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Free Convection Heat Transfer over a Vertical Cylinder in a Saturated Porous Medium Using a Local Thermal Non-equilibrium Model

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Abstract

In this article, free convection heat transfer over a vertical cylinder with variable surface temperature distributions in a porous medium is analyzed. It is assumed that the fluid and solid phases are not in local thermal equilibrium and, therefore, a two-temperature model of heat transfer is applied. The coupled momentum and energy equations are presented and then they are transformed into ordinary differential equations. The similarity equations are solved numerically. The resulting velocity, streamlines, temperature distributions for fluid and solid phases are shown for different values of parameters entering into the problem. The calculated values of the local Nusselt numbers for both solid and fluid phases are also shown.

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Abbreviations

A :

Constant (>0)

c p :

Specific heat at constant pressure (J kg−1 k−1)

f :

Dimensionless velocity

g :

Acceleration due to gravity (m s−2)

h :

Volumetric heat transfer coefficient between solid and fluid (W m−2 K−1)

H :

Dimensionless scaled value of h

k :

Thermal conductivity of porous medium

K :

Permeability of the porous medium (m2)

Nu :

Local Nusselt number

r :

Radial coordinate

r 0 :

Radius of the cylinder

Ra x :

Modified local Rayleigh number

T :

Temperature (K)

u :

Velocity component in x direction

v :

Velocity component in r direction

x :

Axial coordinate

α :

Thermal diffusivity (m2 s−1)

β :

Coefficient of thermal expansion (k−1)

\({\varepsilon}\) :

Porosity

θ :

Dimensionless temperature

ν :

Fluid kinematic viscosity (m2 s−1)

ρ :

Density (kg m−3)

Ψ:

Stream function (m2 s−1)

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Authors and Affiliations

  1. Department of Mechanical Engineering, Shahrood University of Technology, P.O. Box 3619995161, Shahrood, Iran

    E. Shakeri, M. Nazari & M. H. Kayhani

Authors
  1. E. Shakeri
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  2. M. Nazari
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  3. M. H. Kayhani
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Correspondence to E. Shakeri.

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Shakeri, E., Nazari, M. & Kayhani, M.H. Free Convection Heat Transfer over a Vertical Cylinder in a Saturated Porous Medium Using a Local Thermal Non-equilibrium Model. Transp Porous Med 93, 453–460 (2012). https://doi.org/10.1007/s11242-012-9962-7

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  • DOI: https://doi.org/10.1007/s11242-012-9962-7

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