caa a22 4500 463162889 CHVBK 20180406164753.0 cr unu---uuuuu 170326e20070901xx s 000 0 eng 10.1007/s11242-006-9076-1 doi (NATIONALLICENCE)springer-10.1007/s11242-006-9076-1 Onset of convection in a horizontal porous channel with uniform heat generation using a thermal nonequilibrium model [Elektronische Daten] [Ali Nouri-Borujerdi, Amin Noghrehabadi, D. Rees] This paper considers the onset of free convection in a horizontal fluid-saturated porous layer with uniform heat generation. Attention is focused on cases where the fluid and solid phases are not in local thermal equilibrium, and where two energy equations describe the evolution of the temperature of each phase. Standard linearized stability theory is used to determine how the criterion for the onset of convection varies with the inter-phase heat transfer coefficient, H, and the porosity-modified thermal conductivity ratio, γ. We also present asymptotic solutions for small values of H. Excellent agreement is obtained between the asymptotic and the numerical results. Springer Science+Business Media, Inc., 2006 Local thermal non-equilibrium nationallicence Instability nationallicence Natural convection nationallicence Porous media nationallicence Internal heat generation nationallicence C : Specific heat nationallicence Da : Darcy number nationallicence h : Inter-phase heat transfer coefficient nationallicence H : Nondimensional inter-phase heat transfer coefficient nationallicence g : Gravity nationallicence k : Wavenumber of the disturbance nationallicence K : Permeability nationallicence L : Depth of the convection layer nationallicence LTE : Local thermal equilibrium nationallicence LTNE : Local thermal nonequilibrium nationallicence P : Pressure nationallicence q ′′′ : Rate of heat generation nationallicence Q : Overall rate of heat generation nationallicence Ra : Darcy-Rayleigh number (Eq. 6) nationallicence t : Time nationallicence T : Temperature nationallicence u , v : Horizontal and vertical velocities nationallicence x , y : Horizontal and vertical Cartesian coordinates nationallicence Greek symbols nationallicence α : Diffusivity ratio nationallicence γ : Porosity-scaled conductivity ratio nationallicence β : Coefficient of cubical expansion nationallicence ρ : Density nationallicence σ : Heat capacity ratio nationallicence μ : Dynamic viscosity nationallicence λ : Constant nationallicence ν : Kinematic viscosity nationallicence $$\varepsilon$$ : Porosity nationallicence $$\varsigma$$ : Constant denoting internal heating contribution nationallicence $$\psi$$ : Streamfunction nationallicence $$\psi$$ : Streamfunction disturbance nationallicence $$\theta,\phi$$ : Scaled fluid and solid temperatures nationallicence $$\theta,\phi$$ : Fluid and solid temperature disturbances nationallicence ω : Amplification rate of disturbances nationallicence Superscripts and subscripts nationallicence ∧ : Dimensional nationallicence basic : Basic state nationallicence PM : Porous media nationallicence f : Fluid nationallicence s : Solid nationallicence 0 : Wall temperature nationallicence • : k-derivative nationallicence ′ : y-derivative nationallicence Nouri-Borujerdi Ali School of Mechanical Engineering, Sharif University of Technology, Tehran, Iran aut Noghrehabadi Amin School of Mechanical Engineering, Sharif University of Technology, Tehran, Iran aut Rees D. Department of Mechanical Engineering, University of Bath, BA2 7AY, Bath, UK aut Transport in Porous Media Kluwer Academic Publishers 69/3(2007-09-01), 343-357 0169-3913 69:3<343 2007 69 11242 https://doi.org/10.1007/s11242-006-9076-1 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s11242-006-9076-1 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Nouri-Borujerdi Ali School of Mechanical Engineering, Sharif University of Technology, Tehran, Iran aut NATIONALLICENCE 700 1- Noghrehabadi Amin School of Mechanical Engineering, Sharif University of Technology, Tehran, Iran aut NATIONALLICENCE 700 1- Rees D. Department of Mechanical Engineering, University of Bath, BA2 7AY, Bath, UK aut NATIONALLICENCE 773 0- Transport in Porous Media Kluwer Academic Publishers 69/3(2007-09-01), 343-357 0169-3913 69:3<343 2007 69 11242 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer