Heat Transfer in a Magnetohydrodynamic Boundary Layer Flow of a Non-Newtonian Casson Fluid Over an Exponentially Stretching Magnetized Surface

In this current paper, an investigation has been conducted on the magnetohydrodynamic boundary layer flow of non-Newtonian Casson fluids on magnetized sheet with an exponentially stretching sheet. The similarity approach has been used to transform the governing models for Casson fluid to ordinary differential equations. We presented numerical results for momentum, energy and concentration equation parameters. Effects of the magnetized sheet and varying all the emerged parameters on the flow of Casson fluid with respect to the friction between the fluid and the surface, temperature and concentration are presented in tables. As a result of the induced magnetization of the sheet, the thickness of the thermal boundary layer has been enhanced. This behaviour brings a considerable reduction to the heat transfer. The induced magnetized sheet has a similar influence on the skin friction, Nusselt number and the Sherwood number. We however proposed incorporation of magnetized surfaces in MHD flows for controlling the flow rate of the fluid and heat transfer characteristics.

An optimal control problem related to a 3D-chemotaxis-Navier-Stokes model

In this paper, we study an optimal control problem associated to a 3D-chemotaxis-Navier-Stokes model. First we prove the existence of global weak solutions of the state equations with a linear reaction term on the chemical concentration equation, and an external source on the velocity equation, both acting as controls on the system. Second, we establish aregularity criterion to get global-in-time strong solutions. Finally, we prove the existence of an optimal solution, and we establish a first-order optimality condition.

Verification of Time of Concentration Equation for Improved Drainage Design

This study focused on verifying the Time of concentration Equation for a more reliable design of drains. Tracer studies were carried out in 1000m long rectangular drains at the University of Nigeria Nsukka. Sodium Chloride which was used as the tracer was introduced at station 1 and samples were collected after 20secs simultaneously at the 9 collection points. Flow parameters including velocity and slope of channel were determined. The collected samples were analyzed in the laboratory for determination of chloride concentration in mg/l. The maximum concentration was 42.11mg/l. Thereafter the time of concentrated was computed by dividing the summation of product of concentration and measured time with the summation of concentration. Through regression analysis, a modified formula for computing time of concentration (tc). Model verification was carried out using experimental data. The results from obtained from the modified Equations were compared respectively with computed results from the commonly used Kirpich formula and measured times of concentration. The results showed no correlation between measured and computed values. There were also marked variations between results from existing and modified formulae. There is therefore need for further verification and validation of the modified Equation. This is necessary in view of the fact that a reliable prediction of time of concentration is key to a cost effective drainage design.

Aiding and opposing of mixed convection Casson nanofluid flow with chemical reactions through a porous Riga plate

In the present study, simultaneous effects of the chemical reaction and electromagnetohydrodynamic on the Casson nanofluid over porous Riga plate has been investigated. The governing flow problem consists of linear momentum, thermal energy, and nanoparticle concentration equation, which is modeled with the help of Oberbeck–Boussinesq approximation. Shooting method is employed to obtain the solution of the resulting nonlinear coupled ordinary differential equation. The behavior of the velocity profile, temperature profile, and nanoparticle concentration profile are discussed against modified Hartman number, porosity parameter, chemical reaction parameter, Prandtl number, Brownian motion parameter, thermophoresis parameter, Schmidt number, nanoparticle flux parameter, and Richardson number, respectively. The governing flow is also discussed for aiding and opposing flow by considering the negative and positive values of the modified Hartman number. The Nusselt number and Sherwood number are also computed numerically. Moreover, it is also found that the porosity parameter also enhances the velocity profile. A numerical comparison is also presented with previously published results to ensure the validity of the current methodology and results.

Assessment of Nitrogen Leaching of Cropping Pattern by Soil Nitrogen Balance Equation (Case Study: Varamin Irrigation and Drainage Network)

Nitrogen is often one of the most important limiting factors for biomass production. Usually few soils have proper amount of nitrogen, so it is usually added by fertilizers. In cropping systems, nitrogen fertilization practices can provide a sufficient nitrogen supply for plants to achieve the potential yield. However, to ensure reaching to this potential yield, farmers often apply more nitrogen fertilizers than the required nitrogen for achieving maximum yield. Nitrogen fertilizer should be given to soil according to nitrogen content of soil, water and crop nitrogen demand during the growth periods. Especially in the lands that apply wastewater and groundwater for irrigation and irrigation sources have large quantities of nitrogen, therefore we Should reduce the amount of fertilizer used in agricultural lands, In other words for planning the plant fertilizer demand, nitrogen balance in soil should be considered. Nitrogen overuse increases the risk of nitrogen leaching to groundwater, contaminating groundwater and threatening the human health. In recent years, critical plant nitrogen concentration equation is used to determine crop nitrogen demand during the different growth stages of plants. The purpose of this study is to determine the nitrogen demand of Varamin network’s cropping pattern by using the critical plant nitrogen concentration equation and comparing the result with the amount of nitrogen fertilizer commonly applied in the study area. In this study, monthly biomass production for growing period was determined based on normalized water productivity index and plant canopy development. Coefficient of critical nitrogen concentration equation for each plant was determined by previous researches. The result of this study showed that for barley, the amount of nitrogen applied in Varamin network is equal to nitrogen demand of the cropsand for wheat, maize and tomato are 25%, 61% and 18%, respectively, higher than the amount obtained from critical plant nitrogen concentration equation.also according to the results of soil Nitrogen balance in lands covered by AU canal of Varamin network, 707 ton of nitrogen entered to soil and groundwater by leaching and we should considered appropriate solutions to reduce leaching, such as using high-yielding crops that remove a significant amount of N in the harvested portion, synchronizing fertilizer application with crop demand, conjunctive use of wastewater and groundwater with proper nitrogen concentration and etc.

A Combined Discontinuous Galerkin Method for Saltwater Intrusion Problem with Splitting Mixed Procedure

In this paper, a new combined method is presented to simulate saltwater intrusion problem. A splitting positive definite mixed element method is used to solve the water head equation, and a symmetric discontinuous Galerkin (DG) finite element method is used to solve the concentration equation. The introduction of these two numerical methods not only makes the coefficient matrixes symmetric positive definite, but also does well with the discontinuous problem. The convergence of this method is considered and the optimal L2-norm error estimate is also derived.

Effects of thermal radiation and electromagnetohydrodynamics on viscous nanofluid through a Riga plate

Purpose The purpose of this paper is to analyze theoretically the effects of thermal radiation with electrohydrodynamics through a Riga plate. An incompressible and irrotational fluid with constant density is taken into account. The governing flow problem is modeled with the help of linear momentum, thermal energy equation and nanoparticle concentration equation. Design/methodology/approach Numerical integration is used with the help of the shooting technique to examine the novel features of the velocity profile, temperature profile and nanoparticle concentration profile. The impact of all the emerging parameters is sketched with the help of graphs. The numerical values of local Nusselt number and Sherwood number are also presented. Findings The no-slip condition is considered for the present study. The effects of electromagnetohydrodynamics enhance the velocity profile while thermal radiation effects tend to raise the temperature profile. The present study depicts many interesting behaviors that warrant further study on Riga plates with different non-Newtonian fluid models. A comparison is also presented with the existing published results which confirms the validity of the presented methodology. Originality/value The results of this paper are new and original.

Two-Grid Method for Miscible Displacement Problem by Mixed Finite Element Methods and Mixed Finite Element Method of Characteristics

The miscible displacement of one incompressible fluid by another in a porous medium is governed by a system of two equations. One is elliptic form equation for the pressure and the other is parabolic form equation for the concentration of one of the fluids. Since only the velocity and not the pressure appears explicitly in the concentration equation, we use a mixed finite element method for the approximation of the pressure equation and mixed finite element method with characteristics for the concentration equation. To linearize the mixed-method equations, we use a two-grid algorithm based on the Newton iteration method for this full discrete scheme problems. First, we solve the original nonlinear equations on the coarse grid, then, we solve the linearized problem on the fine grid used Newton iteration once. It is shown that the coarse grid can be much coarser than the fine grid and achieve asymptotically optimal approximation as long as the mesh sizes satisfy h = H2 in this paper. Finally, numerical experiment indicates that two-grid algorithm is very effective.