Concentration Boundary Conditions Research Articles

Correlation between Electrostatic and Hydration Forces on Silica and Gibbsite Surfaces: An Atomic Force Microscopy Study.

The balance between hydration and Derjaguin–Landau–Verwey–Overbeek (DLVO) forces at solid–liquid interfaces controls many processes, such as colloidal stability, wetting, electrochemistry, biomolecular self-assembly, and ion adsorption. Yet, the origin of molecular scale hydration forces and their relation to the surface charge density that controls the continuum scale electrostatic forces is poorly understood. We argue that these two types of forces are largely independent of each other. To support this hypothesis, we performed atomic force microscopy experiments using intermediate-sized tips that enable the simultaneous detection of DLVO and molecular scale oscillatory hydration forces at the interface between composite gibbsite:silica–aqueous electrolyte interfaces. We extract surface charge densities from forces measured at tip–sample separations of 1.5 nm and beyond using DLVO theory in combination with charge regulation boundary conditions for various pH values and salt concentrations. We simultaneously observe both colloidal scale DLVO forces and oscillatory hydration forces for an individual crystalline gibbsite particle and the underlying amorphous silica substrate for all fluid compositions investigated. While the diffuse layer charge varies with pH as expected, the oscillatory hydration forces are found to be largely independent of pH and salt concentration, supporting our hypothesis that both forces indeed have a very different origin. Oscillatory hydration forces are found to be distinctly more pronounced on gibbsite than on silica. We rationalize this observation based on the distribution of hydroxyl groups available for H bonding on the two distinct surfaces.

Flow investigation of second grade micropolar nanofluid with porous medium over an exponentially stretching sheet.

This article mainly focuses on the influence of heat and mass transportation of micropolar second grade nanofluid toward porous medium of an exponentially stretched surface. The significance of activation energy and viscous dissipation with magnetic effect are taken into deliberated. Furthermore, to analyze the heat and mass transport scrutiny the concentration and thermal slip boundary conditions are assessed on the surface of the sheet. The convenient similarity variables are adopted to transfer the non-linear governing PDEs into the dimensionless ODEs and their corresponding boundary conditions also transformed. The nonlinear coupled ODEs are numerically solved by the usage of BVP4C MATLAB technique. The obtained numerical estimations are displayed graphically to display the significance of the various parameters against the velocity, temperature, microrotation, concentration distributions. It is noticed that larger estimations of micropolar and second grade parameter improves the fluid velocity consequently, while opposite trend is found for the higher estimation of porous medium parameter. Further, it is observed that the skin friction rate is boosted by the increment of and , whereas opposite trend is noted against the mass transfer rate and heat transfer rate.

Solute Transport Control at Channel Junctions Using Adjoint Sensitivity

Water quality control and the control of contaminant spill in water in particular are becoming a primary need today. Gradient descent sensitivity methods based on the adjoint formulation have proved to be encouraging techniques in this context for river and channel flows. Taking into account that most channels and rivers include junctions with other branches, the objective of this study is to explore the adjoint technique on a channel network to reconstruct the upstream boundary condition of the convection-reaction equation. For this purpose, the one-dimensional shallow water equations and the transport equation for a reactive solute are considered. The control is formulated through the gradient-descent technique supplied with a first-order iterative process. Both the physical and the adjoint equations are supplied with suitable internal boundary conditions at the junction and are numerically solved using a finite volume upwind scheme. The results reveal that the adjoint technique is capable of reconstructing the inlet solute concentration boundary condition in an acceptable number of iterations for both steady state and transient configurations using a downstream measurement location. It was also observed that the reconstruction of the boundary condition tends to be less effective the further away the measurement station is from the target.

Numerical analysis of hydromagnetic transport of Casson nanofluid over permeable linearly stretched cylinder with Arrhenius activation energy

The current study is modelled to evaluate numerous flow applications in applied sciences espeically in nuclear reacting cooling, geothermal reservoirs, chemical engineering and thermal oil recovery. The present research investigates the magnetohydrodynamic transport of non-Newtonian Casson Nano fluid past due to stretching permeable cylinder by employing Buongiorno's mathematical model. Unlike the frequently used constant temperature and concentration boundary conditions, the present study employed convective boundary conditions. The influences of important sundary parameters like an inclination of magnetic field, joule heating, viscous dissipation, thermophoresis, Brownian motion, Arrhenius activation energy, and chemical reaction are taken into account. The physical flow phenomenon is modelled and after that transformed into a non-dimensional form by incorporating suitable similarity transforms. For solution purpose, Runge-Kutta-Fehlberg fourth-fifth order (RKF45) numerical integrating procedure along with shooting algorithm is adopted. Impacts of several emerging parameters on the velocity distribution, temperature distribution, and concentration distribution, coefficient of skin friction, Sherwood number, and Nusselt number are clarified via graphical and tabular results. It seems to establish that with the rise of chemical reaction parameter chemical reaction parameter the nanoparticles concentration distributions decline while the contrasting trend is perceived for activation energy parameter.

CFD modelling of mass transfer in liquid–liquid core-annular flow in a microchannel

This work reports Computational Fluid Dynamics (CFD) modelling of mass transfer in liquid–liquid Core-Annular Flow (CAF) in a microchannel. The model solves Navier-Stokes and convection–diffusion equations after incorporating interfacial boundary conditions of velocity, shear stress, flux and concentration jump. The model has been validated with the analytical and previously reported results. The validated model has been used to understand and quantify the dependence of concentrations boundary layer thicknesses on the core side and annulus side on Reynolds number, Schmidt number, dimensionless length and distribution coefficient. Furthermore, the dependenceof local mass transfer coefficients on the core and annulus side on diffusivity and concentration boundary layer thicknesses is quantified and compared with the predictions of film theory and penetration theory. Finally, the results obtained from the CFD model have been used to obtain the correlations of Sherwood number on the core side and the annulus side.

Analytical solutions of advection-dispersion-reaction equation with first decay under constant and time-dependent boundary conditions: Mass transfer shape factor effects

To describe the combined dispersion and convection mechanisms of solute transport through porous media, one may typically refer to the advection-dispersion equation (ADE). In this study, a generalized analytical solution to the ADE combined with first order decay term is derived for the problem of solute transport through porous media in one-dimensional finite region considering transient boundary conditions. First, the addressed convection-dispersion-reaction equation is simplified into a diffusion equation. Subsequently, an analytical solution is generated for a general fractured porous medium for a case where a fracture is viewed as the transient boundary condition. To verify the proposed analytical solution, experimental data acquired from literature as well as numerical techniques of finite difference and element are utilized. Previous studies have utilized fixed values for mass transfer shaper factor which is deployed in dual porosity modeling approach of fractured reservoirs, while in reality this parameter changes over time. In this regard, an attempt is made to attain mass transfer shape factor while considering the impacts of important parameters such as Péclet number, and decay coefficient during both pseudo steady state (PSS) and transient periods. Moreover, for two circumstances of linearly ascending and constant concentration boundary conditions, a correlation is developed to compute PSS mass transfer shape factor as a function of Péclet number, dimensionless time, and decay coefficient. The results illustrated the dependency of PSS shape factor on the decay coefficient, Péclet number, and time while transient shape factor solely depended on time. In addition, the findings showed that the larger the Péclet number, the larger the PSS matrix-fracture mass transfer shape factor. The obtained analytical solution is helpful when validating the numerical simulation results and for performing fast sensitivity analysis. The developed mass transfer shape factor can be applied in the dual porosity modeling part of the commercial reservoir simulation software packages for more accurately modeling the solute transport in the fractured reservoirs.

Maxwell Nanofluid Flow over an Infinite Vertical Plate with Ramped and Isothermal Wall Temperature and Concentration

The aim of this study is to investigate how heat and mass transfer impacts the unsteady incompressible flow of Maxwell fluid. An infinite vertical plate with ramped and isothermal wall temperature and concentration boundary conditions is considered with the Maxwell fluid. Furthermore, in this study, engine oil has been taken as a base fluid due to its enormous applications in modern science and technologies. To see the importance of nanofluids, we have suspended molybdenum disulfide in engine oil base fluid to enhance its heat transfer rate. To investigate the flow regime, the system of equations was derived in the form of partial differential equations. The exact solutions to the complex system are obtained using the Laplace transform technique. Graphically, the impact of different embedded parameters on velocity, temperature, and concentration distributions has been shown. Through using the graphical analysis, we were interested in comparing the velocity, temperature, and concentration profiles for ramped and isothermal wall temperature and concentration. The magnitude of velocity, temperature, and concentration distributions is greater for an isothermal wall and less for a ramped wall, according to our observations. We observed that adding molybdenum disulfide nanoparticles to the engine oil increased the heat transfer up to 12.899%. Finally, the corresponding skin friction, Nusselt number, and Sherwood number have been calculated and presented in a tabular form.

Interior Electroneutrality in Nernst–Planck–Navier–Stokes Systems

We consider the limit of vanishing Debye length for ionic diffusion in fluids, described by the Nernst-Planck-Navier-Stokes system. In the asymptotically stable cases of blocking (vanishing normal flux) and uniform selective (special Dirichlet) boundary conditions for the ionic concentrations, we prove that the ionic charge density $\rho$ converges in time to zero in the interior of the domain, in the limit of vanishing Debye length ($\epsilon\to 0$). For the unstable regime of Dirichlet boundary conditions for the ionic concentrations, we prove bounds that are uniform in time and $\epsilon$. We also consider electroneutral boundary conditions, for which we prove that electroneutrality $\rho\to 0$ is achieved at any fixed $\epsilon> 0$, exponentially fast in time in $L^p$, for all $1\le p<\infty$. The results hold for two oppositely charged ionic species with arbitrary ionic diffusivities, in bounded domains with smooth boundaries.

Optical model for the Baltic Sea with an explicit CDOM state variable: a case study with Model ERGOM (version 1.2)

Abstract. Colored dissolved organic matter (CDOM) in marine environments impacts primary production due to its absorption effect on the photosynthetically active radiation. In coastal seas, CDOM originates from terrestrial sources predominantly and causes spatial and temporal changing patterns of light absorption which should be considered in marine biogeochemical models. We propose a model approach in which Earth Observation (EO) products are used to define boundary conditions of CDOM concentrations in an ecosystem model of the Baltic Sea. CDOM concentrations in riverine water derived from EO products serve as forcing for the ecosystem model. For this reason, we introduced an explicit CDOM state variable in the model. We show that the light absorption by CDOM in the model can be improved considerably in comparison to approaches where CDOM is estimated from salinity. The model performance increases especially with respect to spatial CDOM patterns due to the consideration of single river properties. A prerequisite is high-quality CDOM data with sufficiently high spatial resolution which can be provided by the new generation of ESA satellite sensor systems (Sentinel 2 MSI and Sentinel 3 OLCI). Such data are essential, especially when local differences in riverine CDOM concentrations exist.

Numerical Analysis of the Local Current Efficiency Distribution in a Protonic Ceramic Fuel Cell Considering Gas Concentration Distributions

Protonic ceramic fuel cells (PCFCs) are expected as highly efficient energy conversion devices due to the high proton conductivity at relatively lower operating temperature (400 ºC~600 ºC) compared to solid oxide fuel cells (SOFCs). The water steam is generated at air side so that there is less fuel dilution at fuel side. Therefore, PCFCs could operate with higher fuel utilization. However, besides the main proton conductivity, some other chargers including electron holes, oxygen ions, and electrons can also be conductive in PCFCs leading a performance decrement. Especially, the electron hole conductivity cannot be neglected inducing a decrease of current efficiency under some operating conditions. The conductivities in PCFCs are not only affected by the operating temperature, but the gas concentrations also strongly influence their values [1]. The conductivities of proton and hole are respectively show positive relationship to steam and oxygen concentrations [2-3]. These properties of PCFCs cause complex for investigating the performances.In this study, the defect transports in a PCFC electrolyte with BaZr0.8Yb0.2O3-δ (BZYb20) material were numerical solved with a quasi-two-dimensional Nernst-Planck-Poisson (NPP) model and the effect of gas concentration on the cell performance was discussed. For the NPP model calculation algorithm, the Nernst-Planck equation (or flux continuity equation) and the Poisson equation are successively solved by finite difference method (FDM) until convergence criteria are obtained with the defect concentration boundary conditions. The defect concentrations at electrolyte membrane surfaces (boundary conditions of NPP model) are derived by equilibrium assumptions of the reactions such as hydration and oxidation reactions. The charge neutrality condition is also added to the boundary conditions for the exact solutions [4]. Subsequently, the local defects (i.e., proton and electron hole) concentrations are revealed, so that the local current efficiency distribution in the PCFC can be revealed.The utilizations of fuel and oxygen are set at 80% and 30%, respectively. The vapor concentration at anode and cathode side are assumed as 3%. The electrolyte thickness is 8 μm in the present study. A constant temperature distribution is assumed in the numerical model. An example result under co-flow gas supply including proton current density and current efficiency distributions is shown in the following figure. The proton current density along fuel flow direction is found to increase from inlet to outlet. The reason can be considered as the influences of water steam distributions. The water steam concentration (or partial pressure) at both fuel and air side increase from inlet to outlet. The current efficiency at downstream are higher than that of upstream. This is contributed by the increase of oxygen in gas flow direction. Moreover, the influences of gas flow direction on cell performances have also been investigated. Acknowledgements This research is primarily based on results obtained from a project commissioned by the New Energy and Industrial Technology Development Organization (NEDO) Grand Number JPNP20003, Japan. We also extend out special thanks to members of AIST Solid State Ionics Materials Group for useful information and discussions. References Li, et al ., Int. J. Hydrogen Energy, 45 (2020), 34139-149.Okuyama, et al ., Int. J. Hydrogen Energy, 39 (2014), 20829-36.Somekawa T, et al ., Int. J. Hydrogen Energy, 41 (2016), 17539-47.Vøllestad E, et al ., Int. J. Electrochem Soc, 161 (2014), F114-24. Figure 1

Nernst–Planck–Navier–Stokes Systems far from Equilibrium

We consider ionic electrodiffusion in fluids, described by the Nernst-Planck-Navier-Stokes system. We prove that the system has global smooth solutions for arbitrary smooth data: arbitrary positive Dirichlet boundary conditions for the ionic concentrations, arbitrary Dirichlet boundary conditions for the potential, arbitrary positive initial concentrations, and arbitrary regular divergence-free initial velocities. The result holds for any positive diffusivities of ions, in bounded domains with smooth boundary in three space dimensions, in the case of two ionic species, coupled to Stokes equations for the fluid. The result also holds in the case of Navier-Stokes coupling, if the velocity is regular. The global smoothness of solutions is also true for arbitrarily many ionic species, if all their diffusivities are the same.

Assessing long-term evolution of the fine sediment budget in the Iffezheim reservoir: temporal upscaling of numerical simulations

ABSTRACT Since the construction of a weir at Iffezheim (Rhine-km 334) in 1977, a continuous deposition of sediments in the weir channel has been observed. The aim of this paper’s underlying investigations was to assess the long-term riverbed evolution of the Iffezheim reservoir in terms of deposition and erosion. The computational fluid dynamic model SSIIM-3D was applied to simulate the morphological changes in the weir channel. To reduce the computation time of long-term simulation (e.g. several decades), a reduced complexity approach called ‘classification of the boundary conditions for discharges (Q) and suspended sediment concentrations (SSC)’ was developed and applied to the Iffezheim reservoir. The basic idea of the approach was to replace instationary simulations by a precalculated series of simulations with stationary boundary conditions. For doing so, daily volume changes were precalculated by combining representative discharge and suspended sediment concentration regimes. To determine the results of the instationary simulation, the number of days in each bin of Q and SSC was counted, multiplied with the precalculated result and added up. The amount of the volume change in the reservoir for a certain period could then be obtained by adding up the calculated daily volume changes. The results of this method showed an acceptable agreement with measurements for long-term periods (years) and for short-term periods (months) with remarkably shortened computation times compared to the instationary simulations (of 97%).

On the process of filtration of fractional viscoelastic liquid food

In the process of filtration, fluid impurities precipitate/accumulate; this results in an uneven inner wall of the filter, consequently leading to non-uniform suction/injection. The Riemannian–Liouville fractional derivative model is used to investigate viscoelastic incompressible liquid food flowing through a permeable plate and to generalize Fick’s law. Moreover, we consider steady-state mass balance during ultrafiltration on a plate surface, and a fractional-order concentration boundary condition is established, thereby rendering the problem real and complex. The governing equation is numerically solved using the finite difference algorithm. The effects of the fractional constitutive models, generalized Reynolds number, generalized Schmidt number, and permeability parameter on the velocity and concentration fields are compared. The results show that an increase in fractional-order α in the momentum equation leads to a decrease in the horizontal velocity. Anomalous diffusion described by the fractional derivative model weakens the mass transfer; therefore, the concentration decreases with increasing fractional derivative γ in the concentration equation.

On a new block method for an MHD nanofluid flow with an exponentially decaying internal heat generation

AbstractThis study is an investigation of an exponentially decaying internal heat generation rate and free nanoparticle movement on the boundary layer. The equations describing the hydromagnetic flow and heat transfer in a viscous nanofluid moving over an isothermal stretching sheet are solved using a novel numerical approach. A comparison of flow and heat transfer characteristics between an actively controlled (AC) and a passively controlled (PC) nanoparticle concentration boundary is considered. The boundary value partial differential equations are transformed into a system of ordinary differential equations using similarity transformations. The system of ODEs is solved using a new block method without having to reduce the equivalent system to first‐order equations. The solutions are verified using the spectral local linearization method and further validation of the results is confirmed by comparing the current results, for some limiting cases, with those in existing literature. The solutions obtained using the block method are in good agreement with the solution obtained using the spectral local linearization method. The results are in good agreement with existing findings in previous studies. The solutions obtained using the AC and PC nanoparticle concentration boundary conditions are analyzed.

Computational modelling of non-dispersive solvent extraction of uranium in hollow fiber contactor operated in recycle mode

Extraction of uranium and acidity by using TBP (tri-n-butyl phosphate)-n-dodecane through hollow fiber contactor operated in the Non-Dispersive Solvent Extraction (NDSX) configuration with recycle mode is simulated by using a two-dimensional axisymmetric multi-component Computational Fluid Dynamics (CFD) model. This multi-component model solves continuity and momentum transport equations for the feed and shell sides and solute transport equation for the feed side, shell side as well as for the membrane phase. Complex boundary conditions of flux continuity and concentration jump are implemented in the model. Recycle mode of operation is simulated by solving the differential equations representing transient mass balance for feed and solvent reservoirs bottles simultaneously with the governing equations of the CFD model. Validation of the model has been done by comparing predicted and experimentally measured percentage extraction of uranium and nitric acid for different parametric conditions. The validated model has been used to have detailed insights into the spatial and temporal variation of concentration and flux profiles inside the contactor. The CFD model of hollow fiber contactor, which is widely accepted as a separation process intensification tool, will be useful for optimization of the design, operation and scale-up.

CFD prediction of shell-side flow and mass transfer in regular fiber arrays

Numerical simulations were conducted for fully developed, steady-state flow with mass transfer in fiber bundles arranged in regular lattices. The porosity was 0.5 and the Schmidt number 500. Several combinations of axial flow, transverse flow and flow attack angles in the cross-section plane were considered. The axial and transverse Reynolds numbers Rez, ReT were made to vary from 10−4 to 102. Concentration boundary conditions, and the definition of an average Sherwood number, were addressed. Results for the hydraulic permeability were compared with the literature. Both hexagonal and square lattices were found to be hydraulically almost isotropic up to transverse flow Reynolds numbers ReT of ~10, while they behaved anisotropically in regard to mass transfer even at ReT as low as 0.1. A larger anisotropy was exhibited by the square lattice. In mixed (axial+transverse) flow, the transverse friction coefficient was almost completely unaffected by the simultaneous presence of axial flow, while the axial friction coefficient (and thus the axial pressure loss) increased with the transverse Reynolds number for ReT>~5-10. In regard to mass transfer, the Sherwood number settled in all cases to the higher between the Sherwood number in purely transverse flow and that in purely axial flow.

From diffusive mass transfer in Stokes flow to low Reynolds number Marangoni boats

We present a theory for the self-propulsion of symmetric, half-spherical Marangoni boats (soap or camphor boats) at low Reynolds numbers. Propulsion is generated by release (diffusive emission or dissolution) of water-soluble surfactant molecules, which modulate the air–water interfacial tension. Propulsion either requires asymmetric release or spontaneous symmetry breaking by coupling to advection for a perfectly symmetrical swimmer. We study the diffusion–advection problem for a sphere in Stokes flow analytically and numerically both for constant concentration and constant flux boundary conditions. We derive novel results for concentration profiles under constant flux boundary conditions and for the Nusselt number (the dimensionless ratio of total emitted flux and diffusive flux). Based on these results, we analyze the Marangoni boat for small Marangoni propulsion (low Peclet number) and show that two swimming regimes exist, a diffusive regime at low velocities and an advection-dominated regime at high swimmer velocities. We describe both the limit of large Marangoni propulsion (high Peclet number) and the effects from evaporation by approximative analytical theories. The swimming velocity is determined by force balance, and we obtain a general expression for the Marangoni forces, which comprises both direct Marangoni forces from the surface tension gradient along the air–water–swimmer contact line and Marangoni flow forces. We unravel whether the Marangoni flow contribution is exerting a forward or backward force during propulsion. Our main result is the relation between Peclet number and swimming velocity. Spontaneous symmetry breaking and, thus, swimming occur for a perfectly symmetrical swimmer above a critical Peclet number, which becomes small for large system sizes. We find a supercritical swimming bifurcation for a symmetric swimmer and an avoided bifurcation in the presence of an asymmetry.Graphic abstract

Computational fluid dynamics modeling of uranium(VI) transport through hollow fiber supported liquid membrane

ABSTRACT Uranium(VI) ions transport through hollow fibre supported liquid membrane (HFSLM) using TBP (tri-n-butyl phosphate) in n-dodecane as the extractant and 0.01 M HNO3 as strippant is modelled by using Computational Fluid Dynamics (CFD) model for once-through the mode of operation. The model solves the momentum transport equation for the feed on the lumen side and the stripping phase on the shell side. The species transport equation is solved for the feed on the lumen side, the liquid membrane phase within the pores of the lumen and the stripping phase on the shell side. The boundary conditions of flux continuity and concentration jump at the feed-liquid membrane and the liquid membrane–strip interfaces are implemented. The results obtained from the CFD model at different parametric conditions are compared with the experimental data and found a good agreement between them. Validated CFD model is used to have in-depth insights into mass transfer phenomena at different hydrodynamic and chemical conditions. The effect of geometry on mass transfer is also evaluated. Overall this study will give valuable input to the supported liquid membrane (SLM) processes using hollow fibre contactor in the optimization of process design, operation and scale-up.

Sensitivity of spatial aerosol particle distributions to the boundary conditions in the PALM model system 6.0

Abstract. High-resolution modelling is needed to understand urban air quality and pollutant dispersion in detail. Recently, the PALM model system 6.0, which is based on large-eddy simulation (LES), was extended with the detailed Sectional Aerosol module for Large Scale Applications (SALSA) v2.0 to enable studying the complex interactions between the turbulent flow field and aerosol dynamic processes. This study represents an extensive evaluation of the modelling system against the horizontal and vertical distributions of aerosol particles measured using a mobile laboratory and a drone in an urban neighbourhood in Helsinki, Finland. Specific emphasis is on the model sensitivity of aerosol particle concentrations, size distributions and chemical compositions to boundary conditions of meteorological variables and aerosol background concentrations. The meteorological boundary conditions are taken from both a numerical weather prediction model and observations, which occasionally differ strongly. Yet, the model shows good agreement with measurements (fractional bias &lt;0.67, normalised mean squared error &lt;6, fraction of the data within a factor of 2 &gt;0.3, normalised mean bias factor &lt;0.25 and normalised mean absolute error factor &lt;0.35) with respect to both horizontal and vertical distribution of aerosol particles, their size distribution and chemical composition. The horizontal distribution is most sensitive to the wind speed and atmospheric stratification, and vertical distribution to the wind direction. The aerosol number size distribution is mainly governed by the flow field along the main street with high traffic rates and in its surroundings by the background concentrations. The results emphasise the importance of correct meteorological and aerosol background boundary conditions, in addition to accurate emission estimates and detailed model physics, in quantitative high-resolution air pollution modelling and future urban LES studies.

Gas diffusion coefficient estimation of coal: A dimensionless numerical method and its experimental validation

The diffusion coefficient is one of the key parameters to control gas desorption and transport kinetics in coal with pressure evolution. Accurate estimation of diffusion coefficient of coal is of great significance for coalbed methane production planning and coal mine gas control management. However, the most commonly used analytical method was found to underestimate the gas diffusion coefficient due the assumption of constant surface concentration in solving the Fick diffusion model. This study conducted a series of experiments to measure the gas adsorption and diffusion using the volumetric method. The Fick diffusion model was solved by both analytical method and the numerical method to estimate the gas diffusion coefficient based on the experimental data. We compared estimated diffusion coefficients from both the analytical and numerical approaches. It is found that the diffusion coefficient is a pressure dependent parameter and it negatively correlates with the pressure. The gas diffusivity in coal is also a gas type-dependent property. As observed, the CO2 diffusion coefficients were found to be higher than of CH4. It suggests CO2 molecules diffuse faster than CH4 molecules through the same porous coal matrix. This may be attributed to CO2 molecules own relative smaller kinetic diameter than CH4 molecules. The analytical method will underestimate the gas diffusion coefficient because it assumes a constant gas concentration boundary condition. The numerical method is a better representation of the real gas diffusion process and we recommend to using the numerical method for the diffusion coefficient estimation if possible.