Numerical Modeling of Contaminant Transport with Spatially-Dependent Dispersion and Non-Linear Chemical Reaction

A one-dimensional advective-dispersive contaminant transport model with scale-dependent dispersion coefficient in the presence of a nonlinear chemical reaction of arbitrary order is considered. Two types of variations of the dispersion coefficient with the downstream distance are considered. The first type assumes that the dispersivity increases as a polynomial function with distance while the other assumes an exponentiallyincreasing function. Since the general problem is nonlinear and possesses no analytical solutions, a numerical solution based on an efficient implicit iterative tri-diagonal finitedifference method is obtained. Comparisons with previously published analytical and numerical solutions for special cases of the main transport equation are performed and found to be in excellent agreement. A parametric study of all physical parameters is conducted and the results are presented graphically to illustrate interesting features of the solutions. It is found that the chemical reaction order and rate coefficient have significant effects on the contaminant concentration profiles. Furthermore, the scale-dependent polynomial type dispersion coefficient is predicted to obtain significant changes in the contaminant concentration at all dimensionless time stages compared with the constant dispersion case. However, relatively smaller changes in the concentration level are predicted for the exponentially-increasing dispersion coefficient

Transient Laminar MHD Free Convective Flow past a Vertical Cone with Non-Uniform Surface Heat Flux

Numerical solution of unsteady laminar free convection from an incompressible viscous fluid flow past a vertical cone with non-uniform surface heat flux qw(x) = axm varying as a power function of the distance from the apex of the cone (x = 0) in the presence of a transverse magnetic field applied normal to the surface is considered. The dimensionless governing coupled partial differential boundary layer equations are formulated and solved numerically using an efficient and unconditionally stable finite-difference scheme of the Crank-Nicolson type. The numerical results are validated by comparisons with previously published work and are found to be in excellent agreement. The velocity and temperature fields have been studied for various combinations of physical parameters (Prandtl number Pr, exponent and magnetic parameter M). The local as well as the average skin-friction parameter and the Nusselt number are also presented and analyzed graphically

Unsteady Laminar Free Convection from a Vertical Cone with Uniform Surface Heat Flux

Numerical solutions of, unsteady laminar free convection from an incompressible viscous fluid past a vertical cone with uniform surface heat flux is presented in this paper. The dimensionless governing equations of the flow that are unsteady, coupled and non-linear partial differential equations are solved by an efficient, accurate and unconditionally stable finite difference scheme of Crank-Nicolson type. The velocity and temperature fields have been studied for various parameters Prandtl number and semi vertical angle. The local as well as average skin-friction and Nusselt number are also presented and analyzed graphically. The present results are compared with available results in literature and are found to be in good agreement

Unsteady Laminar Natural Convection from a Non-Isothermal Vertical Cone

Natural convection effects of the numerical solution for unsteady, laminar, free convection flow over an incompressible viscous fluid past a non-isothermal vertical cone with surface temperature T′w(x) = T′∞ + axn varying as power function of distance from the apex (x = 0) is presented here. The dimensionless governing equations of the flow that are unsteady, coupled and non-linear partial differential equations are solved by an efficient, accurate and unconditionally stable finite difference scheme of Crank-Nicolson type. The velocity and temperature fields have been studied for various parameters Prandtl number, semi vertical angle 0◦ < φ < 90◦ and n. The local as well as average skin-friction and Nusselt number are also presented and analyzed graphically. The present results are compared with available results in literature and are found to be in good agreement

Unsteady natural convective power-law fluid flow past a vertical plate embedded in a non-Darcian porous medium in the presence of a homogeneous chemical reaction

A numerical solution is presented for unsteady coupled heat and mass transfer by natural convection from a non-Newtonian power-law fluid flow past a vertical plate embedded in a non-Darcian porous medium in the presence of viscous dissipation and chemical reaction effects. The governing equations are formulated and a numerical solution is obtained by using an explicit finite-difference scheme. The solutions at each time step have been found to reach the steady state solution properly. The numerical results are presented in tabular and graphical form to show the effects of material parameters of the problem on the solution

Unsteady Oscillatory Flow and Heat Transfer in a Horizontal Composite Porous Medium Channel

The problem of unsteady oscillatory flow and heat transfer in a horizontal composite porous medium is performed. The flow is modeled using the Darcy-Brinkman equation. The viscous and Darcian dissipation terms are also included in the energy equation. The partial differential equations governing the flow and heat transfer are solved analytically using two-term harmonic and non-harmonic functions in both regions of the channel. Effect of the physical parameters such as the porous medium parameter, ratio of viscosity, oscillation amplitude, conductivity ratio, Prandtl number and the Eckert number on the velocity and/or temperature fields are shown graphically. It is observed that both the velocity and temperature fields in the channel decrease as either of the porous medium parameter or the viscosity ratio increases while they increase with increases in the oscillation amplitude. Also, increasing the thermal conductivity ratio is found to suppress the temperature in both regions of the channel. The effects of the Prandtl and Eckert numbers are found to decrease the thermal state in the channel as well

MHD Flow of a Micropolar Fluid past a Stretched Permeable Surface with Heat Generation or Absorption

This work considers steady, laminar, MHD flow of a micropolar fluid past a stretched semi-infinite, vertical and permeable surface in the presence of temperature dependent heat generation or absorption, magnetic field and thermal radiation effects. A set of similarity parameters is employed to convert the governing partial differential equations into ordinary differential equations. The obtained self-similar equations are solved numerically by an efficient implicit, iterative, finite-difference method. The obtained results are checked against previously published work for special cases of the problem in order to access the accuarcy of the numerical method and found to be in excellent agreement. A parametric study illustrating the influence of the various physical parameters on the skin friction coefficient, microrotaion coefficient or wall couple stress as well as the wall heat transfer coefficient or Nusselt number is conducted. The obtained results are presented graphically and in tabular form and the physical aspects of the problem are discussed

Transient Mixed Convection Flow of A Second-Grade Visco-Elastic Fluid over a Vertical Surface

The viscoelastic boundary layer flow and mixed convection heat transfer near a vertical isothermal surface have been examined in this paper. The governing equations are formulated and solved numerically using an explicit finite difference technique. The velocity and temperature profiles, boundary layer thicknesses, Nusselt numbers and the local skin friction coefficients are shown graphically for different values of the viscoelsatic parameter. In general, it is found that the velocity decreases inside the boundary layer as the viscoelsatic parameter is increased and consequently, the local Nusselt number decreases. This is due to higher tensile stresses between viscoelsatic fluid layers which has a retardation effects on the motion of these layers and consequently, on the heat transfer rates for the mixed convection heat transfer problem under investigation. A Comparison with available published results on special cases of the problem shows excellent agreement

Similarity Solution for Unsteady MHD Flow Near a Stagnation Point of a Three-Dimensional Porous Body with Heat and Mass Transfer, Heat Generation/Absorption and Chemical Reaction

The problem of unsteady mixed convection heat and mass transfer near the stagnation point of a three-dimensional porous body in the presence of magnetic field, chemical reaction and heat source or sink is analyzed. An efficient, iterative, tri-diagonal implicit finite difference method is used to solve the transformed similarity equations in the boundary layer. Three cases were considered, namely, accelerating flow, decelerating flow and the steady-state case. The obtained results are presented in graphical and tabulated forms to illustrate the influence of the different physical parameters such as the magnetic field parameter, transpiration parameter, unsteadiness parameter, ratio of velocity gradients at the edge of the boundary layer parameter, heat generation/absorption parameter and the chemical reaction parameter on the velocity components in the x-and y- directions, temperature and concentration distributions, as well as the skin-friction coefficients and Nusselt and Sherwood numbers