caa a22 4500 463162897 CHVBK 20180406164753.0 cr unu---uuuuu 170326e20070901xx s 000 0 eng 10.1007/s11242-006-9074-3 doi (NATIONALLICENCE)springer-10.1007/s11242-006-9074-3 A theoretical analysis of forced convection in a porous-saturated circular tube: Brinkman-Forchheimer model [Elektronische Daten] [K. Hooman, H. Gurgenci] Fully developed forced convection inside a circular tube filled with saturated porous medium and with uniform heat flux at the wall is investigated on the basis of a Brinkman-Forchheimer model. The matched asymptotic expansion method is applied at small Darcy numbers. For large Darcy numbers, the solution for the Brinkman-Forchheimer momentum equation is found in terms of an asymptotic expansion. Once the velocity distribution is determined, the energy equation is solved using the same asymptotic technique. The results for the two limiting cases of clear fluid and Darcy flow conditions show good agreement with those available in the literature. Springer Science+Business Media, Inc., 2006 Forced convection nationallicence Porous media nationallicence Pipe flow nationallicence Brinkman-Forchheimer model nationallicence C : Constant defined in Eq. 25e nationallicence C F : Inertial coefficient nationallicence c P : Specific heat at constant pressure [J/kgK] nationallicence Da : Darcy number, K/R 2 nationallicence F : Forchheimer number nationallicence G : Negative of the applied pressure gradient [Pa/m] nationallicence k : Effective (stagnant) thermal conductivity of the porous medium [W/mK] nationallicence k f : Fluid thermal conductivity [W/mK] nationallicence K : Permeability [m2] nationallicence M : μeff/μ nationallicence Nu : Nusselt number defined by Eq. 11 nationallicence O : Symbol for order of magnitude nationallicence Pe : Péclet number defined by Eq. 3 nationallicence Pr : Prandtl number, $$Pr=\frac{\mu c_p }{k}$$ nationallicence Pr f : Fluid Prandtl number, $$Pr =\frac{\mu c_p}{k_{\rm f}}$$ nationallicence q ′′ : Wall heat flux [W/m2] nationallicence R : Tube radius [m] nationallicence Re : Pore-Reynolds number, $$Re_K =\frac{\rho U\sqrt K }{\mu }$$ nationallicence s : (MDa )−1/2 nationallicence T * : Temperature [K] nationallicence T m : Bulk mean temperature [K] nationallicence T w : Downstream wall temperature [K] nationallicence u : μ u */GR 2 nationallicence u * : Filtration velocity [m/s] nationallicence û : u */U nationallicence U : Mean velocity [m/s] nationallicence x * : Longitudinal coordinate [m] nationallicence x : x */PeR nationallicence r * : Radial coordinate [m] nationallicence r : r */R nationallicence Greek symbols nationallicence η : Stretched variable nationallicence γ : Dimensionless number (γ=0.025) nationallicence θ : (T * − T w ) / (T m − T w ) nationallicence μ : Fluid viscosity [Ns/m2] nationallicence μeff : Effective viscosity in the Brinkman term [Ns/m2] nationallicence ρ : Fluid density [kg/m3] nationallicence Subscripts nationallicence 0, 1 : Term sequence in asymptotic expansion nationallicence Superscripts nationallicence in, out : Inner and outer expansion nationallicence Hooman K. School of Engineering, The University of Queensland, Brisbane, Australia aut Gurgenci H. School of Engineering, The University of Queensland, Brisbane, Australia aut Transport in Porous Media Kluwer Academic Publishers 69/3(2007-09-01), 289-300 0169-3913 69:3<289 2007 69 11242 https://doi.org/10.1007/s11242-006-9074-3 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s11242-006-9074-3 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Hooman K. School of Engineering, The University of Queensland, Brisbane, Australia aut NATIONALLICENCE 700 1- Gurgenci H. School of Engineering, The University of Queensland, Brisbane, Australia aut NATIONALLICENCE 773 0- Transport in Porous Media Kluwer Academic Publishers 69/3(2007-09-01), 289-300 0169-3913 69:3<289 2007 69 11242 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer