On Darcy's law for growing porous media

Preziosi, Luigi; Farína, Angiolo

doi:10.1016/s0020-7462(01)00022-1

Cited by 101 publications

(55 citation statements)

References 3 publications

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“…However, the contribution due to mass exchange is negligible with respect to that due to the interaction forces [PF01], compatibly with the fact that inertial terms are negligible. Hence, one can say that the interaction forces sum up to zero, as it might be expected since they act as internal forces among the constituents of the whole mixture.…”

Section: Interaction Forcesmentioning

confidence: 61%

Multiphase Models of Tumour Growth

Astanin

Preziosi

2008

Modeling and Simulation in Science, Engineering and Technology

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Section: Interaction Forcesmentioning

confidence: 61%

Multiphase Models of Tumour Growth

Astanin

Preziosi

2008

Modeling and Simulation in Science, Engineering and Technology

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“…(27) under suitable assumptions (see Bowen, 1976;Preziosi and Farina, 2001), also in the case of a growing porous material (in this case the permeability tensor includes a correction term related to growth). Neglecting inertial terms and assuming the constitutive equation…”

Section: Porous Media Modelsmentioning

confidence: 99%

Multiscale Modeling and Mathematical Problems Related to Tumor Evolution and Medical Therapy

Bellomo

Angelis

Preziosi

2003

Computational and Mathematical Methods in Medicine

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This paper provides a survey of mathematical models and methods dealing with the analysis and simulation of tumor dynamics in competition with the immune system. The characteristic scales of the phenomena are identified and the mathematical literature on models and problems developed on each scale is reviewed and critically analyzed. Moreover, this paper deals with the modeling and optimization of therapeutical actions. The aim of the critical analysis and review consists in providing the background framework towards the development of research perspectives in this promising new field of applied mathematics.

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“…They treated the clogged region as a porous medium and assumed the permeability parameter to be either a constant or varying in the radial direction. Preziosi and Farina [25] analyzed flow of a Newtonian fluid in a porous medium in the presence of mass exchange between the constituents.…”

Section: Introductionmentioning

confidence: 99%

Effect of thermal radiation on MHD flow of blood and heat transfer in a permeable capillary in stretching motion

Misra

Sinha

2013

Heat Mass Transfer

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In this paper, a theoretical analysis is presented for magnetohydrodynamic flow of blood in a capillary, its lumen being porous and wall permeable. The unsteadiness in the flow and temperature fields is caused by the timedependence of the stretching velocity and the surface temperature. Thermal radiation, velocity slip and thermal slip conditions are taken into account. In order to study the flow field as well as the temperature field, the problem is formulated as a boundary value problem consisting of a system of nonlinear coupled partial differential equations. The problem is analysed by using similarity transformation and boundary layer approximation. Solution of the problem is achieved by developing a suitable numerical method and using high speed computers. Computational results for the variation in velocity, temperature, skin-friction co-efficient and Nusselt number are presented in graphical/tabular form. Effects of different parameters are adequately discussed. Since the study takes care of thermal radiation in blood flow, the results reported here are likely to have an important bearing on the therapeutic procedure of hyperthermia, particularly in understanding/regulating blood flow and heat transfer in capillaries.

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On Darcy's law for growing porous media

Cited by 101 publications

References 3 publications

Multiphase Models of Tumour Growth

Multiphase Models of Tumour Growth

Multiscale Modeling and Mathematical Problems Related to Tumor Evolution and Medical Therapy

Effect of thermal radiation on MHD flow of blood and heat transfer in a permeable capillary in stretching motion

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