Existence of Strong Solutions for Nonlinear Systems of PDEs Arising in Convective Flow by Khaled Bouazzaoui, Mohammed Aiboudi, Sameh Elsayed Ahmed

“…In this paper, we will study the existence of strong solutions for a nonlinear system of partial differential equations arising in convective flow, modeling a phenomenon of mixed convection created by a heated and diving plate in a porous medium saturated with a fluid. The main tools are Schäfer’s fixed-point theorem, the Fredholm alternative, and some theorems on second-order elliptic operators.…”
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Mixed Convective-Radiative Dissipative Magnetized Micropolar Nanofluid Flow over a Stretching Surface in Porous Media with Double Stratification and Chemical Reaction Effects: ADM-... by P. K. Pattnaik, M. M. Bhatti, S. R. Mishra, Munawwar Ali Abbas, O. Anwar Bég

“…Darcy’s model is employed for the porous medium and a Rosseland diffusion flux approximation for nonlinear thermal radiation. …”
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An efficient approach for solving a class of nonlinear 2D parabolic PDEs by Dongjin Kim, Wlodek Proskurowski

“…We apply our scheme to study the finite extinction phenomenon for the porous-medium equation with strong absorption. A comparison of accuracy and computational efficiency of the resulting algorithms for several test problems is presented.…”
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Solvability of the Brinkman-Forchheimer-Darcy Equation by Piotr Skrzypacz, Dongming Wei

“…The nonlinear Brinkman-Forchheimer-Darcy equation is used to model some porous medium flow in chemical reactors of packed bed type. …”
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Asymptotic Behavior of the 3D Compressible Euler Equations with Nonlinear Damping and Slip Boundary Condition by Huimin Yu

“…For polytropic perfect gas (P(ρ)=P0ργ), time asymptotically, it has been proved by Pan and Zhao (2009) that linear damping and slip boundary effect make the density satisfying the porous medium equation and the momentum obeying the classical Darcy's law. …”
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Effect of Colloidal Silicate on the Migration Behaviour of Strontium in Groundwater Environment of Geological Disposal Candidate Site by Rui Zuo, Kexue Han, Rongtao Shi, Fei Ding, Li Liu, Jinsheng Wang, Yanguo Teng, Jie Yang, Xin Liu

“…Three different experimental cases have been designed: (1) effect in the presence of colloidal silicate, (2) effect in the presence of a porous medium, and (3) effect in the presence of both colloidal silicate and porous medium (referred to as CS, PM, and PC, respectively). …”
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On the Lauwerier formulation of the temperature field problem in oil strata by Lyubomir Boyadjiev, Ognian Kamenov, Shyam Kalla

“…The paper is concerned with the fractional extension of the Lauwerier formulation of the problem related to the temperature field description in a porous medium (sandstone) saturated with oil (strata). …”
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RESEARCH ON PERFORMANCE ANALYSIS METHOD OF AUTOMOBILE RADIATOR BASED ON ITERTIVE CALCULATION by ZHUO DongHui, TONG GaoPeng

“…The results of the local iteration method and the porous medium model simulation agree well with the experimental results,and provide a new idea for the performance analysis of the integral radiator.…”
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Darcy-Brinkman free convection about a wedge and a cone subjected to a mixed thermal boundary condition by G. Ramanaiah, V. Kumaran

“…The Darcy-Brinkman free convection near a wedge and a cone in a porous medium with high porosity has been considered. …”
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Response of porous SMA: a micromechanical study by V. Sepe, S. Marfia, F. Auricchio

“…The mechanical response of the heterogeneous porous medium is derived by performing nonlinear finite element micromechanical analyses considering a typical repetitive unit cell made of a circular hole in a dense SMA matrix and prescribing suitable periodicity and continuity conditions. …”
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A Fast Implicit Finite Difference Method for Fractional Advection-Dispersion Equations with Fractional Derivative Boundary Conditions by Taohua Liu, Muzhou Hou

“…Fractional advection-dispersion equations, as generalizations of classical integer-order advection-dispersion equations, are used to model the transport of passive tracers carried by fluid flow in a porous medium. In this paper, we develop an implicit finite difference method for fractional advection-dispersion equations with fractional derivative boundary conditions. …”
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Dufour and Soret Effects on Melting from a Vertical Plate Embedded in Saturated Porous Media by Basant K. Jha, Umaru Mohammed, Abiodun O. Ajibade

“…Thermal-diffusion and diffusion-thermo effects on combined heat and mass transfer in mixed convection boundary layer flow with aiding and opposing external flows from a vertical plate embedded in a liquid saturated porous medium with melting are investigated. The resulting system of nonlinear ordinary differential equations is solved numerically using Runge Kutta-Fehlberg with shooting techniques. …”
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Unsteady MHD Mixed Convection Flow of Chemically Reacting Micropolar Fluid between Porous Parallel Plates with Soret and Dufour Effects by Odelu Ojjela, N. Naresh Kumar

“…The objective of the present study is to investigate the first-order chemical reaction and Soret and Dufour effects on an incompressible MHD combined free and forced convection heat and mass transfer of a micropolar fluid through a porous medium between two parallel plates. Assume that there are a periodic injection and suction at the lower and upper plates. …”
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Mathematical Model and Solution for Fingering Phenomenon in Double Phase Flow through Homogeneous Porous Media by Piyush R. Mistry, Vikas H. Pradhan, Khyati R. Desai

“…Fingering phenomenon is a physical phenomenon which occurs when a fluid contained in a porous medium is displaced by another of lesser viscosity which frequently occurred in problems of petroleum technology. …”
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Numerical Validation of Analytical Estimates for Propagation of Thermal Waves Generated by Gas-Solid Combustion by Weslley da Silva Pereira, Grigori Chapiro

“…Using numerical simulation we show that they can be adapted and then applied to describe more general two-dimensional models for in situ combustion in a nonhomogeneous porous medium.…”
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Mathematical analysis of a quorum sensing induced biofilm dispersal model and numerical simulation of hollowing effects by Blessing O. Emerenini, Stefanie Sonner, Hermann J. Eberl

“…The governing equation for the sessile biomass comprises two non-linear diffusion effects, a degeneracy as in the porous medium equation and fast diffusion. This equation is coupled with three semi-linear diffusion-reaction equations for the concentrations of growth limiting nutrients, autoinducers, and dispersed cells. …”
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Numerical analysis of sodium diffusion in aluminum electrolysis cathode carbon blocks based on a microstructure multi-factor corrected model. by Chenglong Gong, Tianqi Xu, Huarong Qi, Yan Li

“…However, the microscopic structure is often underexplored. As a porous medium, the diffusion performance of cathode carbon blocks is closely tied to their internal pore structure. …”
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Permeability Properties of Jointed Rock with Periodic Partially Filled Fractures by Fei Ye, Jun-Chao Duan, Wen-Xi Fu, Xing-Yu Yuan

“…In this model, the clear fluid in fractures is governed by the Navier-Stokes equation, and the fluid both in the porous medium and rock matrix are subjected to the Brinkman-Extended Darcy equation. …”
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Study of Magnetohydrodynamic Pulsatile Blood Flow through an Inclined Porous Cylindrical Tube with Generalized Time-Nonlocal Shear Stress by Nehad Ali Shah, A. Al-Zubaidi, S. Saleem

“…The effects of pulsatile pressure gradient in the presence of a transverse magnetic field on unsteady blood flow through an inclined tapered cylindrical tube of porous medium are discussed in this article. The fractional calculus technique is used to provide a mathematical model of blood flow with fractional derivatives. …”
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Modeling and Simulation of a Chemical Vapor Deposition by J. Geiser, M. Arab

“…To model the gaseous transport in the apparatus we employ mobile gas phase streams, immobile and mobile phases in a chamber that is filled with porous medium (plasma layers). Numerical methods are discussed to solve such multi-scale and multi phase models and to obtain qualitative results for the delicate multiphysical processes in the chamber. …”
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