Convective Part Research Articles

Conjugate direct resistance heating of metallic plates. multiplicities and stability

A numerical bifurcation analysis is presented for an industrial application where direct resistance heating through a DC is applied to a flat metallic plate, which is cooled by a turbulent boundary layer and radiation. The process is modeled with a conjugate heat transfer between the plate and the cooling air steam. The convective part of the heat transfer mechanism is formulated in the framework of an integral approach, considering a turbulent core based on power law velocity and temperature profiles and a thin laminar sublayer thermally coupled with axial conduction along the plate. The analysis reveals that the problem admits two solutions: one stable and one unstable, separated by a limit point. The existence of multiple solutions is a consequence of the nonlinear electric resistivity–temperature relationship, allowing thermal equilibrium between heat generation and heat dissipation in multiple points. The application of realistic boundary conditions at the wall–fluid interface shows that the thermal to the hydrodynamic boundary layer thicknesses ratio along the plate is no longer close to the value of 1.25, as it is the case with a constant wall temperature. Instead, significant deviations occur due to the thermal coupling between the wall and the cooling fluid. The multiplicity structure and, consequently, the limit points depend on the plate Reynolds number and on the conduction–convection parameter. The locus of the limit points defines an instability threshold beyond which any excess applied current will trigger a thermal runaway phenomenon. This is also an equivalent of the maximum current carrying capacity of the plate.

Microphysical Prescriptions for Parameterized Water Cloud Formation on Ultra-cool Substellar Objects

Water must condense into ice clouds in the coldest brown dwarfs and exoplanets. When they form, these icy clouds change the emergent spectra, temperature structure, and albedo of the substellar atmosphere. The properties of clouds are governed by complex microphysics but these complexities are often not captured by the simpler parameterized cloud models used in climate models or retrieval models. Here, we combine microphysical cloud modeling and 1D climate modeling to incorporate insights from microphysical models into a self-consistent, parameterized cloud model. Using the 1D Community Aerosol and Radiation Model for Atmospheres (CARMA), we generate microphysical water clouds and compare their properties with those from the widely used EddySed cloud model for a grid of Y dwarfs. We find that the mass of water condensate in our CARMA water clouds is significantly limited by available condensation nuclei; in models without additional seed particles for clouds added, the atmosphere becomes supersaturated. We incorporate water latent heat release in the convective and radiative parts of the atmosphere and find no significant impact on water-ice cloud formation for typical gas giant compositions. Our analysis reveals the CARMA cloud profiles have a gradual decrease in opacity of approximately 4% per bar below the cloud base. Incorporating this gradual cloud base falloff and a variable f sed parameter allows spectra generated from the parameterized Eddysed model to better match those of the microphysical CARMA model. This work provides recommendations for efficiently generating microphysically informed water clouds for future models of cold substellar objects with H/He atmospheres.

On the study of three-dimensional compressible Navier–Stokes equations

This work is devoted to the study of three-dimensional compressible Navier–Stokes equations on unstructured meshes. The approach used is based on separating the convection and diffusion parts. The convective flux is computed using the Godunov method. For the diffusive part, we present a new finite volume scheme. Numerical results are provided to demonstrate the efficiency of the developed technique.

Nowcasting convective activity for the Sahel: A simple probabilistic approach using real‐time and historical satellite data on cloud‐top temperature

AbstractFlash flooding from intense rainfall frequently results in major damage and loss of life across Africa. In the Sahel, automatic prediction and warning systems for these events, driven by Mesoscale Convective Systems (MCSs), are limited, and Numerical Weather Prediction (NWP) forecasts continue to have little skill. The ground observation network is also sparse, and very few operational meteorological radars exist to facilitate conventional nowcasting approaches. Focusing on the western Sahel, we present a novel approach for producing probabilistic nowcasts of convective activity out to six hours ahead, using the current location of observed convection. Convective parts of the MCS, associated with extreme and heavy precipitation, are identified from 16 years of Meteosat Second Generation thermal–infrared cloud‐top temperature data, and an offline database of location‐conditioned probabilities calculated. From this database, real‐time nowcasts can be quickly produced with minimal calculation. The nowcasts give the probability of convection occurring within a square neighbourhood surrounding each grid point, accounting for the inherent unpredictability of convection at small scales. Compared to a climatological reference, formal verification approaches show the nowcasts to be skilful at predicting convective activity over the study region, for all times of day and out to the six‐hour lead time considered. The nowcasts are also skilful at capturing extreme 24‐hour rain gauge accumulations over Dakar, Senegal. The nowcast skill peaks in the afternoon, with a minimum in the evening. We find that the optimum neighbourhood size varies with lead time, from 10 km at the nowcast origin to around 100 km at a six‐hour lead time. This simple and skilful nowcasting method could be highly valuable for operational warnings across West Africa and other regions with long‐lived thunderstorms, and help to reduce the impacts from heavy rainfall and flooding.

Flux-corrected transport stabilization of an evolutionary cross-diffusion cancer invasion model

In the present work, we investigate a model of the invasion of healthy tissue by cancer cells which is described by a system of nonlinear PDEs consisting of a cross-diffusion-reaction equation and two additional nonlinear ordinary differential equations. We show that when the convective part of the system, the haptotaxis term, is dominant, then straightforward numerical methods for the studied system may be unstable. We present an implicit finite element method using conforming P1 or Q1 finite elements to discretize the model in space and the θ-method for discretization in time. The discrete problem is stabilized using a nonlinear flux-corrected transport approach. It is proved that both the nonlinear scheme and the linearized problems used in fixed-point iterations are solvable and positivity preserving. Several numerical experiments are presented in 2D to demonstrate the performance of the proposed method.

Development of technology for ingots production using electroslag remelting at direct current with consumable electrode rotation

The paper describes the problem of increasing the productivity of electroslag remelting (ESR) furnaces. The remelting technology on direct current is proposed as the most effective method. The description of the technology touches upon positive and negative effects affecting the specific productivity of smelting, energy consumption, and quality of the obtained ingots in terms of their physical and mechanical properties and chemical purity. The authors proposed the electroslag remelting method with rotation of the consumable electrode as a new technology, and realized a brief comparison with the external magnetic field application technology. The schemes that clearly demonstrate the principle of controlling the crystallization front shape and the thermal center localization in the slag bath are considered. A stationary numerical model for the slag bath of the operating semi-industrial furnace ESR A-550 on direct current with polarity reversing ability was developed. The mathematical apparatus consisting of electrothermal, hydrodynamic and convective parts was constructed. The authors designed the mesh domain for a slag bath located between the consumable electrode and the water-cooled crystallizer with diameters of 60 and 90 mm, respectively. The height of the sub-electrode zone is 10 mm. The current limit is 800 A and the voltage is 46 V. Numerical fields of current density and temperature distribution in the slag bath volume are obtained. The range of temperature values is located in the range from 1400 to 2200 °C at the peripheral and subelectrode zones of the slag bath, respectively. The scheme of the ESR furnace modernization is given in terms of mechanical part automation and transferring to direct current.

Calculation of reconstruction volumes of hot-water boilers during the transition to a methane-hydrogen fuel

The ongoing research provides for the development of general technical solutions for the creation of a methane-hydrogen water-heating boiler unit. The advantages of this source of thermal energy over similar units is the reduction in specific carbon dioxide emissions per unit of thermal energy produced, which is relevant for the decarbonization of the Russian heat and power industry. As part of the work, a mathematical model was created for the mixed thermal calculation of a hot water boiler unit (calibration for the furnace and constructive for the convective part) in the Python programming language. The calculation in the model is carried out on the basis of the normative method. Implemented the ability to calculate the conversion of the most popular standard sizes of hot water boilers to another gas composition: KVGM-10, KVGM-20, KVGM-30, KVGM-50, KVGM-100, KVGM-180, PTVM-30, PTVM-50, PTVM-100 and PTVM-180. The result of the calculation of the reconstruction of the convective part is the required area of the heat-receiving surface, which makes it possible to estimate the volume of reconstruction. The paper analyzes the volume of reconstruction of burners RGMG-10, RGMG-20 and RGMG-30 when switching to a methane-hydrogen mixture.

Effect of air layer location and depth on redistribution of convective heat transfer induced by energy source in a sandwiched porous-air-porous enclosure free from temperature difference at external boundaries

The study deals with nonlinear convection in a three-layered porous-air-porous enclosure with zero temperature difference at the external impermeable thermally conductive boundaries. The upper and lower porous matrices are internally heated with a uniform energy source. To describe redistribution of heat energy between the top and bottom surfaces of the enclosure, we introduce a relative heat transfer coefficient qr that has the conduction and convection parts. The former part tends to unity in the fully filled porous domain. The symmetry of heat transfer from the inner area towards the outer surfaces breaks down if one adds an intermediate air layer with low thermal conductivity. Two sandwiched systems which have equal depth ratio d but distinct air layer location are considered. In system 1, the air layer is located in the upper unstably stratified half of the enclosure. In system 2, this layer is in the lower stably stratified half. The total value of qr always increases due to penetrative convection. At d = 0.1, local convection in system 1 is easily initiated in contrast to the hard-to-generate large-scale convection in system 2 due to a strong destabilization. The latter most effectively enhances heat transport though the top surface with increasing the supercriticality.

Stagnant-lid convection: comparison of viscosity laws and uniform scaling approach for temperature and heat flux prediction

SUMMARY Numerical simulations of stagnant-lid convection in a 2-D Cartesian fluid heated from below are carried out in order to study how the temperature dependence of the viscosity affects the vertical profile of temperature in the model. I test different viscosity laws, including the Arrhenius law with realistic parameters for the Earth’s mantle or for icy bodies. No approximation is made, which leads to extremely high viscosity contrasts. Results are compared to different approximations, in particular the Frank–Kamenetskii (FK) one. I propose a new approach for the scaling of the temperature drop across the convective part of the layer beneath the stagnant lid. The vertical profile of temperature as a function of the viscosity law is predicted, with a uniform scaling approach for all formulations of the temperature-dependent viscosity. The predicted profiles are in very good agreement with results of 2-D numerical simulations in Cartesian geometry. The complete scaling given here provides a rapid way to compare viscosity laws and to check how approximations affect the results, in terms of interior temperature, stagnant lid thickness and heat flux, compared to the real Arrhenius law for rocky mantles and for the icy outer shells of satellites. In particular, in the context of 2-D Cartesian convection heated from below, in the stagnant-lid regime, I propose a new approach to properly scale the FK formulation when it is used as an approximation of the Arrhenius law.

An accurate, robust and efficient convection-pressure flux splitting scheme for compressible Euler flows

The popular Roe's flux difference splitting scheme has high resolution for various types of discontinuities but it fails to satisfy the entropy condition and will encounter different forms of instability while calculating shock waves, such as the post-shock oscillation of the slowly moving shock waves and the carbuncle phenomenon of the multidimensional strong shock waves. In the present work, a simple flux difference splitting scheme based on the idea of convection-pressure splitting is proposed. With application of the Toro-Vázquez splitting procedure, the flux of the 3D Euler equations is split into the convection part and the pressure part. Due to having a complete set of linearly independent eigenvectors, the pressure subsystem can be solved by the conventional flux difference splitting method. The weakly hyperbolic convection subsystem, however, does not have a complete set of linearly independent eigenvectors and thus is solved by the flux difference splitting scheme based on the generalized eigenvectors [1]. In addition, a strategy that combines the THINC reconstruction with the BVD algorithm is employed on the numerical dissipation term of the convection flux to further improve the resolution for contact discontinuities. A comprehensive range of numerical simulations for classical 1D, 2D and 3D benchmark test problems demonstrate the good performance of the proposed scheme.

A positivity-preserving implicit-explicit scheme with high order polynomial basis for compressible Navier–Stokes equations

In this paper, we are interested in constructing a scheme solving compressible Navier–Stokes equations, with desired properties including high order spatial accuracy, conservation, and positivity-preserving of density and internal energy under a standard hyperbolic type CFL constraint on the time step size, e.g., Δt=O(Δx). Strang splitting is used to approximate convection and diffusion operators separately. For the convection part, i.e., the compressible Euler equation, the high order accurate postivity-preserving Runge–Kutta discontinuous Galerkin method can be used. For the diffusion part, the equation of internal energy instead of the total energy is considered, and a first order semi-implicit time discretization is used for the ease of achieving positivity. A suitable interior penalty discontinuous Galerkin method for the stress tensor can ensure the conservation of momentum and total energy for any high order polynomial basis. In particular, positivity can be proven with Δt=O(Δx) if the Laplacian operator of internal energy is approximated by the Qk spectral element method with k=1,2,3. So the full scheme with Qk (k=1,2,3) basis is conservative and positivity-preserving with Δt=O(Δx), which is robust for demanding problems such as solutions with low density and low pressure induced by high-speed shock diffraction. Even though the full scheme is only first order accurate in time, numerical tests indicate that higher order polynomial basis produces much better numerical solutions, e.g., better resolution for capturing the roll-ups during shock reflection.

Fire exposure measurements using plate thermometers

AbstractPlate thermometers (PT) are known and utilized in fire testing for more than 30 years. They are simple devices that measure the temperature of the thin plate, made of a thermal conductor, that is exposed to fire from one side and insulated from the opposite side. The main advantage of measuring thermal exposure using a plate thermometer is its ability to capture both the convective and radiative parts of the heat flux. However, thermal exposure is not directly the value the plate thermometer outputs. For this reason, an adiabatic surface temperature (AST), which could be considered as an objective measure of thermal exposure, can be calculated on the basis of the plate thermometer output. In this work, the abilities for fire‐exposure measurements using plate thermometers are discussed.This work introduces the closed‐form analytical solution of the plate thermometer heat balance equation for an adiabatic surface temperature. The authors consider the introduced solution as the best method, at this moment, for the evaluation of AST based on the PT output. This allows several findings to be presented that are not affected by the shortcomings of previously used methods for the AST evaluation.

Conservative semi-Lagrangian method for continuity equation with various time steps in different parts of computational domain

The system of Navier Stokes differential equations describes gas flow near rocket nozzle. To find solution of this system in general case, scientists and engineers use numerical methods. Modern numerical methods do not allow engineers to model all features of gas flow. It happened because of sophisticated physical processes and limitations of computational hardware. So, at least where are two ways to improve it: to enlarge hardware or reduce computational complicacy. The global aim of many science investigations is to develop numerical approach with reduced computational complicacy and at the same time without loss of computational accuracy. In 1959, Aksel C. Wiin-Nielsen proposed a new and effective trajectories method for problem of numerical forecasting. In 1966, K. M. Magomedov developed similar approach (method of characteristics) for numerical modelling of space (three dimensional on space) gas flow. In 1982, O. Pironneau showed a new and effective approach for two dimensional approximation of the Navier Stokes problem. It was based on method of characteristics also. Nowadays, these methods are called semi-Lagrangian or Eulerian Lagrangian methods. They use Lagrangian nature of the transport process. To apply this advantage, scientists decompose each equation of Navier Stokes system into three parts: convective part (hyperbolic type), elliptic part and part of right-hand side. Scientists use semi-Lagrangian approach to approximate the convective parts of equations. To develop and test modern algorithms from family of semi-Lagrangian methods, we use continuity equation from the system of Navier Stokes equations. Conservative versions of semi-Lagrangian approach are based on Gauss Ostrogradsky (divergence) theorem. It allows scientists to get conservation low (balance equation) for numerical solution in norm of L1 space. Aim of our investigation is to use different time steps in different parts of computation domain. It enables us to obtain at the same time three advantages: convergence of numerical solution to exact solution, reduction of computational complicacy, implementation of conservation low (balance equation) without weight coefficients. For this purpose we decompose computational domain into two parts (subdomains) and use different time steps in them. Main complication is design algorithm in the boundaries of computational subdomains. We use one dimensional (on space) problem to demonstrate ability of developing numerical method with described advantages. Generalization of considered approach for two- or even three-dimensional cases allows engineers to model gas flow more accurately and without artificial viscosity. It is essentially important in the parts of computational domain with high level of solution gradient.

Extended hydrodynamical models for plasmas

We propose an extended hydrodynamical model for plasmas, based on the moments of the electron distribution function which satisfies the Fokker–Planck–Landau (FPL) transport equation. The equations for the moments can be obtained by multiplying the FPL equation by the corresponding weight functions and integrating over the velocity space. The moments are decomposed in their convective and non–convective parts and closure relations for the fluxes and production terms can be obtained by using the maximum entropy distribution function, which depends on Lagrangian multipliers. These latter can be expressed in terms of the state variables by imposing the constraints that the maximum entropy distribution function reproduces the moments chosen as state variables. In particular, we will concentrate on the 13-moment system. As a first application, we treat the case of the relaxation towards equilibrium of a homogeneous plasma with a temperature anisotropy, showing that the results are in good agreement with those obtained by means of the Kogan solution of the kinetic equation.

Local wall heating effects on aeroacoustic field radiated by an isolated square cylinder in a laminar flow

The aim of this work is to gain an insight on the effect of the wall heating on the aeroacoustic sound radiated by bluff bodies in laminar flows. In particular, the local thermal treatment of the wall boundary was investigated as a possible method for active controlling the emitted noise. This technique was studied performing direct numerical simulations of the aeroacoustic noise produced by an isolated square cylinder operating at a Reynolds and Mach numbers equal to 150 and 0.2, respectively. In the considered case, the Karman vortex street deriving by the flow/cylinder interaction, produces a lift and drag pulsation on the body surface, leading to a dipolar-like noise emission. In this context, different local thermal fluxes were applied to the cylinder wall in order to reduce its aerodynamic forces fluctuation and, consequently, the associated pressure disturbance that produces the radiated sound. The computations are performed using an OpenFOAM solver that adopts an explicit Runge-Kutta scheme for time integration and a second-order, energy conserving scheme for the convective part of the Eulerian flux. Moreover, the spurious numerical waves reflections at the far-field boundary are damped adopting a sponge-layer approach.

A 1-D/3-D coupling approach for compressible non-equilibrium two-phase flows using the Baer-Nunziato model based on the Finite-Volume framework

An efficient bi-directional 1-D/3-D coupling is here proposed for the computation of compressible two-phase flows with the use of the Baer-Nunziato model. The objective is here to couple the 3-D Baer-Nunziato model with its 1-D counterpart involving spatially varying pipe cross-sections. The present coupling acts at the common interface between three-dimensional and one-dimensional computational domains. The proposed approach is built upon the framework of the Finite-Volume method with, in particular, the exchange of the numerical fluxes coming from the approximation of both conservative and non-conservative terms of the convective part of the Baer-Nunziato model. For this purpose, local Riemann problems at the 1-D/3-D common interface are considered for the computation of the corresponding numerical conservative and non-conservative fluxes. These local Riemann problems are based on the variables associated with the 1-D domain on one side and the variables coming from the 3-D domain on the other side of the interface. The potentially non-null tangential phasic velocity components coming from the 3-D domain at the coupling interface are also considered in the local Riemann problems. In addition, adequate approximations of the non-conservative terms associated with changes of volume fraction as well as changes of cross-section are considered at the 1-D/3-D interface. As a consequence, conservation properties such as the uniform pressure and velocity profiles preservation are ensured by the present 1-D/3-D coupling. The pipe cross-section variations are also taken into account in the present method. What is more, no iterative procedure is required in the proposed approach. Several numerical shock-tubes involving both subsonic and supersonic configurations of the Baer-Nunziato model and pipe cross-section variations are then considered to assess the present 1-D/3-D coupling. The influence of the angle between the 1-D and the 3-D domains at the coupling interface is also studied. Finally, the propagation of a shock-wave in a circular tube with a sudden change in cross-section is simulated using a hybrid 1-D/3-D computation showing the potential of the proposed geometrical multi-scale strategy.

DAMPAK KENAIKAN HARGA BAHAN BAKAR MINYAK (BBM) TAHUN 2022 TERHADAP TINGKAT PENDAPATAN PEDAGANG DI PASAR CAKRANEGARA KOTA MATARAM

The increase in fuel prices always has an impact on rising production costs and transportation costs. The increase in production costs will affect the increase in the price of goods or inflation in the country. The increase in fuel prices will always be followed by an increase in commodity prices which can then increase the inflation rate. In addition, traders will automatically have to adjust the price of their merchandise from the increase in fuel prices. This study used a qualitative method with a total of 494 traders and the respondents who were taken were traders with various types of businesses such as convection, sandals, fruits, side dishes, electronics, and auto parts traders. The results showed that the income of the convection business was higher than the income after the increase in fuel prices, the type of sandal business had decreased or stabilized, the type of sandal business remained because it provided selling products through online media (buy online), the type of fruit business Fruits are stable because they take goods from their own area (local), the type of side dishes business which is a primary human need so fuel prices go up, consumers continue to buy products from side dishes, the type of electronic business has not decreased and the increase (stable) has been adjusting product prices with the cost of transportation costs, the type of spare parts business has decreased because they have not adjusted the prices of the products they sell with the prices of transporting goods from outside the island.

Convective and Turbulent Motions in Nonprecipitating Cu. Part III: Characteristics of Turbulence Motions

Abstract Velocity field in a nonprecipitating Cu under BOMEX conditions, simulated by SAM with 10-m resolution and spectral bin microphysics is separated into the convective part and the turbulent part, using a wavelet filtering. In Part II of the study properties of convective motions of this Cu were investigated. Here in Part III of the study, the parameters of cloud turbulence are calculated in the cloud updraft zone at different stages of cloud development. The main points of this study are (i) application of a fine-scale LES model of a single convective cloud allowed a direct estimation of turbulence parameters using the resolved flow in the cloud and (ii) the separation of the resolved flow into the turbulence flow and the nonturbulence flow allowed us to estimate different turbulent parameters with sufficient statistical accuracy. We calculated height and time dependences of the main turbulent parameters such as turbulence kinetic energy (TKE), spectra of TKE, dissipation rate, and the turbulent coefficient. It was found that the main source of turbulence in the cloud is buoyancy whose contribution is described by the buoyancy production term (BPT). The shear production term (SPT) increases with height and reaches its maximum near cloud top, and so does BPT. In agreement with the behavior of BPT and SPT, turbulence in the lower cloud part (below the inversion level) is weak and hardly affects the processes of mixing and entrainment. The fact that BPT is larger than SPT determines many properties of cloud turbulence. For instance, the turbulence is nonisotropic, so the vertical component of TKE is substantially larger than the horizontal components. Another consequence of the fact that BPT is larger than STP manifests itself in the finding that the turbulence spectrum largely obeys the −11/5 Bolgiano–Obukhov scaling. The classical Kolmogorov −5/3 scaling dominates for the low part of a cloud largely at the dissolving stage of cloud evolution. Using the spectra obtained we evaluated an “effective” dissipation rate which increases with height from nearly zero at cloud base up to 20 cm2 s−3 near cloud top. The coefficient of turbulent diffusion was found to increase with height and ranged from 5 m2 s−1 near cloud base to 25 m2 s−1 near cloud top. The possible role of turbulence in the process of lateral entrainment and mixing is discussed. Significance Statement 1) This study investigates the turbulent structure of Cu using a 10-m-resolution LES model with spectral bin microphysics, 2) the main source of turbulence is buoyancy, 3) turbulence in cumulus clouds (Cu) is nonisotropic, 4) turbulence reaches maximum intensity near cloud top, 5) turbulence spectrum obeys largely the −11/5 Bolgiano–Obukhov scaling, and 6) the main turbulent parameters are evaluated.

Intensification of heat-exchange of a direct-flow steam boiler of a coil type based on an educational laboratory stand

In the work under consideration, using an experimental stand formed by a cylindrical coil, the modes of air movement through the flue of a ramjet steam boiler were investigated. Experimental studies have revealed shortcomings in the operation of a direct-flow steam boiler and proposed ways to increase heat transfer in a steam boiler by turbulizing the gas-air flow in the convective part of the boiler flue. The Ansys programmable engineering environment was used to simulate the heat exchange between waste gases and water in the heat exchanger. The Ansys SpaceClaim program was used to design the geometric model. Finite element grid was created using the Ansys Icem CFD program. In the process of creation, materials were selected and designated for each part of the model, water and steam temperatures inside the heat exchanger, exhaust gas temperature, boundary conditions and heat exchange conditions between them were also set. After entering all the parameters the model calculations were carried out and the results were presented in the form of a temperature distribution diagram. In conclusion, a variant of further research of aerodynamic processes in a ramjet steam boiler and a demonstration of the selected option were presented.

Numerical approximation of convective Brinkman-Forchheimer flow with variable permeability

This paper investigates the nonlinear dispersion of a pollutant in a non-isothermal incompressible flow of a temperature-dependent viscosity fluid in a rectangular channel filled with porous materials. The Brinkman-Forch-heimer effects are incorporated and the fluid is assumed to be variably permeable through the porous channel. External pollutant injection, heat sources and nonlinear radiative heat flux of the Rossland approximation are accounted for. The nonlinear system of partial differential equations governing the velocity, temperature and pollutant concentration is presented in non-dimensional form. A convergent numerical algorithm is formulated using an upwind scheme for the convective part and a conservative-type central scheme for the diffusion parts. The convergence of the scheme is discussed and verified by numerical experiments both in the presence and absence of suction. The scheme is then used to investigate the flow and transport in the channel. The results show that the velocity decreases with increasing suction and Forchheimer parameters, but it increases with increasing porosity.