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Fully Developed Forced Convection in a Parallel Plate Channel with a Centered Porous Layer

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Abstract

In this study, fully developed heat and fluid flow in a parallel plate channel partially filled with porous layer is analyzed both analytically and numerically. The porous layer is located at the center of the channel and uniform heat flux is applied at the walls. The heat and fluid flow equations for clear fluid and porous regions are separately solved. Continues shear stress and heat flux conditions at the interface are used to determine the interface velocity and temperature. The velocity and temperature profiles in the channel for different values of Darcy number, thermal conductivity ratio, and porous layer thickness are plotted and discussed. The values of Nusselt number and friction factor of a fully clear fluid channel (Nu cl = 4.12 and fRe cl = 24) are used to define heat transfer increment ratio \(({\varepsilon _{\rm th} =Nu_{\rm p}/Nu_{\rm cl})}\) and pressure drop increment ratio \(({\varepsilon_{\rm p} =fRe_{\rm p}/fRe_{\rm cl} )}\) and observe the effects of an inserted porous layer on the increase of heat transfer and pressure drop. The heat transfer and pressure drop increment ratios are used to define an overall performance \(({\varepsilon = \varepsilon_{\rm th}/\varepsilon_{\rm p})}\) to evaluate overall benefits of an inserted porous layer in a parallel plate channel. The obtained results showed that for a partially porous filled channel, the value of \({\varepsilon}\) is highly influenced from Darcy number, but it is not affected from thermal conductivity ratio (k r) when k r > 2. For a fully porous material filled channel, the value of \({\varepsilon}\) is considerably affected from thermal conductivity ratio as the porous medium is in contact with the channel walls.

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Abbreviations

C p :

Specific heat at constant pressure (J/kg K)

Da :

Darcy number

G :

Pressure gradient in x direction

h :

Convective heat transfer coefficient (W/m2 K)

H :

Half height of channel (m)

k :

Thermal conductivity (W/m K)

k f :

Thermal conductivity of fluid (W/m K)

k eff :

Effective thermal conductivity (W/m K)

k r :

Thermal conductivity ratio

K :

Permeability (m2)

M :

Dimensionless viscosity ratio

Nu :

Nusselt number

P :

Pressure (Pa)

q′′:

Constant heat flux subjected to the channel walls (W/m2)

S :

Porous media shape parameter

T :

Temperature (K)

T w :

Wall temperature (K)

u :

Velocity component along the x direction (m/s)

U :

Dimensionless velocity component along dimensionless X direction

u m :

Average velocity (m/s)

U m :

Dimensionless average velocity

\({{\hat{u}}}\) :

Dimensionless normalized velocity

x, y :

Dimensional coordinates (m)

X, Y :

Dimensionless coordinates

\({\varepsilon}\) :

Overall performance

\({\varepsilon_{\rm th}}\) :

Heat transfer increment ratio

\({\varepsilon_{\rm p}}\) :

Pressure drop increment ratio

ξ :

Dimensionless porous medium thickness

λ :

A constant (Eq.17)

μ :

Dynamic viscosity of fluid (kg/m s)

μ eff :

Effective dynamic viscosity (kg/m s)

ρ :

Density (kg/m3)

θ :

Dimensionless temperature

ν :

Kinematic viscosity of fluid (m2/s)

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Authors and Affiliations

  1. Energy Engineering Program, Izmir Institute of Technology, 35430, Izmir, Turkey

    Ozgur Cekmer

  2. Department of Mechanical Engineering, Izmir Institute of Technology, 35430, Izmir, Turkey

    Moghtada Mobedi & Baris Ozerdem

  3. Department of Energy Systems Engineering, Bahcesehir University, 34353, Istanbul, Turkey

    Baris Ozerdem

  4. Faculty of Mathematics, University of Cluj, CP 253, 3400, Cluj, Romania

    Ioan Pop

Authors
  1. Ozgur Cekmer
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  2. Moghtada Mobedi
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  3. Baris Ozerdem
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  4. Ioan Pop
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Correspondence to Ioan Pop.

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Cekmer, O., Mobedi, M., Ozerdem, B. et al. Fully Developed Forced Convection in a Parallel Plate Channel with a Centered Porous Layer. Transp Porous Med 93, 179–201 (2012). https://doi.org/10.1007/s11242-012-9951-x

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  • DOI: https://doi.org/10.1007/s11242-012-9951-x

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