ahmed golam 1e

8/11/2019 Ahmed Golam 1E

1/19

FORCED CONVECTION IN

POROUS MEDIA

Ahmed Salama and Golam Morshed


2/19

oIntroduction

oMathematical Model

oApplications

oResearch

oConclusion


3/19

Convection is the process of heat transferwithin a fluid due to its motion with respectto a heat source

Components Conduction: Heat transfer through Diffusion and

molecular interaction

Advection: Heat transfer due to the bulk flow of the

fluid


4/19

Forced convection is a type ofconvection where an externalsource provides the fluid motion

Forced convection is a much

faster and more efficient processthan natural convection wheredensity changes create the fluidflow

In some cases, natural convection

can occur in conjunction withforced convection. This is knownas mixed convection


5/19

Introduction(Cont.)

Forced Convection in a heat sink


6/19

Darcy flow is used in the modeling of mostforced convection in porous media. Theequations of conservation of mass,momentum and energy have been modeled in

books and various Articles for differentscenarios

Some results obtained for different scenariosof forced convection in porous media will beillustrated


7/19

Governing equations:

Peclet number:

CONSTANT TEMPERATURE:

Local Nusselt number

Overall Nusslet number

CONSTANT HEAT FLUX:

Local Nusselt number

Overall Nusslet number


8/19

Governing equations

Where

where n = 0 for a cylinder and n = 1 for asphere

The local surface heat was given by:

And in non-dimensionless form by:

Where

and


9/19

Jet blast deflectors are usedon aircraft carriers to preventdamage and injury from the

jets of jets taking off

Currently seawater cooled

which creates problem andfailure points

S. Feng [3] modeled analternative by using finheatsinks modeled as porous

media with air forced throughas a cooling mechanism


10/19

Applications(Cont.)Jet Blast Deflectors

Modeled andexperimented withPin-fin and Plate-fin Pin-fin had a higher heat

transfer coefficient dueto vortex flow Plate-fin had a more

uniform thermaldistribution reducingpeak temperatures

Optimized design of

pin-fin heat sinksproved more efficient atreducing the peaktemperature as well asheat dissipation


11/19

Equivalent porous media

Applications(Cont.)Micro Channel Heat Sink

With decreasing electronic equipment sizes, andincreasing capabilities, micro-scale heat transferhas been gaining increasing attention

Heat sinks when coupled with air flow operateunder the principle of forced convection inporous media

C. Chen [4] carried out analysis on micro channel

heat sinks with a porous media approach

The temperature distribution within the solid was insensitive to thechannel aspect ratio and the fluid inertia forces while the oposite wastrue for the temperature distribution within the fluid

The overall Nusselt number increased with increasing aspect ratio andporosity. It decreased with an increasing thermal conductivity ratio


12/19

Governing equation for force convection boundary layerflow:


13/19

Nusselt number associated with respectivetemperature field


14/19

In the limiting range of small Peclet number,Nusselt number shows logarithmic behavior

Fig: Temperature profile plotted as a function of r/ro


15/19

DarcyBrinkmanForchheimer equation used forobtaining the axial velocity (U)

Temperature equation is solved

Volume fraction is obtained and iterated untilcertain range

Fig: Geometry of problem


16/19

Fig: Comparison of Nusselt number and analytical solution


17/19

Result shows decrease in Nusselt number throughporous channel as the Lewis number increases

Increase in Brownian motion parameters also

decreases the Nusselt number The volume fraction does not have a significant

impact over change in Lewis number

As the Schmidt number is increased, the local

Nusselt number decreases


18/19

Darcy flow is mostly used to model forcedconvection in porous media

Models and analysis of forced convection indifferent scenarios demonstrate the relationships

between the Nusselt number and the Pecletnumber to determine heat transfer rates

A logarithmic behaviour is observed for Nusseltnumber in a limiting range of small Pecletnumber

When mass transfer is also involved, the Nusseltnumber has an inverse relationship to the Lewisnumber of the flow


19/19

[ ] D. Nield, A. Bejan; Convection in Porous Media, Third Edition;2006

[2] P. Cheng; Mixed Convection About a Horizontal Cylinder anda Sphere in a Fluid-Saturated Porous Medium; Int.Journal of Heatand Mass Transfer, Vol. 25, No, 8; 1982

[3] S. Feng, T. Kim, T. Lu; Numerical Investigation of ForcedConvection in Pin/Plate-Fin Heat Sinks Heated by Impinging JetUsing Porous Medium; Int. Journal of Numerical Methods for Heat& Fluid Flow, Vol. 23, Iss. 1; 2013

[4] C. Chen; Forced Convection Heat Transfer in MicrochannelHeat Sinks; Int. Journal of Heat and Mass Transfer, Vol. 50; 2006

[5] Eugen Magyari; Forced Convection Heat Transfer from aHeated Cylinder in an Axial Background Flow in a Porous

Medium: Three Exactly Solvable Cases; Transp Porous Media,96:483493; 2013 [6] M. J. Maghrebi , M. Nazari , T. Armaghani; Forced Convection

Heat Transfer of Nanofluids in a Porous Channel; Transp PorousMedia, 93:401413; 2012

ahmed golam 1e

Documents