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The classical advection-dispersion equation (ADE) model cannot accurately depict the gas transport process in natural geological formations. This paper aims to study the behavior of CO₂ transport in fractal porous media by using an effective Hausdorff fractal derivative advection-dispersion equation (HFDADE) model.

Anomalous dispersion behaviors of CO₂ transport are effectively characterized by the investigation of time and space Hausdorff derivatives on non-Euclidean fractal metrics. The numerical simulation has been performed with different Hausdorff fractal dimensions to reveal characteristics of the developed fractal ADE in fractal porous media. Numerical experiments focus on the influence of the time and space fractal dimensions on flow velocity and dispersion coefficient.

The physical mechanisms of parameters in the Hausdorff fractal derivative model are analyzed clearly. Numerical results demonstrate that the proposed model can well fit the history of gas production data and it can be a powerful technique for depicting the early arrival and long-tailed phenomenon by incorporating a fractal dimension.

To the best of the authors’ knowledge, first time these results are presented.

Recently, the porous media theory has been successively proposed for many bioengineering applications. The purpose of this paper is to analyze if the porous media theory can be applied to model radiofrequency (RF) cardiac ablation.

Blood flow, catheter and tissue are modeled. The latter is further divided into a fluid and a solid phase, and porous media equations are used to model them. The heat source term is modeled using the Laplace equation, and the finite element method is used to solve the governing equations under the appropriate boundary conditions and closure coefficients.

After validation with available literature data, results are shown for different velocities and applied voltages to understand how these parameters affect temperature fields (and necrotic regions).

The model might require further validation with experiments under different conditions after comparisons with available literature. However, this might not be possible due to the experimental complexity.

The improvement in predictions from the model might help the final user, i.e. the surgeon, who uses cardiac ablation to treat arrhythmia.

This is the first time that the porous media theory is applied to RF cardiac ablation. The robustness of the model, in which many variables are taken into account, makes it suitable to better predict temperature fields, and damaged regions, during RF cardiac ablation treatments.

The purpose of this paper is to analytically perform gaseous slip flow and heat transfer analysis within a parallel-plate microchannel partially filled with a centered porous medium under local thermal non-equilibrium (LTNE) condition. Heat transfer of gaseous flow in a porous microchannel is analytically studied. Energy communication at the porous-fluid interface is considered by two approaches: the gas rarefaction negatively impacts the heat transfer performance, and the optimum ratio of porous thickness is found to be around 0.8.

Both Models A and B are utilized to consider the heat flux splitting for the fluid and solid phases at the porous-fluid interface.

Analytical solutions for the fluid and solid phase temperature distributions and the Nusselt number are derived. In the no-slip flow limit, the present analytical solutions are validated by the partially and fully filled cases available in the literature.

The continuum flow (no-slip flow) is only a special case of the slip flow. Meanwhile, the effects of pertinent parameters on the heat transfer are also discussed.

A survey of available literature mentioned above indicates a shortage of information for slip flow and heat transfer in partially filled porous systems. The main objective of the present study is to investigate the slip flow and heat transfer characteristics for forced convection through a microchannel partially filled with a porous medium under LTNE condition. The porous substrate is placed at the center of the microchannel. Analytical solutions for the temperature distributions of the fluid and solid phases and the Nusselt number at the microchannel wall are obtained.

Heat transfer of gaseous flow in a porous microchannel is analytically studied. Energy communication at the porous-fluid interface is considered by two approaches: the gas rarefaction negatively impacts the heat transfer performance, and the optimum ratio of porous thickness is found to be around 0.8. Gaseous slip flow and heat transfer analysis is analytically performed within a parallel-plate microchannel partially filled with a centered porous medium under LTNE condition. Analytical solutions for the fluid and solid phase temperature distributions and the Nusselt number are derived for the first time. The effects of pertinent parameters on the heat transfer are also discussed. Compared with the results obtained for the continuum flow regime, the gas rarefaction negatively impacts the heat transfer efficiency and has little influence on the optimal porous thickness.

The purpose of this paper is to analyze two different approaches (Models A and B) for an adiabatic boundary condition at the wall of a channel filled with a porous medium. The analytical solutions for the velocity distribution, the fluid and solid phase temperature distributions are derived and compared with numerical solutions. The phenomenon of heat flux bifurcation for Model A is demonstrated. The effects of pertinent parameter C on the applicability of the Models A and B are discussed. Analytical solutions for the overall Nusselt number and the heat flux distribution at the channel wall are derived and the influence of pertinent parameters Da and k on the overall Nusselt number and the heat flux distribution is discussed.

Two approaches (Models A and B) for an adiabatic boundary condition in porous media under local thermal non-equilibrium (LTNE) conditions are analyzed in this work. The analysis is applied to a microchannel which is modeled as a porous medium.

The phenomenon of heat flux bifurcation at the wall for Model A is demonstrated. The effect of pertinent parameter C on the applicability of each model is discussed. Model A is applicable when C is relatively large and Model B is applicable when C is small. The heat flux distribution is obtained and the influence of Da and k is discussed. For Model A, ϕ_Afin increases and ϕ_Asub, ϕ_Acover decrease as Da decreases and k is held constant, ϕ_Asub increases and ϕ_Afin, ϕ_Acover decrease as k increases while Da is held constant; for Model B, ϕ_Bfin increases and ϕ_Bsub decreases either as Da decreases or k decreases. The overall Nusselt number is also obtained and the effect of Da and k is discussed: Nu increases as either Da or k decrease for both models. The overall Nusselt number for Model A is larger than that for Model B when Da is large, the overall Nusselt numbers for Models A and B are equivalent when Da is small.

Proper representation of the energy equation and the boundary conditions for heat transfer in porous media is very important. There are two different models for representing energy transfer in porous media: local thermal equilibrium (LTE) and LTNE. Although LTE model is more convenient to use, the LTE assumption is not valid when a substantial temperature difference exists between the solid and fluid phases.

Fluid flow and convective heat transfer in porous media have many important applications such as thermal energy storage, nuclear waste repository, electronic cooling, geothermal energy extraction, petroleum processing and heat transfer enhancement.

This work has important fundamental implications.

In this work the microchannel is modeled as an equivalent porous medium. The analytical solutions for the velocity distribution, the fluid and solid phase temperature distributions are obtained and compared with numerical solutions. The first type of heat flux bifurcation phenomenon, which indicates that the direction of the temperature gradient for the fluid and solid phases is different at the channel wall, occurs when Model A is utilized. The effect of pertinent parameter C on the applicability of the models is also discussed. The analytical solutions for the overall Nusselt number and the heat flux distribution at the channel wall are derived, and the effects of pertinent parameters Da and k on the overall Nusselt number and the heat flux distribution are discussed.

The purpose of this paper is to study steady, laminar, and two-dimensional flow around and through a porous diamond cylinder.

The governing equations are written for two zones: the clear fluid zone and the porous zone. For the porous zone, the modified Navier-Stokes equations, including Darcy, Brinkman, and Forcheimer terms are used. The governing equations are solved numerically using a finite volume approach.

It was found that as the apex angle and Reynolds number decreases the wake length decreases and the separation is delayed.

There is no published research in the literature about flow around and into porous diamond cylinders to study the effect of important parameters, such as apex angle, Darcy number, and Reynolds number.