Kinematic cell model of macropore flow from intermittent irrigation pulses

Soil Research ◽  
2001 ◽  
Vol 39 (4) ◽  
pp. 837
Author(s):  
V. J. Bidwell ◽  
H. R. Thorpe
Keyword(s):  
Model Simulation ◽  
Cell Model ◽  
Water Flux ◽  
Pulse Sequences ◽  
Good Prediction ◽  
Macropore Flow ◽  
Linear Ordinary Differential Equations ◽  
Model Response ◽  
Non Linear ◽  
Linear State

Significant fluctuations in soil water flux were observed in the drainage hydrographs from lysimeters (1220 mm diam., 900 mm deep) of undisturbed field soil, recorded at 5-min intervals, in response to intermittent 1-min pulses of irrigation water (3.4 or 6.8 mm) at irregular time intervals (4–17 min). The hypothetical process for this phenomenon was flow through soil macropores, in association with non-linear sorption into soil micropores. The kinematic wave approach to analysing macropore flow was modelled as a series of bi-continuum cells, which can be expressed as a set of non-linear ordinary differential equations. This non-linear state-space description enables the use of MATLAB software for convenient coding of the model and numerical integration of the model response to transient water flux input. Model simulation of drainage response to the irrigation pulse sequences showed good prediction of the wetting and draining fronts of the hydrograph but gave only indicative prediction of the magnitudes and wavelengths of the flow fluctuations. The model demonstrates the sensitivity of macropore flow to variations in the intervals between irrigation pulses, and supports previous evidence of fluctuations in macropore flow even for single water flux input pulses under laboratory conditions.

MHD STAGNATION POINT FLOW OF HYPERBOLIC TANGENT FLUID WITH VISCOUS DISSIPATION AND CHEMICAL REACTION

2021 ◽  
Vol 21 (2) ◽  
pp. 569-588
Author(s):  
KINZA ARSHAD ◽  
MUHAMMAD ASHRAF
Keyword(s):  
Magnetic Field ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Stagnation Point ◽  
Viscous Dissipation ◽  
Chemical Reaction ◽  
Normal Velocity ◽  
Hyperbolic Tangent ◽  
Linear Ordinary Differential Equations ◽  
Non Linear

In the present work, two dimensional flow of a hyperbolic tangent fluid with chemical reaction and viscous dissipation near a stagnation point is discussed numerically. The analysis is performed in the presence of magnetic field. The governing partial differential equations are converted into non-linear ordinary differential equations by using appropriate transformation. The resulting higher order non-linear ordinary differential equations are discretized by finite difference method and then solved by SOR (Successive over Relaxation parameter) method. The impact of the relevant parameters is scrutinized by plotting graphs and discussed in details. The main conclusion is that the large value of magnetic field parameter and wiessenberg numbers decrease the streamwise and normal velocity while increase the temperature distribution. Also higher value of the Eckert number Ec results in increases in temperature profile.

Convective transport of thermal and solutal energy in unsteady MHD Oldroyd-B nanofluid flow

2021 ◽  
Author(s):  
Muhammad Yasir ◽  
Masood Khan ◽  
Awais Ahmed ◽  
Malik Zaka Ullah
Keyword(s):  
Boundary Layer ◽  
Differential Equations ◽  
Thermal Radiation ◽  
Ordinary Differential Equations ◽  
Heat Generation ◽  
Axisymmetric Flow ◽  
Convective Transport ◽  
Buongiorno’S Model ◽  
Linear Ordinary Differential Equations ◽  
Non Linear

Abstract In this work, an analysis is presented for the unsteady axisymmetric flow of Oldroyd-B nanofluid generated by an impermeable stretching cylinder with heat and mass transport under the influence of heat generation/absorption, thermal radiation and first-order chemical reaction. Additionally, thermal and solutal performances of nanofluid are studied using an interpretation of the well-known Buongiorno's model, which helps us to determine the attractive characteristics of Brownian motion and thermophoretic diffusion. Firstly, the governing unsteady boundary layer equation's (PDEs) are established and then converted into highly non-linear ordinary differential equations (ODEs) by using the suitable similarity transformations. For the governing non-linear ordinary differential equations, numerical integration in domain [0, ∞) is carried out using the BVP Midrich scheme in Maple software. For the velocity, temperature and concentration distributions, reliable results are prepared for different physical flow constraints. According to the results, for increasing values of Deborah numbers, the temperature and concentration distribution are higher in terms of relaxation time while these are decline in terms of retardation time. Moreover, thermal radiation and heat generation/absorption are increased the temperature distribution and corresponding boundary layer thickness. With previously stated numerical values, the acquired solutions have an excellent accuracy.

Dynamics of spreader motion in a gantry crane

1998 ◽  
Vol 212 (2) ◽  
pp. 85-105 ◽  
Author(s):  
M P Cartmell ◽  
L Morrish ◽  
A J Taylor
Keyword(s):  
Fuzzy Logic Control ◽  
Rigid Bodies ◽  
Gantry Crane ◽  
Lateral Motion ◽  
Dynamic Simulations ◽  
General Direction ◽  
Linear Ordinary Differential Equations ◽  
Logic Control ◽  
Non Linear ◽  
Performance Gains

This paper illustrates the steps necessary to model the dynamics of a model rubber-tyred gantry (RTG) crane as used in container-handling operations. Various modelling criteria are discussed with the emphasis placed on the importance of non-linear coupling between the chosen system coordinates. The machine is treated as three rigid bodies, these being the gantry itself, the trolley (which is constrained to lateral motion across the top beam) and the spreader. Tyre deformations and structural deflections are not considered in this work. The paper culminates in three non-linear ordinary differential equations, which are then solved numerically for a variety of different cases. An important feature of this work is that the dynamic simulations include complicated gantry motions, not currently designed for, such as combined translations and simultaneous rotations. Such motions are more commonly encountered in mobile robots. However, RTG design needs to move in this general direction in the future if significant and potential performance gains are actually to be realized in practise. The paper concludes with suggestions for implementation of the dynamic model within a fuzzy logic control system.

NUMERICAL STUDY OF MIXED BIOCONVECTION IN POROUS MEDIA SATURATED WITH NANOFLUID CONTAINING OXYTACTIC MICROORGANISMS

2013 ◽  
Vol 13 (04) ◽  
pp. 1350067 ◽  
Author(s):  
O. ANWAR BÉG ◽  
V. R. PRASAD ◽  
B. VASU
Keyword(s):  
Boundary Layer ◽  
Peclet Number ◽  
Mechanical Design ◽  
Numerical Study ◽  
Lewis Number ◽  
Nanoparticle Concentration ◽  
Péclet Number ◽  
Linear Ordinary Differential Equations ◽  
Non Linear ◽  
Oxytactic Microorganisms

A mathematical model has been developed for steady-state boundary layer flow of a nanofluid past an impermeable vertical flat wall in a porous medium saturated with a water-based dilute nanofluid containing oxytactic microorganisms. The nanoparticles were distributed sufficiently to permit bioconvection. The product of chemotaxis constant and maximum cell swimming speed was assumed invariant. Using appropriate transformations, the partial differential conservation equations were non-dimensionalised to yield a quartet of coupled, non-linear ordinary differential equations for momentum, energy, nanoparticle concentration and dimensionless motile microorganism density, with appropriate boundary conditions. The dominant parameters emerging in the normalised model included the bioconvection Lewis number, bioconvection Peclet number, Lewis number, buoyancy ratio parameter, Brownian motion parameter, thermophoresis parameter, local Darcy-Rayleigh number and the local Peclet number. An implicit numerical solution to the well-posed two-point non-linear boundary value problem is developed using the well-tested and highly efficient Keller box method. Computations are validated with the Nakamura tridiagonal implicit finite difference method, demonstrating excellent agreement. Nanoparticle concentration and temperature were found to be generally enhanced through the boundary layer with increasing bioconvection Lewis number, whereas dimensionless motile microorganism density was only increased closer to the wall. Temperature, nanoparticle concentration and dimensionless motile microorganism density were all greatly increased with a rise in Peclet number. Temperature and dimensionless motile microorganism density were reduced with increasing buoyancy parameter, whereas nanoparticle concentration was increased. The present study found applications in the fluid mechanical design of microbial fuel cell and bioconvection nanotechnological devices.

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