caa a22 4500 463163419 CHVBK 20180406164754.0 cr unu---uuuuu 170326e20070401xx s 000 0 eng 10.1007/s11242-006-9036-9 doi (NATIONALLICENCE)springer-10.1007/s11242-006-9036-9 Forced convection of gaseous slip-flow in porous micro-channels under Local Thermal Non-Equilibrium conditions [Elektronische Daten] [O. Haddad, M. Al-Nimr, J. Al-Omary] Steady laminar forced convection gaseous slip-flow through parallel-plates micro-channel filled with porous medium under Local Thermal Non-Equilibrium (LTNE) condition is studied numerically. We consider incompressible Newtonian gas flow, which is hydrodynamically fully developed while thermally is developing. The Darcy-Brinkman-Forchheimer model embedded in the Navier-Stokes equations is used to model the flow within the porous domain. The present study reports the effect of several operating parameters on velocity slip and temperature jump at the wall. Mainly, the current study demonstrates the effects of: Knudsen number (Kn), Darcy number (Da), Forchheimer number (Γ), Peclet number (Pe), Biot number (Bi), and effective thermal conductivity ratio (K R) on velocity slip and temperature jump at the wall. Results are given in terms of skin friction (C f Re *) and Nusselt number (Nu). It is found that the skin friction: (1) increases as Darcy number increases; (2) decreases as Forchheimer number or Knudsen number increases. Heat transfer is found to (1) decreases as the Knudsen number, Forchheimer number, or K R increases; (2) increases as the Peclet number, Darcy number, or Biot number increases. Springer Science+Business Media B.V., 2006 Forced convection nationallicence Slip-flow nationallicence Porous media nationallicence Micro-channel nationallicence Graetz problem nationallicence Local thermal non-equilibrium nationallicence Bi : Biot number $$({h_{\rm sf} L^2}\mathord{\left/ {\vphantom {{h_{\rm sf} L^2} {\varepsilon k_{\rm f}}}} \right. \kern-\nulldelimiterspace} {\varepsilon k_{\rm f}})$$ nationallicence c f : Coefficient in the Forchheimer term nationallicence Cf : Skin friction coefficient nationallicence C p : Constant pressure specific heat nationallicence C v : Constant volume specific heat nationallicence D : Pore diameter nationallicence Da : Darcy number $$(K/\varepsilon L^2)$$ nationallicence h : Local heat transfer coefficient nationallicence h sf : Interstitial heat transfer coefficient nationallicence k : Thermal conductivity nationallicence K : Intrinsic permeability of the porous medium nationallicence Kn : Modified Knudsen number $$\left(\frac{\lambda}{D}\,\frac{D}{L}\right)$$ nationallicence K R : Effective thermal conductivity ratio $$(\varepsilon {k_{\rm f}} \mathord{\left/ {\vphantom {{k_{\rm f}}{(1-\varepsilon)k_{\rm s}}}}\right. \kern-\nulldelimiterspace} {(1-\varepsilon)k_{\rm s}})$$ nationallicence L : Half channel width nationallicence Nu : Nusselt number $$(hL/\varepsilon k_{\rm f})$$ nationallicence p : Pressure nationallicence Pe : Peclet number $$({u_{\rm o} L} \mathord{\left/ {\vphantom {{u_o L} {\varepsilon \alpha}}} \right. \kern-\nulldelimiterspace} {\varepsilon \alpha)}$$ nationallicence Pr : Prandtl number (μ /α ρf) nationallicence q w : Heat transfer rate from the plate wall nationallicence Re * : Modified Reynolds number in porous media $$(\rho_{\rm f} u_o L/\mu \varepsilon)$$ nationallicence t : Time nationallicence t 0 : Reference time(ρ L 2/μ) nationallicence T : Temperature nationallicence u : Axial velocity nationallicence u 0 : Reference axial velocity $$(\varepsilon L^2/\mu (-{\rm d}p/{\rm d}x))$$ nationallicence U : Non-dimensional axial velocity (u/u o) nationallicence x : Axial coordinate nationallicence X : Dimensionless axial coordinate (x/L) nationallicence y : Transverse coordinate nationallicence Y : Dimensionless transverse coordinate (y/L) nationallicence Greek symbols nationallicence α : Thermal diffusivity nationallicence γ : Specific heat ratio (C p /C ν) nationallicence Γ : Dimensionless coefficient of Forchheimer $$(\rho_{\rm f} c_{\rm f} \varepsilon^2(-{\rm d}p/{\rm d}x)L^4/\mu^2\sqrt k)$$ nationallicence λ : Mean free path of the gas molecules nationallicence $$\varepsilon $$ : Porosity of the porous medium nationallicence μ : Dynamic viscosity nationallicence ρf : Fluid density nationallicence σT : Thermal accommodation coefficient nationallicence σv : Tangential momentum accommodation coefficient nationallicence θ : Non-dimensional temperature (T−T ∞ /T w −T ∞) nationallicence τ : Non-dimensional time (t/t o) nationallicence τw : Shear stress at the wall $$(-\mu (\partial u/\partial y)\left.)\right|_{\rm w} $$ nationallicence Subscripts nationallicence f : Fluid nationallicence mf : Mean value for the fluid nationallicence s : Solid nationallicence w : Wall nationallicence Haddad O. Department of Mechanical Engineering, Jordan University of Science and Technology, P.O. Box 3030, 22110, Irbid, Jordan aut Al-Nimr M. Department of Mechanical Engineering, Jordan University of Science and Technology, P.O. Box 3030, 22110, Irbid, Jordan aut Al-Omary J. Department of Mechanical Engineering, Jordan University of Science and Technology, P.O. Box 3030, 22110, Irbid, Jordan aut Transport in Porous Media Kluwer Academic Publishers 67/3(2007-04-01), 453-471 0169-3913 67:3<453 2007 67 11242 https://doi.org/10.1007/s11242-006-9036-9 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s11242-006-9036-9 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Haddad O. Department of Mechanical Engineering, Jordan University of Science and Technology, P.O. Box 3030, 22110, Irbid, Jordan aut NATIONALLICENCE 700 1- Al-Nimr M. Department of Mechanical Engineering, Jordan University of Science and Technology, P.O. Box 3030, 22110, Irbid, Jordan aut NATIONALLICENCE 700 1- Al-Omary J. Department of Mechanical Engineering, Jordan University of Science and Technology, P.O. Box 3030, 22110, Irbid, Jordan aut NATIONALLICENCE 773 0- Transport in Porous Media Kluwer Academic Publishers 67/3(2007-04-01), 453-471 0169-3913 67:3<453 2007 67 11242 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer