Modified Hazen-Dupuit-Darcy Model for Forced Convection of a Fluid With Temperature-Dependent Viscosity

2000 ◽  
Vol 123 (1) ◽  
pp. 31-38 ◽  
Author(s):  
Arunn Narasimhan ◽  
Jose´ L. Lage
Keyword(s):  
Heat Flux ◽  
Pressure Drop ◽  
Surface Heat Flux ◽  
Surface Heat ◽  
Bulk Temperature ◽  
Fluid Viscosity ◽  
Temperature Dependent ◽  
Temperature Dependent Viscosity ◽  
New Model ◽  
Dependent Viscosity

We investigate numerically the global pressure-drop of fluids with temperature dependent viscosity, flowing through a porous medium channel bounded by two parallel isoflux surfaces. By reviewing the development of the Hazen-Dupuit-Darcy (HDD) equation we bring to light the inappropriateness of the model in estimating the global pressure-drop of fluids with temperature dependent viscosity. Albeit this observation, we tested the accuracy of the HDD model in comparison with numerical results by using three alternatives, namely (1) fluid viscosity determined at the average bulk temperature, (2) fluid viscosity determined at the log-mean bulk temperature and (3) fluid viscosity replaced by a channel-length averaged fluid viscosity. The HDD model is inadequate because the temperature dependent fluid viscosity surprisingly affects both, viscous and form, global drag terms. We propose and validate a new global model, which accounts for the effects of temperature dependent viscosity in both drag terms of the original HDD model. Based on our new model, two regimes are discovered as the surface heat flux increases. In the first regime both drag terms are affected, while in the second regime only the form drag term is affected, prior to the model reaching an inviscid limit. Predictive empirical relations correcting the viscous and form drag terms, complementing the new model, are obtained as functions of the surface heat flux.

Heat Transfer in Turbulent Pipe Flow for Liquids Having a Temperature-Dependent Viscosity

1978 ◽  
Vol 100 (2) ◽  
pp. 224-229 ◽  
Author(s):  
O. T. Hanna ◽  
O. C. Sandall
Keyword(s):  
Heat Transfer ◽  
Friction Factor ◽  
Pipe Flow ◽  
Turbulent Pipe Flow ◽  
Fluid Viscosity ◽  
Temperature Dependent ◽  
Temperature Dependent Viscosity ◽  
Analytical Approximations ◽  
Constant Viscosity ◽  
Dependent Viscosity

Analytical approximations are developed to predict the effect of a temperature-dependent viscosity on convective heat transfer through liquids in fully developed turbulent pipe flow. The analysis expresses the heat transfer coefficient ratio for variable to constant viscosity in terms of the friction factor ratio for variable to constant viscosity, Tw, Tb, and a fluid viscosity-temperature parameter β. The results are independent of any particular eddy diffusivity distribution. The formulas developed here represent an analytical approximation to the model developed by Goldmann. These approximations are in good agreement with numerical solutions of the model nonlinear differential equation. To compare the results of these calculations with experimental data, a knowledge of the effect of variable viscosity on the friction factor is required. When available correlations for the friction factor are used, the results given here are seen to agree well with experimental heat transfer coefficients over a considerable range of μw/μb.

Predicting Inlet Temperature Effects on the Pressure-Drop of Heated Porous Medium Channel Flows Using the M-HDD Model

2004 ◽  
Vol 126 (2) ◽  
pp. 301-303 ◽  
Author(s):  
Arunn Narasimhan ◽  
Jose´ L. Lage
Keyword(s):  
Porous Medium ◽  
Pressure Drop ◽  
Inlet Temperature ◽  
Temperature Dependent ◽  
Temperature Dependent Viscosity ◽  
Viscosity Effects ◽  
Nonisothermal Flows ◽  
Nonlinear Temperature ◽  
Global Pressure ◽  
Dependent Viscosity

A Modified Hazen-Dupuit-Darcy (M-HDD) model, incorporating nonlinear temperature-dependent viscosity effects, has been proposed recently for predicting the global pressure-drop of nonisothermal flows across a heated (or cooled) porous medium channel. Numerical simulations, mimicking the flow of a liquid with nonlinear temperature-dependent viscosity, are presented now for establishing the influence of inlet temperature on the pressure-drop and on the predictive capabilities of the M-HDD model. As a result, new generalized correlations for predicting the coefficients of the M-HDD model are derived. The results not only demonstrate the importance of fluid inlet temperature on predicting the global pressure-drop but they also extend the applicability of the M-HDD model.

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.

Entrance, Viscous Dissipation and Temperature Dependent Viscosity Effects on the Laminar Forced Convection in Straight Microchannels With Uniform Wall Heat Flux

2008 ◽  
Author(s):  
C. Nonino ◽  
S. Savino ◽  
S. Del Giudice
Keyword(s):  
Heat Flux ◽  
Forced Convection ◽  
Viscous Dissipation ◽  
Laminar Flows ◽  
Uniform Heat Flux ◽  
Temperature Dependent ◽  
Temperature Dependent Viscosity ◽  
Wide Range ◽  
Dependent Viscosity ◽  
Laminar Forced Convection

A parametric investigation is carried out on the effects of viscous dissipation and temperature dependent viscosity in simultaneously developing laminar flows of liquids in straight microchannels of constant cross-sections. Reference is made to fluid heating conditions with a uniform heat flux imposed on the walls of the microchannels. Three different cross-sectional geometries are considered, chosen among those usually adopted for microchannels (rectangular, trapezoidal and hexagonal). 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. Due to the high value of the ratio between the total length and the hydraulic diameter in microchannels, such an approach is very advantageous with respect to the one based on the steady-state solution of the elliptic form of the governing equations in a three-dimensional domain corresponding to the whole duct. Computed axial distributions of the local Nusselt number and of the apparent Fanning friction factor are presented. Numerical results confirm that, in the laminar forced convection in the entrance region of straight microchannels, the effects of viscous dissipation and temperature dependent viscosity cannot be neglected in a wide range of operative conditions.

Thermal radiation and buoyancy effects on MHD free convective heat generating flow over an accelerating permeable surface with temperature-dependent viscosity

2001 ◽  
Vol 79 (4) ◽  
pp. 725-732 ◽  
Author(s):  
M A Seddeek
Keyword(s):  
Thermal Radiation ◽  
Shooting Method ◽  
Skin Friction Coefficient ◽  
Permeable Surface ◽  
Fluid Viscosity ◽  
Governing Equations ◽  
Temperature Dependent ◽  
Temperature Dependent Viscosity ◽  
Thermal Buoyancy ◽  
Dependent Viscosity

The paper presents a study of the flow of a viscous incompressible fluid over an accelerating permeable surface with temperature-dependent viscosity, taking into account the effect of thermal radiation and thermal buoyancy in the presence of a magnetic field. The fluid viscosity is assumed to vary as an inverse linear function of temperature. The governing equations for laminar free convection of fluid are changed to dimensionless ordinary differential equations by similarity transformation. They are solved by a shooting method. The effects of various parameters on the velocity and temperature profiles as well as the skin friction coefficient and wall heat transfer are presented graphically and in tabulated form. PACS Nos.: 47.65ta, 52.30–q

Sign in / Sign up

Export Citation Format

Share Document