Temperature Dependent Viscosity and Thermal Conductivity Effects on the Laminar Forced Convection in Straight Microchannels

2012 ◽  
Author(s):  
Stefano Del Giudice ◽  
Stefano Savino ◽  
Carlo Nonino
Keyword(s):  
Thermal Conductivity ◽  
Nusselt Number ◽  
Viscous Dissipation ◽  
The Other ◽  
Superposition Method ◽  
Brinkman Number ◽  
Temperature Dependent ◽  
Temperature Dependent Viscosity ◽  
Fluid Properties ◽  
Dependent Viscosity

A parametric investigation is carried out on the effects of viscous dissipation and temperature dependent viscosity and thermal conductivity in simultaneously developing laminar flows of liquids in straight microchannels of constant cross-sections. Uniform heat flux boundary conditions are specified at the heated walls. Viscosity is assumed to vary with temperature according to an exponential relation, while a linear dependence of thermal conductivity on temperature is assumed. The other fluid properties are held constant. Two different cross-sectional geometries are considered, corresponding to both axisymmetric (circular) and three-dimensional (square) microchannel geometries. A finite element procedure is employed for the solution of the parabolized momentum and energy equations. Computed axial distributions of the local Nusselt number and of the apparent Fanning friction factor are presented for different values of the Brinkman number and of the viscosity and thermal conductivity Pearson numbers. Moreover, a superposition method is proved to be applicable in order to obtain the correct value of the Nusselt number by considering separately the effects of temperature dependent viscosity and viscous dissipation and those of temperature dependent thermal conductivity. In fact, it is found that the influence of the temperature dependence of thermal conductivity on the value of the Nusselt number is independent of the value of the Brinkman number, i.e., it is the same no matter whether viscous dissipation is negligible or not. Finally, it is demonstrated that, in liquid flows, the main effects on pressure drop of temperature dependent fluid properties can be retained even if only viscosity is allowed to vary with temperature, the other properties being assumed constant.

Temperature Dependent Viscosity and Thermal Conductivity Effects on the Laminar Forced Convection in Straight Microchannels

2013 ◽  
Vol 135 (10) ◽  
Author(s):  
Stefano Del Giudice ◽  
Stefano Savino ◽  
Carlo Nonino
Keyword(s):  
Thermal Conductivity ◽  
Nusselt Number ◽  
Viscous Dissipation ◽  
The Other ◽  
Brinkman Number ◽  
Temperature Dependent ◽  
Temperature Dependent Viscosity ◽  
Fluid Properties ◽  
Effects Of Temperature ◽  
Dependent Viscosity

A parametric investigation is carried out on the effects of temperature dependent viscosity and thermal conductivity and of viscous dissipation in simultaneously developing laminar flows of liquids in straight microchannels of constant cross sections. Uniform heat flux boundary conditions are specified at the heated walls. A superposition method is proved to be applicable in order to predict the value of the Nusselt number by considering separately the effects of temperature dependent viscosity and those of temperature dependent thermal conductivity. In addition, it is found that the influence of the temperature dependence of thermal conductivity on the value of the Nusselt number is independent of the value of the Brinkman number, i.e., it is the same no matter whether viscous dissipation is negligible or not. Finally, it is demonstrated that, in liquid flows, the main effects on pressure drop of temperature dependent fluid properties can be retained even if only viscosity is allowed to vary with temperature, the other properties being assumed constant. Viscosity is assumed to vary with temperature according to an exponential relation, while a linear dependence of thermal conductivity on temperature is assumed. The other fluid properties are held constant. Two different cross-sectional geometries are considered, corresponding to both axisymmetric (circular) and three-dimensional (square) microchannel geometries. A finite element procedure is employed for the solution of the parabolized momentum and energy equations. Computed axial distributions of the local Nusselt number and of the apparent Fanning friction factor are presented for different values of the viscosity and thermal conductivity Pearson numbers and of the Brinkman number.

Effects of Temperature Dependent Properties on the Laminar Forced Convection in Straight Microchannels With Uniform Wall Temperature

2013 ◽  
Author(s):  
Stefano Del Giudice ◽  
Stefano Savino ◽  
Carlo Nonino
Keyword(s):  
Thermal Conductivity ◽  
Nusselt Number ◽  
Forced Convection ◽  
Superposition Method ◽  
Brinkman Number ◽  
Temperature Dependent ◽  
Temperature Dependent Viscosity ◽  
Effects Of Temperature ◽  
Dependent Viscosity ◽  
Energy Equations

The paper reports the results of a parametric investigation on the effects of temperature dependent viscosity and thermal conductivity on forced convection in simultaneously developing laminar flows of liquids in straight microchannels of constant cross-sections. Uniform temperature boundary conditions are specified at the microchannel walls. Viscosity is assumed to vary with temperature according to an exponential relation, while a linear dependence of thermal conductivity on temperature is assumed. The other fluid properties are held constant. Two different cross-sectional geometries, namely circular and flat microchannels, are considered. A finite element procedure is employed for the solution of the parabolized momentum and energy equations. The parabolic approximation of the Navier-Stokes and energy equations can be considered adequate for values of the Reynolds and Péclet numbers larger than 50. Computed axial distributions of the local Nusselt number are presented for different values of the Brinkman number and of the viscosity and thermal conductivity Pearson numbers. Moreover, a superposition method is proved to be applicable in order to obtain an approximate value of the Nusselt number by separately considering the effects of temperature dependent viscosity and those of temperature dependent thermal conductivity. Finally, it is found that the influence of the temperature dependence of thermal conductivity on the value of the Nusselt number is almost independent of the value of the Brinkman number, i.e., it is approximately the same no matter whether viscous dissipation is negligible or not.

Entrance and Temperature-Dependent Property Effects on Laminar Duct Flows of Liquids

2016 ◽  
Vol 139 (3) ◽  
Author(s):  
Stefano Del Giudice ◽  
Stefano Savino ◽  
Carlo Nonino
Keyword(s):  
Thermal Conductivity ◽  
Nusselt Number ◽  
Local Nusselt Number ◽  
Three Dimensional ◽  
Laminar Flows ◽  
Uniform Heat Flux ◽  
Superposition Method ◽  
Temperature Dependent ◽  
Temperature Dependent Viscosity ◽  
Cross Sectional

The results of a numerical investigation on the effects of the temperature dependence of viscosity and thermal conductivity in simultaneously developing laminar flows of liquids in straight ducts of constant cross sections are used to obtain new correlations for the axial distributions of the peripherally averaged local Nusselt number. Three different cross-sectional geometries are considered, corresponding to both axisymmetric (circular and concentric annular) and three-dimensional (square) ducts. Uniform heat flux boundary conditions are specified at the heated walls. Viscosity is assumed to vary with temperature according to an exponential relation, while a linear dependence of thermal conductivity on temperature is assumed. The other fluid properties are held constant. A superposition method is applied to obtain the values of the peripherally averaged local Nusselt number by separately considering the effects of temperature-dependent viscosity and those of temperature-dependent thermal conductivity.

Extensional flows with viscous heating

2007 ◽  
Vol 571 ◽  
pp. 359-370 ◽  
Author(s):  
JONATHAN J. WYLIE ◽  
HUAXIONG HUANG
Keyword(s):  
Critical Value ◽  
The Other ◽  
Viscous Heating ◽  
Constant Force ◽  
Temperature Dependent ◽  
Downstream Location ◽  
Temperature Dependent Viscosity ◽  
Pulling Forces ◽  
Extensional Flows ◽  
Dependent Viscosity

In this paper we investigate the role played by viscous heating in extensional flows of viscous threads with temperature-dependent viscosity. We show that there exists an interesting interplay between the effects of viscous heating, which accelerates thinning, and inertia, which prevents pinch-off. We first consider steady drawing of a thread that is fed through a fixed aperture at given speed and pulled with a constant force at a fixed downstream location. For pulling forces above a critical value, we show that inertialess solutions cannot exist and inertia is crucial in controlling the dynamics. We also consider the unsteady stretching of a thread that is fixed at one end and pulled with a constant force at the other end. In contrast to the case in which inertia is neglected, the thread will always pinch at the end where the force is applied. Our results show that viscous heating can have a profound effect on the final shape and total extension at pinching.

Analysis of the Effects of Joule Heating and Viscous Dissipation on Combined Pressure-Driven and Electrokinetic Flows in a Two-Parallel Plate Channel with Unequal Constant Temperatures

2018 ◽  
Vol 233 (4) ◽  
pp. 871-879 ◽  
Author(s):  
Harshad Sanjay Gaikwad ◽  
Pranab Kumar Mondal ◽  
Dipankar Narayan Basu ◽  
Nares Chimres ◽  
Somchai Wongwises
Keyword(s):  
Viscous Dissipation ◽  
Entropy Generation ◽  
Joule Heating ◽  
Generation Rate ◽  
Entropy Generation Rate ◽  
Local Entropy ◽  
Temperature Dependent ◽  
Temperature Dependent Viscosity ◽  
Dependent Viscosity ◽  
Local Entropy Generation

In this article, we perform an entropy generation analysis for the micro channel heat sink applications where the flow of fluid is actuated by combined influences of applied pressure gradient and electric field under electrical double layer phenomenon. The upper and lower walls of the channels are kept at different constant temperatures. The temperature-dependent viscosity of the fluid is considered and hence the momentum equation and energy equations are coupled in this study. Also, a hydrodynamic slip condition is employed on the viscous dissipation. For complete analysis of the entropy generation, we use a perturbation approach with lubrication approximation. In this study, we discuss the results depicting variations in the velocity and temperature distributions and their effect on local entropy generation rate and Bejan number in the system. It can be summarized from this analysis that the enhanced velocity gradients in the flow field due to combined effect of temperature-dependent viscosity and Joule heating and viscous dissipative effects, leads to an enhancement in the local entropy generation rate in the system.

Entrance, Viscous Dissipation and Temperature Dependent Viscosity Effects in Microchannel Flows With Convective Boundary Conditions

2006 ◽  
Author(s):  
C. Nonino ◽  
S. Del Giudice ◽  
S. Savino
Keyword(s):  
Boundary Conditions ◽  
Viscous Dissipation ◽  
Circular Cross Section ◽  
Laminar Flows ◽  
Projection Algorithm ◽  
Convective Boundary Conditions ◽  
Temperature Dependent ◽  
Temperature Dependent Viscosity ◽  
Convective Boundary ◽  
Dependent Viscosity

The effects of viscous dissipation and temperature dependent viscosity in simultaneously developing laminar flows of liquids in straight microchannels of circular cross-section are studied with reference to convective boundary conditions. Viscosity is assumed to vary linearly with temperature, in order to allow a parametric investigation, while the other fluid properties are held constant. A finite element procedure, based on a projection algorithm, is employed for the step-by-step solution of the parabolized momentum and energy equations. Axial distributions of the local overall Nusselt number and of the apparent Fanning friction factor are presented with reference to both heating and cooling conditions for three different values of the Biot number. Examples of temperature profiles at different axial locations are also shown.

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