By Peter Vadasz
The first actual significant reference textual content in this subject, this publication offers a different choice of articles reviewing the state-of-the-art within the box. It provides specific emphasis to rising applied sciences, from bioengineering and bio-tissues to nanotechnology. the mixing of the various issues is gifted through a mixture of theoretical and utilized method to supply a self-contained significant reference that's beautiful to either the scientist and the engineer.
Read Online or Download Emerging Topics in Heat and Mass Transfer in Porous Media: From Bioengineering and Microelectronics to Nanotechnology (Theory and Applications of Transport ... Applications of Transport in Porous Media) PDF
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Additional resources for Emerging Topics in Heat and Mass Transfer in Porous Media: From Bioengineering and Microelectronics to Nanotechnology (Theory and Applications of Transport ... Applications of Transport in Porous Media)
Sample text
Discarding the coupled conductive terms in (144) and (145) assumes k f s =0 so that τT /τq is always larger than 1, and exclude the possibility of thermal oscillation and resonance (Vad´asz 2005a, b, 2006a, b, Vad´asz et al. 2005). The coupled conductive terms in (144) and (145) are thus responsible for the thermal oscillation and resonance in the porous-medium heat conduction subject to lack of local thermal equilibrium. Although each of τT and τq is hav -dependent, their ratio τT /τq is not. This makes its evaluation much simpler as detailed by Vad´asz (2005a).
155) We then obtain a uncoupled form by evaluating the operator determinant such that 34 L. Wang et al. γf Ѩ −kf Ѩt +hav γs Ѩ − ks Ѩt +hav − k f s −hav 2 < Ti >i = 0, (156) where the index i can take f or s. Its explicit form reads, after dividing by hav (γ f + γs ) Ѩ Ti i Ѩ2 Ti +τq Ѩt Ѩt 2 i =α → ѨS( x , t) α → Ti )+ [S( x , t)+τq ], (157) k Ѩt Ѩ Ti +ατT ( Ѩt i i where τq = γ f γs , hav (γ f + γs ) γ f k s + γs k f , hav (k f + ks + 2k f s ) k f + ks + 2k f s k = α= , ρc γ f + γs τT = k = k f + ks + 2k f s , → S( x , t) + τq → k 2f s − k f ks ѨS( x , t) = Ѩt hav 2 Ti i .
21a) for θ f (r, t) has two components, and it takes the following form θ f (r, t) = θ I (r, t) + θ S (r, t) (22) The function θ I (r, t) represents the contribution from the initial condition while θ S (r, t) represents the contribution of the volumetric heat source. 1 Temperature Solutions For constant thermophysical properties, the analytical solution of Eq. (21a) is possible by applying the standard separation of variables technique; in the absence of the volumetric hear source terms. This leads to the following series solution for regular geometries, ∞ θ f (r, t) = n=1 ψn (t)Fn (r)e−γn t (23) Heat Transfer Analysis Under Local Thermal Non-equilibrium Conditions 47 The function Fn (r) is the eigenfunction in the diffusion equation under local thermal equilibrium condition; it satisfies the relation ∇ · [K ∇ Fn (r)] = −γn C Fn (r) (24) Furthermore, in accordance with the Sturm-Liouville problem, the eigenfunctions Fn (r) are orthogonal and the orthogonality condition is Fn (r) Fm (r) d V = 0 when n = m Nn when n = m (25) V for regular geometries.