Nopparat Pochai

A water quality computation in the uniform channel

Abstract In this research, two mathematical models are used to simulate pollution due to sewage effluent in the uniform channel with varied current velocity. The first is the hydrodynamic model that provides the velocity field and elevation of the water flow. The second is the dispersion model that gives the pollutant concentration field. In the simulating processes, we used the Crank-Nicolson method to system of hydrodynamic model and the backward-implicit and central different technique to the dispersion model. The accuracy of the models are tested by the illustrative example.

Numerical simulation of groundwater measurement using alternating direction methods

Abstract The groundwater measurement is obliged to take care of the issue of need water assets in numerous dry season ranges for agricultural use. In this study, we propose a groundwater stream model demonstrate that gives the pumping rates and the infusion rates individually. The objective are to propose a simply and flexible groundwater simulation using the implicit and explicit traditional finite difference methods and alternating direction methods. The groundwater model is giving the water driven head that gives the groundwater level. The understood limited distinction technique is utilized to surmise the groundwater flow. The complex geometry in the model is considered by variable grid sizes aquifer parameters, sinks and source terms. The proposed alternating direction methods are shown that they are able to use in groundwater simulation for the real-world cases.

Stagnation Point Flow of Nanofluid over a Moving Plate with Convective Boundary Condition and Magnetohydrodynamics

A theoretical investigation is carried out to examine the effects of volume fraction of nanoparticles, suction/injection, and convective heat and mass transfer parameters on MHD stagnation point flow of water-based nanofluids (Cu and Ag). The governing partial differential equations for the fluid flow, temperature, and concentration are reduced to a system of nonlinear ordinary differential equations. The derived similarity equations and corresponding boundary conditions are solved numerically using Runge-Kutta Fehlberg fourth-fifth order method. To exhibit the effect of the controlling parameters on the dimensionless velocity, temperature, nanoparticle volume fraction, skin friction factor, and local Nusselt and local Sherwood numbers, numerical results are presented in graphical and tabular forms. It is found that the friction factor and heat and mass transfer rates increase with magnetic field and suction/injection parameters.

A water quality computation in the uniform reservoir

Abstract In this research, two mathematical models are used to simulate pollution due to sewage effluent in the uniform reservoir with varied current velocity. The first is the hydrodynamic model that provides the velocity field and elevation of the water flow. The second is the dispersion model that gives the pollutant concentration fields. In the simulating processes, we used the Lax-Wendroff method to system of hydrodynamic model and the forward in time and backward in space technique to the dispersion model. The accuracy of the models is tested by the illustrative example.

A numerical treatment of a non-dimensional form of a water quality model in the Rama-nine reservoir

Abstract The purposes of this research are to develop mathematical models and numerical methods for approximating water flow directions and pollution levels in a Rama-nine reservoir, Pathumthani, Thailand with non-uniform current. The Rama-nine reservoir is opened with two parallel canals. The pollution levels in a reservoir are assessing via data collection at the real field. It is quite complex and the results obtained tentatively deviate from one point of time and position to another. There are many research works applied a mathematical model called the dispersion model to estimate the water pollutant concentration. The approximation accuracy received is seemingly unsatisfied, especially, when the water flow is not uniformly distributed.The research begins with revising a mathematical model that combines two existing mathematical models: a non-dimensional form of hydrodynamic model and a dispersion model. The model is to make suitable to the Rama-nine reservoir.The Lax- Wendroff method is subsequently used in a non-dimensional form of a shallow water equation to approximate the water velocity and elevation. Next, we use the forward differences in time and backward difference in space in advection-diffusion equation. Combined the equation with the calculated velocity is thus used in the dispersion model to approximate the concentration levels of the pollutants. The result of this research showed that the proposed concentration of the pollutants in a Rama-nine reservoir at any various time and position. The accuracy of approximation is within the units of centimeters and seconds. In addition, this research has shown that the proposed model can be applied to other water sources having non-uniformly distributed water flows.

Comparison of Optimal Homotopy Asymptotic and Adomian Decomposition Methods for a Thin Film Flow of a Third Grade Fluid on a Moving Belt

We have investigated a thin film flow of a third grade fluid on a moving belt using a powerful and relatively new approximate analytical technique known as optimal homotopy asymptotic method (OHAM). The variation of velocity profile for different parameters is compared with the numerical values obtained by Runge-Kutta Fehlberg fourth-fifth order method and with Adomian Decomposition Method (ADM). An interesting result of the analysis is that the three terms OHAM solution is more accurate than five terms of the ADM solution and this thus confirms the feasibility of the proposed method.

Analytical Investigation of Magnetohydrodynamic Flow over a Nonlinear Porous Stretching Sheet

We investigated the magnetohydrodynamic (MHD) boundary layer flow over a nonlinear porous stretching sheet with the help of semianalytical method known as optimal homotopy asymptotic method (OHAM). The effects of different parameters on fluid flow are investigated and discussed. The obtained results are compared with numerical Runge-Kutta-Fehlberg fourth-fifth-order method. It is found that the OHAM solution agrees well with numerical as well as published data for different assigned values of parameters; this thus indicates the feasibility of the proposed method (OHAM).

Asymptotic Solution for a Water Quality Model in a Uniform Stream

We employ approximate analytical method, namely, Optimal Homotopy Asymptotic Method (OHAM), to investigate a one-dimensional steady advection-diffusion-reaction equation with variable inputs arises in the mathematical modeling of dispersion of pollutants in water is proposed. Numerical values are obtained via Runge-Kutta-Fehlberg fourth-fifth order method for comparison purpose. It was found that OHAM solution agrees well with the numerical solution. An example is included to demonstrate the efficiency, accuracy, and simplicity of the proposed method.

Numerical Simulation to Air Pollution Emission Control near an Industrial Zone

A rapid industrial development causes several environment pollution problems. One of the main problems is air pollution, which affects human health and the environment. The consideration of an air pollutant has to focus on a polluted source. An industrial factory is an important reason that releases the air pollutant into the atmosphere. Thus a mathematical model, an atmospheric diffusion model, is used to estimate air quality that can be used to describe the sulfur dioxide dispersion. In this research, numerical simulations to air pollution measurement near industrial zone are proposed. The air pollution control strategies are simulated to achieve desired pollutant concentration levels. The monitoring points are installed to detect the air pollution concentration data. The numerical experiment of air pollution consisted of different situations such as normal and controlled emissions. The air pollutant concentration is approximated by using an explicit finite difference technique. The solutions of calculated air pollutant concentration in each controlled and uncontrolled point source at the monitoring points are compared. The air pollutant concentration levels for each monitoring point are controlled to be at or below the national air quality standard near industrial zone index.

Optimal Homotopy Asymptotic Solution for Exothermic Reactions Model with Constant Heat Source in a Porous Medium

The heat flow patterns profiles are required for heat transfer simulation in each type of the thermal insulation. The exothermic reaction models in porous medium can prescribe the problems in the form of nonlinear ordinary differential equations. In this research, the driving force model due to the temperature gradients is considered. A governing equation of the model is restricted into an energy balance equation that provides the temperature profile in conduction state with constant heat source on the steady state. The proposed optimal homotopy asymptotic method (OHAM) is used to compute the solutions of the exothermic reactions equation.