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**Convection in porous media.
2nd ed.**
*(English)*
Zbl 0924.76001

New York, NY: Springer. xxi, 546 p. DM 148,00; öS 1.081,00; sFr 135,00; £57,00; $ 79,95 (1999).

The first edition of this book in 1992 proved the usefulness of the book to researchers working in various areas such as building insulation, energy storage, nuclear waste disposal, grain and coal storage, chemical reactor engineering, ground water flow etc.

In chapter 1, the authors present various types of equations governing the flow of viscous incompressible fluids through porous media based on Darcy’s law, Brinkman model, Forchheimer’s model, and discuss the limitations of these models from the physical point of view. Then various models of hydrodynamic boundary conditions and of variable porosity are discussed. The last section in this chapter is devoted to turbulence, specially pointing out that the Rudraiah’s theory of turbulence is totally wrong, which is a warning to those research workers trying to apply the Rudraiah’s theory of turbulence.

Chapter 2 deals with heat transfer phenomenon in flow through porous media. In particular, a new phenomenon known as thermal dispersion in porous media, is discussed in detail. In chapter 3, the authors examine the mass transfer, combined heat and mass transfer, and multiphase flows in porous media. Chapter 4 is devoted to the application of the Darcy’s model to boundary layer flows in porous media along a flat plate, sphere and cylinder. The authors study transient effects and effects of boundary friction and variable porosity on confined flows. The most important application – compact heat exchangers — is discussed together with other applications such as hotlines for visualizing convection in porous media, networks for minimal resistance in volume-to-point flows, etc.

Chapter 5 deals with external natural convection under different physical conditions and is also based on Darcy’s model. Here the authors mention effects of boundary friction, inertia, thermal dispersion, etc. Vortex instability in flows past horizontal bodies is discussed in short. The authors also discuss without mathematical details flows due to horizontal line heat source. Finally, the authors examine a surface covered by hair taking into account the free convection. Chapter 6 deals with the stability of flows heated from below (classical Bénard problem) in porous media. Different types of physical situations are discussed. Both linear and weakly nonlinear stability and the effects of rotation and magnetic field on the stability are discussed.

Chapter 7 presents under different physical conditions the flows through porous media, bounded by two walls. Mixed convection problems for vertical and horizontal geometries, in particular for vertical channel and annulus, are examined in chapter 8. In chapter 9, the authors examine linear and nonlinear stability of horizontal fluid layers in the presence of external mass fluxes. They discuss the Soret diffusion, and then the boundary layer flow past a vertical semi-infinite plate embedded in a porous medium, in the presence of the mass transfer. A short account of flows due to point source and horizontal line source is given.

Chapter 10 treats rigorously convection with the phase change, such as ice melting of freezing in a porous medium. An another important phenomenon is the solidification of binary alloys based on Darcy model. The authors study the boiling due to heating from below or film boiling, and give a short account of condensation phenomenon in a porous medium. Also the “themally active fibers”, which have the property of energy storage and release, are presented. The last chapter 11 deals with geophysical aspects of convection in porous media. In fact, the research of flows through porous medium before 1970 was mainly due to its applications in geophysics. Different physical situations like snow, ground patterns, oceanic crust, geothermal reservoirs, flow of vapor through solid rock (two-phase flow), and the working of heat-pipes in cooler regions are mentioned in short. A large number of contemporary papers on the book topics are collected at the end in the list of references. This will definitely help a specialist working in this field to do further research work.

The reviewer highly recommends this book to students, engineers and researchers with an interest in flows in porous media, and hopes that the authors will soon publish the 3rd edition of this useful book.

In chapter 1, the authors present various types of equations governing the flow of viscous incompressible fluids through porous media based on Darcy’s law, Brinkman model, Forchheimer’s model, and discuss the limitations of these models from the physical point of view. Then various models of hydrodynamic boundary conditions and of variable porosity are discussed. The last section in this chapter is devoted to turbulence, specially pointing out that the Rudraiah’s theory of turbulence is totally wrong, which is a warning to those research workers trying to apply the Rudraiah’s theory of turbulence.

Chapter 2 deals with heat transfer phenomenon in flow through porous media. In particular, a new phenomenon known as thermal dispersion in porous media, is discussed in detail. In chapter 3, the authors examine the mass transfer, combined heat and mass transfer, and multiphase flows in porous media. Chapter 4 is devoted to the application of the Darcy’s model to boundary layer flows in porous media along a flat plate, sphere and cylinder. The authors study transient effects and effects of boundary friction and variable porosity on confined flows. The most important application – compact heat exchangers — is discussed together with other applications such as hotlines for visualizing convection in porous media, networks for minimal resistance in volume-to-point flows, etc.

Chapter 5 deals with external natural convection under different physical conditions and is also based on Darcy’s model. Here the authors mention effects of boundary friction, inertia, thermal dispersion, etc. Vortex instability in flows past horizontal bodies is discussed in short. The authors also discuss without mathematical details flows due to horizontal line heat source. Finally, the authors examine a surface covered by hair taking into account the free convection. Chapter 6 deals with the stability of flows heated from below (classical Bénard problem) in porous media. Different types of physical situations are discussed. Both linear and weakly nonlinear stability and the effects of rotation and magnetic field on the stability are discussed.

Chapter 7 presents under different physical conditions the flows through porous media, bounded by two walls. Mixed convection problems for vertical and horizontal geometries, in particular for vertical channel and annulus, are examined in chapter 8. In chapter 9, the authors examine linear and nonlinear stability of horizontal fluid layers in the presence of external mass fluxes. They discuss the Soret diffusion, and then the boundary layer flow past a vertical semi-infinite plate embedded in a porous medium, in the presence of the mass transfer. A short account of flows due to point source and horizontal line source is given.

Chapter 10 treats rigorously convection with the phase change, such as ice melting of freezing in a porous medium. An another important phenomenon is the solidification of binary alloys based on Darcy model. The authors study the boiling due to heating from below or film boiling, and give a short account of condensation phenomenon in a porous medium. Also the “themally active fibers”, which have the property of energy storage and release, are presented. The last chapter 11 deals with geophysical aspects of convection in porous media. In fact, the research of flows through porous medium before 1970 was mainly due to its applications in geophysics. Different physical situations like snow, ground patterns, oceanic crust, geothermal reservoirs, flow of vapor through solid rock (two-phase flow), and the working of heat-pipes in cooler regions are mentioned in short. A large number of contemporary papers on the book topics are collected at the end in the list of references. This will definitely help a specialist working in this field to do further research work.

The reviewer highly recommends this book to students, engineers and researchers with an interest in flows in porous media, and hopes that the authors will soon publish the 3rd edition of this useful book.

Reviewer: V.M.Soundalgekar (Thane)

### MSC:

76-02 | Research exposition (monographs, survey articles) pertaining to fluid mechanics |

76S05 | Flows in porous media; filtration; seepage |

76R10 | Free convection |

76R05 | Forced convection |

76E15 | Absolute and convective instability and stability in hydrodynamic stability |

80A20 | Heat and mass transfer, heat flow (MSC2010) |

86A05 | Hydrology, hydrography, oceanography |