDS

2019 ◽  
Vol 18 (1) ◽  
pp. 85
Author(s):  
J. F. Bueno ◽  
A. R. S. Silva ◽  
T. A. Hirt ◽  
G. F. C. Bogo ◽  
F. S. F. Zinani ◽  
...  
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Aspect Ratio ◽  
Newtonian Fluids ◽  
Rheological Parameters ◽  
Flow Index ◽  
Pseudoplastic Fluid ◽  
High Reynolds ◽  
Energy Equations ◽  
Rayleigh Numbers

The present work investigates the Construtal Design of fins inserted in cavities submitted to mixed convection by non-Newtonian fluids. The objective is to obtain the optimum aspect ratio for the fin considering different flow conditions and variations in the rheological parameters of the fluid. The phenomena of flow and heat transfer are modeled by mass balance, momentum and energy equations, and by the generalized Newtonian liquid constitutive equation. The viscosity is modeled as that of a pseudoplastic fluid, using the Carreau function. The optimization problem consists in maximizing heat transfer from the fin using the average Nusselt number. The investigated project variable is the aspect ratio between the edges of the rectangular plane fin profile. The restrictions are the volume of the cavity and the fin. The results are obtained numerically using a finite volume code and a two-dimensional geometry, through exhaustive searching. The results show that the fin geometry influences the maximum Nusselt number mainly for the cases with high Reynolds and Rayleigh numbers, such as was shown in previous studies. The results show that the fin geometry influences the maximum Nusselt number mainly for the cases with high Reynolds and Rayleigh numbers, as was shown in previous studies. It was also found that the Nusselt number increases as the increase in flow intensity, represented by the parameter p, and that the result of the maximum Nusselt number does not change monotonically with the non-Newtonian dimensionless viscosity and with the flow index, showing that the pseudoplasticity of the fluid implies optimal configurations very different from those predicted for Newtonian fluids.

Simultaneous Wall and Fluid Axial Conduction in Laminar Pipe-Flow Heat Transfer

1980 ◽  
Vol 102 (1) ◽  
pp. 58-63 ◽  
Author(s):  
M. Faghri ◽  
E. M. Sparrow
Keyword(s):  
Heat Transfer ◽  
Pipe Flow ◽  
Numerical Solutions ◽  
Transfer Problem ◽  
Upstream Region ◽  
Heated Region ◽  
Axial Conduction ◽  
Conductance Parameter ◽  
Flow Heat ◽  
Laminar Pipe Flow

Consideration is given to a laminar pipe flow in which the upstream portion of the wall is externally insulated while the downstream portion of the wall is uniformly heated. An analysis of the problem is performed whose special feature is the accounting of axial conduction in both the tube wall and in the fluid. This conjugate heat transfer problem is governed by two dimensionless groups—a wall conductance parameter and the Peclet number, the latter being assigned values from 5 to 50. From numerical solutions, it was found that axial conduction in the wall can carry substantial amounts of heat upstream into the non directly heated portion of the tube. This results in a preheating of both the wall and the fluid in the upstream region, with the zone of preheating extending back as far as twenty radii. The preheating effect is carried downstream with the fluid, raising temperatures all along the tube. The local Nusselt number exhibits fully developed values in the upstream (non directly heated) region as well as in the downstream (directly heated) region. Of the two effects, wall axial conduction can readily overwhelm fluid axial conduction.

Heat Transfer Enhancement in Pipe Flow Problems of a Magnetic Fluid

2007 ◽  
Author(s):  
P. N. Kaloni ◽  
F. Lin ◽  
G. W. Rankin
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Internal Rotation ◽  
Magnetic Fluid ◽  
Pipe Flow ◽  
Magnetic Particles ◽  
Transfer Enhancement ◽  
Cylindrical Pipe ◽  
Flow Problems ◽  
Dissipation Term

Analytical solutions are presented for the temperature distribution and heat transfer coefficient in the forced convection of a magnetic fluid in cylindrical pipe flow. The theory of a ferro-fluid with internal rotation of magnetic particles is employed. Effects of the conventional dissipation term along with the dissipation reflecting the effect of internal rotation are considered and discussed. By computing the Nusselt number in various cases, the influence that different parameters have on the flow are revealed.

scholarly journals Heat transfer of coal water mixture under laminar pipe flow condition.

1987 ◽  
Vol 13 (6) ◽  
pp. 741-748 ◽  
Author(s):  
Yoshihiko Ninomiya ◽  
Toshiyuki Mori ◽  
Mitsuho Hirato
Keyword(s):  
Heat Transfer ◽  
Pipe Flow ◽  
Flow Condition ◽  
Water Mixture ◽  
Laminar Pipe Flow

Thermal Transport Phenomenon in Circular Pipe Flow Using Different Nanofluids

2013 ◽  
Author(s):  
Shuichi Torii
Keyword(s):  
Heat Transfer ◽  
Transport Phenomenon ◽  
Nusselt Number ◽  
Pipe Flow ◽  
Viscosity Ratio ◽  
Volume Fraction ◽  
Circular Tube ◽  
Flow Transport ◽  
Circular Pipe Flow ◽  
Thermal Fluid Flow

The aim of the present study is to investigate the thermal fluid flow transport phenomenon of nanofluids in the heated horizontal circular tube. Consideration is given to the effects of volume fraction of the nanoparticle on the laminar heat transfer and thermal properties. Alumina (Al2O3) and oxide copper (CuO) are employed here as nanoparticles. It is found from the study that (1) the viscosity ratio of nanofluids increases in accordance with an increase of the volume fraction of the nanoparticles, (2) the nanofluids have substantially higher value of Nusselt number than the same liquids without nanoparticles and the Nusselt number of nanofluids increase with an increase of the Reynolds number, and (3) the dispersibility of particle in the nanofluid becomes worse slightly with an increase of the volume fraction of the nanoparticles.

Roughness Effect on the Heat Transfer Coefficient for Gaseous Flow in Microchannels

2010 ◽  
Author(s):  
Metin B. Turgay ◽  
Almila G. Yazicioglu ◽  
Sadik Kakac
Keyword(s):  
Heat Transfer ◽  
Surface Roughness ◽  
Nusselt Number ◽  
Flow Regime ◽  
Viscous Dissipation ◽  
Slip Flow ◽  
Roughness Height ◽  
Working Fluid ◽  
Axial Conduction ◽  
Slip Flow Regime

Effects of surface roughness, axial conduction, viscous dissipation, and rarefaction on heat transfer in a two–dimensional parallel plate microchannel with constant wall temperature are investigated numerically. Roughness is simulated by adding equilateral triangular obstructions with various heights on one of the plates. Air, with constant thermophysical properties, is chosen as the working fluid, and laminar, single-phase, developing flow in the slip flow regime at steady state is analyzed. Governing equations are solved by finite element method with tangential slip velocity and temperature jump boundary conditions to observe the rarefaction effect in the microchannel. Viscous dissipation effect is analyzed by changing the Brinkman number, and the axial conduction effect is analyzed by neglecting and including the corresponding term in the energy equation separately. Then, the effect of surface roughness on the Nusselt number is observed by comparing with the corresponding smooth channel results. It is found that Nusselt number decreases in the continuum case with the presence of surface roughness, while it increases with increasing roughness height in the slip flow regime, which is also more pronounced at low-rarefied flows (i.e., around Kn = 0.02). Moreover, the presence of axial conduction and viscous dissipation has increasing effects on heat transfer with increasing roughness height. Even in low velocity flows, roughness increases Nusselt number up to 33% when viscous dissipation is considered.

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