Permeability Parameters Research Articles

Numerical study of chemical reaction and heat transfer of MHD slip flow with Joule heating and Soret–Dufour effect over an exponentially stretching sheet

AbstractA study of Soret–Dufour effects along with chemical reaction, viscous dissipation combining on MHD Joule heating for viscous incompressible flow is presented. It is assumed that fluid is flowing past an angled stretching sheet saturated in porous means. The slip conditions of velocity, concentration, and temperature are accounted for at the boundary. The mathematical expression of the problem contains highly nonlinear interconnected partial differential equations. To convert governing equations into ordinary differential equations, appropriate similarity transformations were utilized. These differential equations with boundary constraints are resolved by homotopy analysis method. Expression for velocity, concentration, and temperature are derived in the form of series. Effects of numerous physical parameters, for example, Schmidt number, Soret number, buoyancy ratio parameter, slip parameter, and so forth, on various flow characteristics are presented through graphs. Numerous values of velocity, concentration, and temperature gradient are tabulated against different parameters. Results show that the fluid velocity increases by enhancing the Soret number, Dufour number, or permeability parameter. The fluid's concentration rises as the Soret number increases, while it falls as the Dufour number, chemical reaction parameter, or permeability parameter increases.

An Inclination in Thermal Energy Using Nanoparticles with Casson Liquid Past an Expanding Porous Surface

The physical aspects of inclined MHD nanofluid toward a stretching sheet embedded in a porous medium were visualized, which has numerous applications in industry. Two types of nanoparticles, namely copper and aluminum oxide, were used, with water (limiting case of Casson liquid) as the base fluid. Similarity transformations were used to convert the partial differential equations into a set of ordinary differential equations. Closed solutions were found to examine the velocity and temperature profiles. It was observed that an increment in the magnitude of the Hartmann number, solid volume fraction, and velocity slip parameter brought a reduction in the velocity profile, and the opposite behavior was shown for the permeability parameter in Cu–water and Al2O3–water nanofluids. The temperature field, local skin friction, and local Nusselt number were further examined. Moreover, the study of Cu and Al2O3 is useful to boost the efficiency of thermal conductivity and thermal energy in particles. Reduction was captured in the velocity gradient and temperature gradient against changes in the thermal radiation number. The opposite trend was tabulated into motion with respect to the volume fraction number for both cases (Cu–water and Al2O3–water).

Research progress on characterization and simulation of shale oil flow in microscale

Clarifying the mechanisms of confined fluid flow in nanoscale space and calculating the permeability and other microscopic parameters are crucial to enhance the recovery of shale oil, which have attracted great attention in recent years. We review the micro flow mechanisms and numerical methods of shale oil, and discuss the effects of the solid-liquid molecular interaction force which leads to boundary slip and viscosity/density heterogeneity on the shale oil flow behaviors. Firstly, we introduce the four analytical models of confined fluid flow in nanopores which are the region-separation model, the effective viscosity model, the apparent viscosity model and the apparent slip length model. Then, we summarize the simulation methods and the applications in the study of fluid flow in nanoporous media Among them, the direct simulation methods are the molecular dynamics simulation (MDS) method and the pore-scale lattice Boltzmann simulation method (LBM), and the indirect simulation methods are the pore network model (PNM) and the coupled direct-indirect simulation method . We discuss the advantages and disadvantages of each simulation method. Finally, on the basis of summarizing the advantages and disadvantages of research results, the future research directions are put forward.

A non-Darcy gas flow model for coalbed methane in mine gobs

The expected extraction efficiency of coalbed methane (CBM) depends significantly on the laws considered to govern its gas flow. This study applies a non-Darcy gas flow model to describe the CBM migration in mine gobs; by mine gob, we mean that it is a fractured zone along with massive cracks and the primary place where gas flows after mining activities. A permeation experiment involving crushed sandstone is first conducted to prove the CBM undergoes Forchheimer-type non-Darcy flow. Subsequently, the three-dimensional continuous distribution functions of the permeability parameters are determined. The non-Darcy flow model includes the influence of inertial force on the gas flow, which is neglected in the Darcy model. A coupling model is established based on the experimental results and the gas flow characteristics in different regions. Thereafter, the model and distribution functions are applied to a series of numerical simulations of CBM extraction at the Sihe coal mine in China, to ascertain the most appropriate location for a ground borehole. These simulations involve boreholes placed in three different zones: the natural accumulation zone (NAZ), the load affected zone (LAZ), and the compaction stable zone (CSZ). The simulation results show that the total extraction quantity expected from the borehole in the NAZ is 2.4 and 13.5 times that from the boreholes in the LAZ and CSZ, respectively. This confirms that the NAZ is the most suitable zone for a borehole. This research ultimately provides a realistic gas flow model for CBM extraction from mine gobs.

Immiscible/Near-Miscible relative permeability for confined fluids at high-pressure and high-temperature for a fractal reservoir

The complex interaction between fluids and solids in reservoirs includes interface slip, capillary confinement and the diffusion and mass transfer between CO2 and oil and results in intensely nonlinear flow complexity. This study proposes a relative permeability model that accommodates a fractal pore size distribution and honors these complex process interactions. The relative permeability to CO2 flooding, in the near-miscible region, is predicted through interpolation based on the Gibbs free energy (GFE). The thermodynamic phase behavior of the fluids in the nanopores is considered by applying critical shifts in the temperatures and pressures. A volume-translated Peng-Robinson equation of state is used to calculate the CO2 and n-alkane densities to high reservoir pressure. Fluid-based correlation and modified volumetric mixing rules are then used to extend the viscosity calculations to mixtures with heavy hydrocarbon components. Predictions from the proposed model better fit experimental observations relative to previous models similarly incorporating fractal theory. The nanopores are shown to increase the relative permeability of the non-wetting phase by decreasing the viscosity ratio of the two phases. Increasing key parameters that are related to the pore structure, e.g. the fractal dimension, Df, and critical pore radius, rc, increases the relative permeability of the non-wetting phase. The GFE-based interpolation contributes to the smooth and continuous change in the relative permeability parameters local to the critical point of the mixture, with the confined fluid more likely to be miscible at the same pressure than the bulk fluid. This model can be integrated with a compositional simulator to solve field-scale problems but accommodating the micro-scale physics of unconventional reservoirs.

Study on Non-Darcian Flow in Interlayer Shear Weakness Zones in the Basalt by High-Pressure Packer Tests

The interlayer shear weakness zone (ISWZ) is a special structural plane with different widths and spacing in stratified rock masses, it has higher permeability compared with surrounding rocks which is a risk factor for the safety of the hydropower station project. The high-pressure packer test (HPPT) by step injection is always applied to characterize the permeability of ISWZ. However, the non-Darcian flow is easy to appear under high pressure, which makes the Darcy law model no longer applicable. In this study, two non-Darcian flow analytical methods for confined aquifer were proposed to investigate the non-Darcian flow permeability parameters. The equivalent permeability coefficients of different non-Darcian models were derived as well. The in situ tests were conducted on the ISWZs at the Baihetan hydropower station to verify the proposed methods. The results indicate that the flow is non-Darcian flow in the test section from integrity to destruction during the whole HPPT process. Izbash’s law has a better fit than Forchheimer’s law in this complicated test situation. The equivalent permeability coefficients after destruction are one or two orders of magnitude larger than those before. Meanwhile, it is necessary to pay attention to the increased difference of two expressions of the equivalent permeability coefficients under higher gradient (i) or velocity (v). In general, these methods can be used to evaluate the characteristic of ISWZ to analyze the impact on engineering stability.

Implementation of the Green-Ampt Infiltration Model: Comparative between different numerical solutions

The phenomena of infiltration and the percolation of water in the soil are of fundamental importance for the evaluation of runoff, groundwater recharge, evapotranspiration, soil erosion and transport of chemical substances in surface and groundwater. Within this context, the quantitative determination of the infiltration values is extremely important for the different areas of knowledge, in order to evaluate, mainly the surface runoff. Several types of changes in vegetation cover and topography result in significant changes in the infiltration process, making it necessary to use mathematical models to assess the consequences of these changes. Thus, this article aims to implement the Green-Ampt model using two numerical methods - Newton-Raphson method and W-Lambert function - to determine soil permeability parameters - K and matric potential multiplied by the difference between initial and of saturation - comparing them to the real data obtained in simulations using an automatic rainfall simulator from the Federal University of Goiás - UFG. The Green-Ampt model adjusted well to the data measured from the rain simulator, with a determination coefficient of 0.978 for the Newton-Raphson method and 0.984 for the W-Lambert function.

Spectral computation of reactive bi-directional hydromagnetic non-Newtonian convection flow from a stretching upper parabolic surface in non-Darcyporous medium

This paper presents a mathematical model for bi-directional convection magnetohydrodynamic (MHD) tangent hyperbolic nanofluid flow from the upper horizontal subsurface of a stretching parabolic surface to a non-Darcian porous medium, as a simulation of nanocoating. Chemical reaction, activation energy and thermo solutal buoyancy effects are included. The Darcy–Brinkman–Forchheimer model is deployed which permits the analysis of inertial (second order) porous drag effects. The Buongiorno nanoscale model is deployed which includes Brownian motion and thermophoresis effects. The dimensionless, transformed, nonlinear, coupled ordinary differential equations are solved by implementing the spectral relaxation method (SRM). Validation with previous studies is included. The numerical influence of key parameters on transport characteristics is evaluated and visualized graphically. Velocity is elevated (and momentum boundary layer thickness is reduced) with increasing wall thickness parameter, permeability parameter, Forchheimer parameter, Weissenberg (rheological) parameter and modified Hartmann (magnetic body force) number. Velocity enhancement is also computed with increment in stretching rate parameter, rheological power-law index, thermal Grashof number, and species (solutal) Grashof number, and momentum boundary layer thickness diminishes. Temperature is suppressed with increasing stretching rate index and Prandtl number whereas it is substantially elevated with increasing Brownian motion and thermophoresis parameters. Velocity and temperature profiles are reduced adjacent to the parabolic surface with larger wall thickness parameter for stretching rate index [Formula: see text]1, whereas the reverse behavior is observed for stretching rate index [Formula: see text]1. Nanoparticle concentration magnitude is depleted with larger numeric of Lewis number and the Brownian motion parameter, whereas it is enhanced with greater values of the stretching index and thermophoresis parameter. The nanoparticle concentration magnitude is reduced with an increase in chemical reaction rate parameter whereas it is boosted with activation energy parameter. Skin friction, Nusselt number and Sherwood number are also computed. The study is relevant to electromagnetic nanomaterials coating processes with complex chemical reactions.

Two‐phase fluid motion through porous medium with volume fraction: An application of MATLAB bvp4c solver technique

AbstractIn this paper, we have attempted to study the steady two‐dimensional hydromagnetic convective flow through porous medium and heat transfer effects. Fluid is containing dust particles and is moving under the influence of Lorentz, buoyancy, Darcy, and viscous forces. Motion is considered to be governed by the volume fraction of the dust grains and the increment of shear stress and rate of heat transfer at the surface has been analyzed. Governing equations of the problem are converted into ordinary differential equations utilizing similarity transformations. The converted differential equations are figured numerically using the MATLAB built‐in technique bvp4c. The results are depicted in graphical forms for different values of the flow parameters. The findings are obtained considering the volume fraction and compared with the results of the previous paper. It is observed that the shear stress enhances with diminishing resistance and decreases for the higher values of the Hartmann number, permeability parameter, and volume fraction of the dust phase. Also, improving the Nusselt number gives a boost to thermal diffusivity.

Framework to characterize nonlinear flow through pervious concrete

Pervious concretes have been increasingly used since they allow for better water flow. Flow through pervious concrete is usually assessed with Darcy's law, which presupposes linearity between flow rate and hydraulic gradient. However, some researchers reported this does not always hold, especially at faster flows. In such cases, Forchheimer's law may be used. In this paper, criteria for delimiting flow regimes was applied to evaluate hydraulic behavior. Forty-two specimens had their porosities measured and were tested in a constant head permeameter. Although low to moderate hydraulic gradients were applied, resulting flows already showed to be non-Darcian. A dimensionless permeability parameter engendered by the mentioned approach was able to adequately and unequivocally grade the flow resistance offered by each specimen. Correlations between this parameter and porosity were obtained and bestowed rich interpretations of how heterogeneity in pervious concretes impacts flow behavior. This may be key for designing better pervious concretes.

Analytical solution based on BEM to oblique waves scattering by thin arc-shaped permeable barrier applied for array of aquaculture cages

In this paper, linear oblique wave incident to a thin arc-shaped permeable barrier and an array of permeable circular cylinders was studied analytically. Two unique research objectives of this work include, considering the thickness for permeable material and the wavefield inside surrounded region by the permeable structure. The conventional boundary element method (BEM) is used to solve the governing equations of the problem. The mathematical relation between Bessel functions leads to representing the BEM-related integrals in the Fourier modes of Hankel function. This approach is useful as the singular integrals are accounted indirectly. Two basic geometries made by the permeable material are studied, including an arc-shaped and a circular geometry. The first geometry can represent a wave-breaking barrier in shallow water, while the latter can represent a floating fish farm in deep water. For the floating fish farm, the study is extended to the interaction between an array of cages. To quantify the amount of wave energy passed through the object, the Energy Transmission Index or ETI concept is introduced. ETI can be used as an indicator for permeable barriers performance.The results indicate that ETI is mostly a function of permeability rather than the wavenumber. In addition, the imaginary part of the permeability parameter plays an essential role in the problem of wave incident to permeable barrier, and it is necessary to be determined with enough accuracy. Furthermore, the shear force and bending moment on the base of the barrier and drift force and heeling moment on circular cylinders are studied. The results show, the drift force decreases as permeability and wavenumber increase. The results of this research are useful in the design of rigid circular offshore aquaculture fish cages and coastal barriers.

Implementing renewable solar energy in presence of Maxwell nanofluid in parabolic trough solar collector: a computational study

The solar radiations are absorbed in the form of heat energy by using the solar centering systems in solar collectors, this energy is then transmitted to nanofluid. This study concerns the production of entropy in a Maxwell nanofluid passed over an infinite horizontal surface. Then the non-linear stretching of the surface causes a flow in parabolic trough solar collector (PTSC). The similarity transformations are employed to transmute the system of PDEs into a system of solvable ODEs provided with the boundary conditions. Eventually, the classical Keller box scheme is applied to find the numerical solutions of transmutes ODEs. The analysis of two distinct nanofluids including copper-engine oil (Cu-EO) and zirconium dioxide-engine oil ZrO2-EO is taken into account and the results for both of them are discussed. The extracted results demonstrate a decline in Nusselt number with growing permeable media parameter and augmentation for increasing values of skin friction coefficient. A recent study is presented to provide information related to the enhancement of heat collector in the PTSC with Maxwell nanofluid. The minimal level of efficiency of Cu-EO over ZrO2-EO is 7.1% and the maximum level is up to 18.7%.

A Significant Solar Energy Note on Powell-Eyring Nanofluid with Thermal Jump Conditions: Implementing Cattaneo-Christov Heat Flux Model

PTSCs (parabolic trough solar collectors) are widely employed in solar-thermal applications to attain high temperatures. The purpose of this study is to determine how much entropy is created when Powell-Eyring nanofluid (P-ENF) flows across porous media on a horizontal plane under thermal jump circumstances. The flow in PTSC was generated by nonlinear surface stretching, thermal radiation, and Cattaneo-Christov heat flux, which was utilized to compute heat flux in the thermal boundary layer. Using a similarity transformation approach, partial differential equations were converted into ordinary differential equations with boundary constraints. Then, the boundary restrictions and partial differential equations were merged to form a single set of nonlinear ordinary differential equations. To obtain approximate solutions to ordinary differential equations, the Keller-Box approach is utilized. Nanofluids derived from silver- and copper-based engine oil (EO) has been employed as working fluids. The researchers observed that changing the permeability parameter reduced the Nusselt number while increasing the skin frictional coefficient. Total entropy variation was also calculated using the Brinkman number for flow rates with Reynolds number and viscosity changes. The key result is that thermal efficiency is inversely proportional to particular entropy production. For example, using Cu-EO nanofluid instead of Ag-EO nanofluid increased the heat transport rate efficiency to 15–36%.

Experimental Study on Mechanical Properties and Seepage Laws of Raw Coal under Variable Loading and Unloading Rates

This manuscript studied the effects of variable axial pressure loading rate and variable confining pressure unloading rate on the deformation behavior and seepage characteristics of raw coal under alternate loading and unloading of axial pressure and confining pressure. It believed that as axial stress increases, axial strain ε 1 decreases, radial strain ε 3 increases, and permeability k decreases, and ε 1 ′ , ε 3 ′ , and k ′ increase when confining pressure is decreases. With the loading of axial stress and the unloading of confining pressure, the variation amplitudes of ε 1 ′ , ε 3 ′ , and k ′ values reduce gradually. During axial stress loading, the rise in the amplitude of ε 1 is larger than that of ε 3 and the reduction in the amplitude of k , indicating that ε 1 is more sensitive to axial stress than ε 3 and k . During unloading of confining pressure, the increase rate of ε 3 is larger than that of ε 1 and k ; also, ε 3 showed a high sensitivity to confining pressure. In the stage of axial stress loading and confining pressure unloading, the evolution law of deformation and permeability parameters is basically consistent with the change in loading and unloading rate.

ANÁLISE DA INFLUÊNCIA DOS GRÃOS FINOS NOS PARÂMETROS DE CONSISTÊNCIA, CONSOLIDAÇÃO E PERMEABILIDADE DO SOLO

Os solos argilosos são frequentemente usados em aplicações de Engenharia Geotécnica. Esse fato torna relevante a ampliação do conhecimento sobre os fatores que influenciam em seus parâmetros de engenharia. Nesse sentido, o presente estudo visou avaliar a influência do percentual de grãos finos sobre os parâmetros de consistência, consolidação e permeabilidade de amostras de solo compactadas. Foram analisadas as misturas com 35, 40, 45, 50, 55, 60, 65, 70, 75 e 80%, em massa de finos. Os resultados apontaram para a influência direta dos grãos finos sobre os parâmetros analisados. Houve um aumento progressivo nos limites de Atterberg em relação ao aumento dos finos, com variação discreta do limite de plasticidade. O índice de vazios e o coeficiente de permeabilidade decaíram com o incremento de finos, apresentando uma taxa de variação decrescente ao longo da consolidação. Os Coeficientes de Consolidação foram obtidos através de duas metodologias distintas, pelo método de Taylor e pela correlação matemática de Terzaghi, que apontaram para o decréscimo sucessivo desse parâmetro ao longo do aumento finos na mistura. Contudo, o método de Taylor rendeu um conjunto de valores com os menores coeficientes de correlação, apresentando maiores desvios.
 Palavras-chave: Consolidação, Solo fino, Consistência, Compressibilidade, Permeabilidade.

A First Insight on the Interaction between Desiccation Cracking and Water Transfer in a Luvisol of Belgium

The present paper presents the interactions between water retention/evaporation and cracking during the desiccation of intact and disturbed Belgian Luvisol. The disturbed (DS) and undisturbed (NDS) samples (reduced-tillage-residue-in (RTRI) and conventional-tillage-residue-out (CTRO)) were collected from an agricultural field in Gembloux, Wallonia, Belgium. The drying experiment took place in controlled laboratory conditions at 25 °C. Moisture content, soil suction and surface cracks were monitored with a precision balance, a tensiometer and a digital camera, respectively. The image processing and analysis were performed using PCAS® and ImageJ® software. The results showed that crack formation was initiated at a stronger negative suction and a lower water content (Wc) in DS > CTRO > RTRI. The suction and the crack propagation were positively correlated until 300 kPa for the DS and far beyond the wilting point for the NDS. For the NDS, the cracking accelerated after reaching the critical water content (~20% Wc) which arrived at the end of the plateau of evaporation (40 h after crack initiation). The Krischer curve revealed that the soil pore size > 50 µm, and that it is likely that cracks are important parameters for soil permeability. The soil structure and soil fibre content could influence the crack formation dynamic during drying. The agricultural tillage management also influences the crack propagation. As retention and conductivity functions are affected by cracks, it is likely that the movement of fluids in the soil will also be affected by the cracks following a desiccation period (i.e., when the cracked soil is rewetted).

Characterization of Pliocene Biogenic Gas Reservoirs from the Western Black Sea Shelf (Romanian Offshore) by Integration of Well Logs and Core Data

The successful interpretation of open-hole well logging data relies on jointly using all available petrophysical and geological information. This paper presents relevant case studies related to the integration of well logs with core measurements for exploration wells drilled in the Romanian continental shelf area of the Western Black Sea basin. The analyzed wells targeted gas-bearing sands and silts complexes of Early Pliocene (Dacian) age, developed in a deltaic to shallow marine sedimentary environment in two distinct fields. The wireline logging programs included conventional formation evaluation logs, pressure surveys, nuclear magnetic resonance, and borehole electrical imaging logs. The core dataset comprised routine and special measurements (porosity, grain density, permeability, water saturation, and Archie parameters) carried out at quasi-reservoir confining pressure. The wireline logging suites were interpreted via a deterministic workflow, including core-derived interpretation parameters. Other core-derived parameters were used for constraining and validating the log interpretations. The results show that a problem related to the ambiguity of formation water resistivity can be overcome through resistivity–porosity dependencies constructed to include potential aquifer zones in the proximity of the Dacian gas-bearing reservoirs. This study also revealed and quantified uncertainties regarding the estimation of gas–water contacts from formation pressure surveys, which can be mitigated by the confirmation or correction of pressure-derived fluid contacts via the well log interpretation results. Lastly, we identified a probable resistivity logs suppression effect related both to high contents of capillary-bound water and also to the limited resolution of electrical logging tools in the presence of sand-shale thin bedding or laminations.

Combined PARP1-Targeted Nuclear Contrast and Reflectance Contrast Enhance Confocal Microscopic Detection of Basal Cell Carcinoma.

Reflectance confocal microscopy (RCM) with endogenous backscattered contrast can noninvasively image basal cell carcinomas (BCCs) in skin. However, BCCs present with high nuclear density, and the relatively weak backscattering from nuclei imposes a fundamental limit on contrast, detectability, and diagnostic accuracy. We investigated PARPi-FL, an exogenous nuclear poly(adenosine diphosphate ribose) polymerase (PARP1)-targeted fluorescent contrast agent, and fluorescence confocal microscopy toward improving BCC diagnosis. Methods: We tested PARP1 expression in 95 BCC tissues using immunohistochemistry, followed by PARPi-FL staining in 32 fresh surgical BCC specimens. The diagnostic accuracy of PARPi-FL contrast was evaluated in 83 surgical specimens. The optimal parameters for permeability of PARPi-FL through intact skin was tested ex vivo on 5 human skin specimens and invivo in 3 adult Yorkshire pigs. Results: We found significantly higher PARP1 expression and PARPi-FL binding in BCCs than in normal skin structures. Blinded reading of RCM-and-fluorescence confocal microscopy images by 2 experts demonstrated a higher diagnostic accuracy for BCCs with combined fluorescence and reflectance contrast than for RCM alone. Optimal parameters (time and concentration) for PARPi-FL transepidermal permeation through intact skin were successfully determined. Conclusion: Combined fluorescence and reflectance contrast may improve noninvasive BCC diagnosis with confocal microscopy.

Numerical Analysis of Effective Permeability of Concrete-Like Material With a Random Three-Phase Mesostructure

Interfacial transition zone (ITZ) is an important component of a concrete-like material. Accurately simulating the ITZ's characteristics of the concrete-like materials is a difficult process in numerical simulation. This article proposed a random three-phase mesostructural modeling method using the incorporation of random aggregate generation, Minkowski sum theory, and polygon union techniques. It was found that this method can better simulate the mesostructure and ITZ characteristics of concrete-like materials. By using this method, a random three-phase mesostructural model had been built for conducting a finite element analysis to investigate the effective permeability parameters of concrete. A good agreement between numerical and experimental results indicates the feasibility of this method in the concrete-like material analysis.

Heat transfer characteristics of MHD flow of Williamson nanofluid over an exponential permeable stretching curved surface with variable thermal conductivity

This study aims to investigate the flow of two-dimensional magnetohydrodynamics (MHD) Williamson nanofluid over the permeable exponential stretching curved surface with variable thermal conductivity and activation energy. The Navier Stokes Equation along with Williamson fluid model is used to govern the partial differential equations (PDEs) and to transfer these PDEs into ordinary differential equations (ODEs), appropriate similarity transformations are utilized. The obtained ODEs are solved numerically. The effect of the physical parameters that are Williamson fluid parameter, curvature parameter, permeability parameter, temperature factors (Biot, Brinkman, thermal conductivity, temperature ratio, temperature difference, radiation, unequal heat source/sink), suction/injection parameter, magnetic parameter, nanofluid parameters (Brownian motion, thermophoresis), activation energy factors (reaction rate, fitted rate constant), Schmidt number, on velocity, pressure, temperature, and concentration profiles are shown through graphs.