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Thermal Analysis of Flow in a Porous Medium Over a Permeable Stretching Wall

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Abstract

This work presents a similarity solution for boundary layer flow through a porous medium over a stretching porous wall. Two considered wall boundary conditions are power-law distribution of either wall temperature or heat flux which are general enough to cover the isothermal and isoflux cases. In addition to momentum, both first and second laws of thermodynamics analyses of the problem are investigated. Independent numerical simulations are also performed for verification of the proposed analytical solution. The results, from the two independent approaches, are found to be in complete agreement. A comprehensive parametric study is presented and it is shown that heat transfer and entropy generation rates increase with Reynolds number, Prandtl number, and suction to the surface.

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Abbreviations

Be :

Bejan number, Eq. 24

f :

Similarity function for velocity

f w :

Injection parameter, \({f_{\rm w} = - v_{\rm w} L/u_0 \sqrt{K}}\)

K :

Permeability, m2

L :

Stretching surface length, m

n :

Power of temperature/heat flux distribution

Nu :

Local Nusselt number

Nu L :

Averaged Nusselt number

Pr :

Prandtl number, Pr = ν/α eff

q 0 :

Wall heat flux coefficient, W/m2

Re :

Reynolds number, Re =  ρ u 0 K/L

S gen :

Entropy generation rate, N/K m2 s

T :

Temperature, K

T 0 :

Wall temperature coefficient, K

u :

Velocity in x-direction, m/s

u 0 :

Wall velocity coefficient, m/s

v :

Velocity in y-direction, m/s

v w :

Injection velocity, m/s

x :

Coordinate system, m

y :

Coordinate system, m

α eff :

Effective thermal diffusivity, m2/s

η :

Similarity parameter, \({\eta =y/\sqrt{K}}\)

θ :

Similarity function for temperature

κ :

Thermal conductivity, W/mK

μ :

Viscosity, N s/m2

μ eff :

Effective viscosity, N s/m2

ν :

Kinematic viscosity, m2/s

τ w :

Wall shear stress, N/m2

τ L :

Averaged wall shear stress, N/m2

ψ :

Stream function, m2/s

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Authors and Affiliations

  1. Mechatronic Systems Engineering, School of Engineering Science, Simon Fraser University, Surrey, BC, V3T 0A3, Canada

    A. Tamayol & M. Bahrami

  2. School of Mechanical and Mining Engineering, The University of Queensland, Brisbane, QLD, 4072, Australia

    K. Hooman

Authors
  1. A. Tamayol
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  2. K. Hooman
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  3. M. Bahrami
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Correspondence to A. Tamayol.

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Tamayol, A., Hooman, K. & Bahrami, M. Thermal Analysis of Flow in a Porous Medium Over a Permeable Stretching Wall. Transp Porous Med 85, 661–676 (2010). https://doi.org/10.1007/s11242-010-9584-x

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