Effects of temperature-dependent viscosity variation on entropy generation, heat and fluid flow through a porous-saturated duct of rectangular cross-section

Abstract

Effect of temperature-dependent viscosity on fully developed forced convection in a duct of rectangular cross-section occupied by a fluid-saturated porous medium is investigated analytically.The Darcy flow model is applied and the viscosity-temperature relation is assumed to be an inverse-linear one. The case of uniform heat flux on the walls, i.e. the H boundary condition in the terminology of Kays and Crawford [1], is treated. For the case of a fluid whose viscosity decreases with temperature, it is found that the effect of the variation is to increase the Nusselt number for heated walls. Having found the velocity and the temperature distribution, the second law of thermodynamics is invoked to find the local and average entropy generation rate.Expressions for the entropy generation rate, the Bejan number, the heat transfer irreversibility, and the fluid flow irreversibility are presented in terms of the Brinkman number, the Péclet number, the viscosity variation number, the dimensionless wall heat flux, and the aspect ratio (width to height ratio). These expressions let a parametric study of the problem based on which it is observed that the entropy generated due to flow in a duct of square cross-section is more than those of rectangular counterparts while increasing the aspect ratio decreases the entropy generation rate similar to what previously reported for the clear flow case [2].

Slip flow forced convection in a microporous duct of rectangular cross-section

“…However, theoretical research on slip flow in porous-saturated microducts of arbitrary cross-section has not been conducted as much as those on clear fluid counterparts. The problem becomes more complicated when one notes that only a handful of papers, see for example (Hooman, Haji-Sheikh and Nield 2007, Hooman and Merrikh 2006, Haji-Sheikh, Nield and Hooman 2006, Haji-Sheikh, Minkowycz and Sparrow 2004, Haji-Sheikh 2006, Hooman and Gurgenci 2007a, Hooman, Gurgenci and Merrikh 2007, Haji-Sheikh and Vafai 2004, Merrikh and Lage 2005, can be mentioned when it comes to name analytical studies on macro-porous ducts of cross-sections other than circular tube or Parallel Plate Channel (PPC), say rectangular shape, even when the saturating fluid is not a rarefied gas. Analytical solutions are not only very useful in benchmarking numerical computations but also they are very powerful for parametric studies when a large number of parameters are involved wherever numerical results cannot be experimentally verified, or no experiments are possible due to time, cost, and other limiting factors.…”

Entropy generation for natural convection by heated partitions in a cavity

“…This method has already been extensively applied to forced [12][13][14][15][16] and free convection [17][18][19][20][21][22][23][24][25] problems, to name a few. However, for the problem considered here there is no solution reported in the literature, to the best knowledge of the authors.…”

Heat transfer and entropy generation optimization of forced convection in porous-saturated ducts of rectangular cross-section

“…In ducts of 6 6 arbitrary cross section, Hooman [12][13][14] has reported closed form solutions for the fully developed temperature distribution and the Nusselt number as well as the local entropy generation rate by applying the Darcy momentum equation.…”