Analysis of the Forced Convection in a Porous Channel Saturated by a Nanofluid: Effects of Brownian Diffusion and Thermophoresis

2014 ◽  
Author(s):  
Eugenia Rossi di Schio
Keyword(s):  
Saturated Porous Medium ◽  
Homogeneous Model ◽  
Concentration Field ◽  
Entrance Region ◽  
Brownian Diffusion ◽  
Galerkin Finite Element ◽  
Coupled Equations ◽  
Thermal Entrance Region ◽  
Longitudinal Coordinate ◽  
Thermal Entrance

The Darcy-Graetz problem for a channel filled by a nanofluid saturated porous medium is studied. The flow is assumed to be fully developed, and a boundary temperature linearly varying with the longitudinal coordinate in the thermal entrance region is prescribed. A study of the thermal behaviour of the nanofluid is performed by solving numerically the fully–elliptic coupled equations. For the model of the nanofluid, both thermophoresis and Brownian diffusion are taken into account. The governing equations have been solved separately for the fully developed region and for the thermal entrance region. With reference to the fully developed region the solution has been obtained analytically, while for the thermal entrance region it has been obtained numerically, by a Galerkin finite element method implemented through the software package Comsol Multiphysics (© Comsol, Inc.). The analysis shows that for physically interesting values of the Péclet number the concentration field depends very weakly on the temperature distribution. Indeed, the homogeneous model could be employed effectively, since the effects of thermophoresis and Brownian diffusion are negligible.

Effects of Brownian Diffusion and Thermophoresis on the Laminar Forced Convection of a Nanofluid in a Channel

2013 ◽  
Vol 136 (2) ◽  
Author(s):  
Eugenia Rossi di Schio ◽  
Michele Celli ◽  
Antonio Barletta
Keyword(s):  
Forced Convection ◽  
Wall Temperature ◽  
Homogeneous Model ◽  
Entrance Region ◽  
Brownian Diffusion ◽  
Boundary Temperature ◽  
Coupled Equations ◽  
Thermal Entrance Region ◽  
Laminar Forced Convection ◽  
Thermal Entrance

A steady laminar forced convection in a parallel–plane channel using nanofluids is studied. The flow is assumed to be fully developed, and described through the Hagen–Poiseuille profile. A boundary temperature varying with the longitudinal coordinate in the thermal entrance region is prescribed. Two sample cases are investigated in detail: a linearly changing wall temperature, and a sinusoidally changing wall temperature. A study of the thermal behavior of the nanofluid is performed by solving numerically the fully–elliptic coupled equations. The numerical solution is obtained by a Galerkin finite element method implemented through the software package Comsol Multiphysics (© Comsol, Inc.). With reference to both the wall temperature distributions prescribed along the thermal entrance region, the governing equations have been solved separately both for the fully developed region and for the thermal entrance region. The analysis shows that if a linearly varying boundary temperature is assumed, for physically interesting values of the Péclet number the concentration field depends very weakly on the temperature distribution. On the other hand, in case of a longitudinally periodic boundary temperature, nonhomogeneities in the nanoparticle concentration distribution arise, which are wrongly neglected whenever the homogeneous model is employed.

Thermal Nonequilibrium and Viscous Dissipation in the Thermal Entrance Region of a Darcy Flow With Streamwise Periodic Boundary Conditions

2011 ◽  
Vol 133 (7) ◽  
Author(s):  
A. Barletta ◽  
E. Rossi di Schio ◽  
L. Selmi
Keyword(s):  
Viscous Dissipation ◽  
Saturated Porous Medium ◽  
Method Of Lines ◽  
Entrance Region ◽  
Solid Matrix ◽  
The Method Of Lines ◽  
Thermal Entrance Region ◽  
Fluid Saturated Porous Medium ◽  
Thermal Entrance ◽  
Two Temperature

The thermal entrance region in a plane-parallel channel filled by a fluid saturated porous medium is investigated with reference to steady forced convection and to a thermal boundary condition given by a wall temperature longitudinally varying with a sinusoidal law. The effect of viscous dissipation in the fluid is taken into account, and a two-temperature model is employed in order to evaluate separately the local fluid and solid matrix temperatures. The asymptotic temperature distributions are determined analytically. The governing equations in the thermal entrance region are solved numerically by a finite element method and by the method of lines.

Periodic Forced Convection in a Darcy Metallic Foam: The LTNE Model

2012 ◽  
Author(s):  
Eugenia Rossi di Schio ◽  
Antonio Barletta
Keyword(s):  
Forced Convection ◽  
Outer Boundary ◽  
Method Of Lines ◽  
Mean Value ◽  
Entrance Region ◽  
Solid Matrix ◽  
Metallic Foam ◽  
The Method Of Lines ◽  
Thermal Entrance Region ◽  
Thermal Entrance

The present paper studies the thermal entrance region in a concentric annular duct filled by a fluid saturated porous metallic foam, with reference to steady forced convection and to a thermal boundary condition given by a wall temperature longitudinally varying with a sinusoidal law. The effect of viscous dissipation in the fluid is taken into account, and a two-temperature model is employed in order to evaluate separately the local fluid and solid matrix temperatures. The governing equations in the thermal entrance region are solved numerically by the method of lines. The Nusselt numer and its mean value in an axial period is evaluated, with reference both to the inner and the outer boundary.

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