![](https://images-na.ssl-images-amazon.com/images/I/51azNBNkBLL._SX328_BO1,204,203,200_.jpg)
By Marcelo J.S. de Lemos
ISBN-10: 3319146653
ISBN-13: 9783319146652
ISBN-10: 3319146661
ISBN-13: 9783319146669
ISBN-10: 3642282768
ISBN-13: 9783642282768
This e-book offers, in a self-contained model, a chain of stories on circulate and warmth move in porous media, during which distinctive strength balances are thought of for the porous matrix and for the permeating fluid. precise mathematical modeling is gifted contemplating either quantity and time averaging operators at the same time utilized to the governing equations. procedure related to combustion within the gaseous part, relocating mattress and double-diffusion mechanism are analyzed. Numerical effects are provided for every case. in spite of everything, this publication comprises the outline of a device that may profit engineers in constructing and designing extra effective thermal equipment.
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Additional info for Thermal Non-Equilibrium in Heterogeneous Media
Sample text
20 2 Modeling of Thermal Non-equilibrium On the symmetry planes: @u @v @k @e ¼ ¼ ¼ ¼ 0; @y @y @y @y ð2:49Þ . where u and v are components of u On the periodic boundaries: ujoutlet ; ujinlet ¼ vjinlet ¼ vjoutlet ; hjinlet ¼ hjoutlet kjinlet ¼ kjoutlet ; ejinlet ¼ ejoutlet ; T À Tw T À Tw , ¼ ; TB ðxÞ À Tw inlet TB ð xÞ À Tw outlet The bulk mean temperature of the fluid is given by: R uTdy TB ð xÞ ¼ R udy ð2:50Þ ð2:51Þ ð2:52Þ Computations are based on the Darcy velocity, the length of structural unit H and the temperature difference ðTB ðxÞ À Tw Þ, as references scales.
16), the momentum equation reads (see [1, 5] for details), q rÁ ! n  Ão D u D u ÀrÁ l þ lt/ r uD Þ T uD þ ðr / : rel j l/ cF /qju urel pffiffiffiffi rel þ ¼ À rð/hpii Þ À u K K ð3:19Þ where lt/ is the macroscopic eddy viscosity given by lt/ ¼ q cl fl hkii 2 heii ; ð3:20Þ cl is dimensionless constant and fl is a damping function, which differs from unit if a Low-Reynolds turbulence model is applied. More on damping functions and model constants will be shown below. Thus, to obtain the eddy viscosity, lt/ , we used here the Low and High Reynolds number k – e models, whose equations for the turbulent kinetic energy and its dissipation rate, incorporating now a relative rel j, are given next [5].
As in the flow case, volume integration is performed over a Representative Elementary Volume (REV), resulting in, 8 0 > > > B i < 6 À Á 6@ /h Tf i B i i Tf ii þ þ r Á / Bh ui hTf ii þ hi u q cp f 6 hu0 ii 0f ii þ > 4 @t @ |fflfflffl{zfflfflffl} |fflfflfflffl{zfflfflfflffl} > > : thermal disperson turbulent heat flux 2 3 Z Z À Á 1 1 6 7 ¼ r Á 4 kf r / hTf ii þ ni kf Tf dA 5 þ ni Á kf rTf dA DV Ai Ai |fflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflffl} |fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl} 2 conduction 1 93 > > >7 C= C 7 i 0 i 0 i h u Tf i C 7 5 A> |fflfflfflffl{zfflfflfflffl} > > ; turbulent thermal dispersion interfacial heat transfer ð2:28Þ where the expansion, hu0 Tf0 ii ¼ hðhu0 ii þ i u0 Þ ðhTf0 ii þ i T 0 Þii ¼ hu0 ii hTf0 ii þ hi u0i Tf0 ii ð2:29Þ has been used in light of the double decomposition concept given by Eqs.
Thermal Non-Equilibrium in Heterogeneous Media by Marcelo J.S. de Lemos
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