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.

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.

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 Viscosity Effects on Laminar Forced Convection in Straight Ducts With Uniform Wall Heat Flux

2011 ◽  
Vol 133 (10) ◽  
Author(s):  
Stefano Del Giudice ◽  
Stefano Savino ◽  
Carlo Nonino
Keyword(s):  
Heat Flux ◽  
Nusselt Number ◽  
Cross Sections ◽  
Local Nusselt Number ◽  
Temperature Dependent ◽  
Temperature Dependent Viscosity ◽  
Effects Of Temperature ◽  
Dependent Viscosity ◽  
Fanning Friction Factor ◽  
Laminar Forced Convection

Abstract In this paper a parametric investigation is carried out on the effects of temperature dependent viscosity in simultaneously, i.e., hydro-dynamically and thermally, developing laminar flows of liquids in straight ducts of constant cross sections. Uniform heat flux boundary conditions are imposed on the heated walls of the ducts. Different cross-sectional geometries are considered, corresponding to both axisymmetric (circular and concentric annular) and three-dimensional (rectangular and trapezoidal) ducts. Viscosity is assumed to vary with temperature according to an exponential relation, while the other fluid properties are held constant. 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 Pearson and Prandtl numbers. Numerical results confirm that, in the laminar forced convection in the entrance region of straight ducts, the effects of temperature dependent viscosity cannot be neglected in a wide range of operative conditions. Correlations are also provided for the local Nusselt number and the apparent Fanning friction factor in simultaneously developing flows in ducts of different cross sections.

Turbulence and internal waves in stably-stratified channel flow with temperature-dependent fluid properties

2012 ◽  
Vol 697 ◽  
pp. 175-203 ◽  
Author(s):  
Francesco Zonta ◽  
Miguel Onorato ◽  
Alfredo Soldati
Keyword(s):  
Reynolds Number ◽  
Thermal Expansion ◽  
Thermal Expansion Coefficient ◽  
Channel Flow ◽  
Expansion Coefficient ◽  
Temperature Dependent ◽  
Temperature Dependent Viscosity ◽  
Fluid Properties ◽  
Effects Of Temperature ◽  
Dependent Viscosity

AbstractDirect numerical simulation (DNS) is used to study the behaviour of stably-stratified turbulent channel flow with temperature-dependent fluid properties: specifically, viscosity ($\ensuremath{\mu} $) and thermal expansion coefficient ($\ensuremath{\beta} $). The governing equations are solved using a pseudo-spectral method for the case of turbulent water flow in a channel. A systematic campaign of simulations is performed in the shear Richardson number parameter space (${\mathit{Ri}}_{\tau } = \mathit{Gr}/ {\mathit{Re}}_{\tau } $, where $\mathit{Gr}$ is the Grashof number and ${\mathit{Re}}_{\tau } $ the shear Reynolds number), imposing constant-temperature boundary conditions. Variations of ${\mathit{Ri}}_{\tau } $ are obtained by changing ${\mathit{Re}}_{\tau } $ and keeping $\mathit{Gr}$ constant. Independently of the value of ${\mathit{Ri}}_{\tau } $, all cases exhibit an initial transition from turbulent to laminar flow. A return transition to turbulence is observed only if ${\mathit{Ri}}_{\tau } $ is below a threshold value (which depends also on the flow Reynolds number). After the transient evolution of the flow, a statistically-stationary condition occurs, in which active turbulence and internal gravity waves (IGW) coexist. In this condition, the transport efficiency of momentum and heat is reduced considerably compared to the condition of non-stratified turbulence. The crucial role of temperature-dependent viscosity and thermal expansion coefficient is directly demonstrated. The most striking feature produced by the temperature dependence of viscosity is flow relaminarization in the cold side of the channel (where viscosity is higher). The opposite behaviour, with flow relaminarization occurring in the hot side of the channel, is observed when a temperature-dependent thermal expansion coefficient is considered. We observe qualitative and quantitative modifications of structure and wall-normal position of internal waves compared to previous results obtained for uniform or quasi-uniform fluid properties. From the trend we observe in the investigated low-Reynolds-number range, we can hypothesize that, whereas the effects of temperature-dependent viscosity may be masked at higher Reynolds number, the effects of temperature-dependent thermal expansion coefficient will persist.

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.

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