Mathematical Model of a Railway Pneumatic Brake System With Varying Cylinder Capacity Effects

1990 ◽  
Vol 112 (3) ◽  
pp. 456-462 ◽  
Author(s):  
S. Bharath ◽  
B. C. Nakra ◽  
K. N. Gupta
Keyword(s):  
Differential Equations ◽  
Volume Effect ◽  
Brake System ◽  
Governing Equations ◽  
Linear Ordinary Differential Equations ◽  
Linear Partial Differential Equations ◽  
Reservoir Volume ◽  
State Approximation ◽  
Piston Displacement ◽  
Non Linear

Governing equations for the analysis of pressure transient are derived from the principle of conservation of mass and momentum for a pneumatic brake system, which consists of a train pipe connected to a number of linear actuators (brake cylinders with piston displacement). The governing one-dimensional non-linear partial differential equations for the train pipe, non-linear ordinary differential equations for the brake cylinders, and second-order differential equation of motion for piston displacement are solved to determine the pressure transients in the brake system for a step change in pressure at the inlet. The governing equations are nondimensionalized and reduced to a set of ordinary nonlinear differential difference equations and integrated by standard numerical methods. The flow is considered isothermal, and the friction effects for turbulent and laminar flow are evaluated by quasi-steady state approximation. The auxiliary reservoir volume effect is also included. The results are compared with the experimental data obtained on a brake test rig.

Mathematical Solution on MHD Stagnation Point Flow of Ferrofluid

2020 ◽  
Vol 399 ◽  
pp. 38-54
Author(s):  
Siti Hanani Mat Yasin ◽  
Muhammad Khairul Anuar Mohamed ◽  
Zulkhibri Ismail ◽  
Mohd Zuki Salleh
Keyword(s):  
Heat Transfer ◽  
Differential Equations ◽  
Stagnation Point ◽  
Volume Fraction ◽  
Stagnation Point Flow ◽  
Governing Equations ◽  
Linear Ordinary Differential Equations ◽  
Linear Partial Differential Equations ◽  
Keller Box Method ◽  
Non Linear

This study presents a numerical investigation on the magnetohydrodynamic (MHD) stagnation point flow of a ferrofluid with Newtonian heating. The black oxide of iron, magnetite (Fe3O4) which acts as magnetic materials and water as a base fluid are considered. The two dimensional stagnation point flow of cold ferrofluid against a hot wall under the influence of the uniform magnetic field of strength is located some distance behind the stagnation point. The effect of magnetic and volume fraction on the velocity and temperature boundary layer profiles are obtained through the formulated governing equations. The governing equations which are in the form of dimensional non-linear partial differential equations are reduced to dimensionless non-linear ordinary differential equations by using appropriate similarity transformation. Then, they are solved numerically by using the Keller-box method which is programmed in the Matlab software. It is found that the cold fluid moves towards the magnetic source that is close to the hot wall. Hence, leads to the better cooling rate and enhances the heat transfer rate. Meanwhile, an increase of the magnetite nanoparticles volume fraction, increases the ferrofluid capabilities in thermal conductivity and consequently enhances the heat transfer.

An Oscillatory Radiating Hydromagnetic Internal Heat Generating Fluid Flow Through a Vertcal Porous Channel with Slip and Temperature Jump

2018 ◽  
Vol 23 (2) ◽  
pp. 503-519 ◽  
Author(s):  
E.O. Titiloye ◽  
J.A. Gbadeyan ◽  
A.T. Adeosun
Keyword(s):  
Fluid Flow ◽  
Differential Equations ◽  
Temperature Jump ◽  
Slip Flow ◽  
Internal Heat ◽  
Porous Channel ◽  
Linear Ordinary Differential Equations ◽  
Linear Partial Differential Equations ◽  
Non Linear ◽  
Flow Through

Abstract The present study concerns the natural convective heat generating/absorbing, radiative magnetohydrodynamic, oscillatory fluid flow through a vertical porous channel with slip and temperature jump. The effect of Joule dissipation is taken into consideration while it is assumed that the flow is fully developed. The differential transforms method(DTM) is employed to solve the system of non-linear ordinary differential equations that is obtained from the non-linear partial differential equations governing the flow. Semi analytical solutions of the steady and unsteady part of the flow in the slip flow regime through a vertical porous channel are obtained. The effects of various flow parameters on the velocity and temperature profiles as well as Nusselt and skin friction are presented graphically and discussed. An excellent agreement between the results of this article and those available in the literature validated the presented approach.

Stokes’ first problem for MHD flow of Casson nanofluid

2017 ◽  
Vol 13 (1) ◽  
pp. 2-10
Author(s):  
Syed Tauseef Mohyud-din ◽  
Umar Khan ◽  
Naveed Ahmed ◽  
M.M. Rashidi
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Mhd Flow ◽  
Governing Equations ◽  
Content Type ◽  
Buongiorno’S Model ◽  
Linear Ordinary Differential Equations ◽  
Flux Condition ◽  
Non Linear ◽  
Flow Heat

Purpose The purpose of this paper is to present investigation of the flow, heat and mass transfer of a nanofluid over a suddenly moved flat plate using Buongiorno’s model. This study is different from some of the previous studies as the effects of Brownian motion and thermophoresis on nanoparticle fraction are passively controlled on the boundary rather than actively. Design/methodology/approach The partial differential equations governing the flow are reduced to a system of non-linear ordinary differential equations. Viable similarity transforms are used for this purpose. A well-known numerical scheme called Runge-Kutta-Fehlberg method coupled with shooting procedure has been used to find the solution of resulting system of equations. Discussions on the effects of different emerging parameters are provided using graphical aid. A table is also given that provides the results of different parameters on local Nusselt and Sherwood numbers. Findings A revised model for Stokes’ first problem in nanofluids is presented in this paper. This model considers a zero flux condition at the boundary. Governing equations after implementing the similarity transforms get converted into a system of non-linear ordinary differential equations. Numerical solution using RK-Fehlberg method is also carried out. Emerging parameters are analyzed graphically. Figures indicate a quite significant change in concentration profile due to zero flux condition at the wall. Originality/value This work can be extended for other problems involving nanofluids for the better understanding of different properties of nanofluids.

scholarly journals Analysis of Ethylene Glycol (EG)-based ((Cu-Al2O3), (Cu-TiO2), (TiO2-Al2O3)) Hybrid Nanofluids for Optimal Car Radiator Coolant

2020 ◽  
pp. 34-50
Author(s):  
J. A. Okello ◽  
W. N. Mutuku ◽  
A. O. Oyem
Keyword(s):  
Differential Equations ◽  
Ethylene Glycol ◽  
Waste Heat ◽  
Cooling System ◽  
Integration Scheme ◽  
Shooting Technique ◽  
Linear Ordinary Differential Equations ◽  
Linear Partial Differential Equations ◽  
Non Linear ◽  
Hybrid Nanofluids

Coolants are vital in any automotive since they manage the heat in the internal combustion of the engines by preventing corrosion in the cooling system as well as assist in eradicating the engine’s waste heat. This paper examines three different types of ethylene glycol-based hybrid nanofluids ((Cu-Al2O3), (Cu-TiO2), (TiO2-Al2O3)) to establish their cooling capabilities for industrial cooling applications. The vertical flow of these hybrid nanofluids combination through a semi-infinite convectively heated flat plate mimicking the flow of coolant in car radiator is modeled. The governing non-linear partial differential equations of fluid flow are transformed into a system of coupled non-linear ordinary differential equations using a suitable similarity transformation variables and the numerical solution executed using the shooting technique together with the fourth-order Runge-Kutta-Fehlberg integration scheme. The numerical simulation is executed using MATLAB and results are displayed graphically. The effects of pertinent parameters on velocity, temperature, skin friction, and local Nusselt number are investigated. From the study (Cu-Al2O3  hybrid nanocoolant leads to a rapid decrease in temperature at the boundary layer.

scholarly journals FERROFLUID FLOW IN MAGNETIC FIELD ABOVE STRETCHING SHEET WITH SUCTION AND INJECTION

2020 ◽  
Vol 25 (3) ◽  
pp. 461-472 ◽  
Author(s):  
Gabriella Bognár ◽  
Krisztián Hriczó
Keyword(s):  
Magnetic Field ◽  
Differential Equations ◽  
Skin Friction ◽  
Stretching Sheet ◽  
Numerical Solutions ◽  
Transfer Coefficients ◽  
Linear Ordinary Differential Equations ◽  
Linear Partial Differential Equations ◽  
Non Linear ◽  
The Impact

The aim of this paper is to investigate the boundary layer of ferrofluid flow induced by a permeable stretching sheet. Fluid is electrically non-conducting in the presence of non-uniform magnetic field. The governing non-linear partial differential equations are reduced to non-linear ordinary differential equations by applying a similarity transformation. Numerical solutions are obtained by using Maple. The effects of the magnetic field, the Reynolds number and the porosity on the velocity and thermal fields are investigated. The impact of the parameters on the skin friction and the local Nusselt number is numerically examined. The skin friction and heat transfer coefficients are decreasing with enhancing the stretching, the values of porosity and the ferromagnetic parameter.

scholarly journals Heat Transfer Exploration of MHD Flow Stream with Changing Viscosity and Thermal Conductivity due to Expandable Surface

2021 ◽  
Vol 8 (6) ◽  
pp. 955-960
Author(s):  
M.C. Kemparaju ◽  
Bommanna Lavanya ◽  
Mahantesh M. Nandeppanavar ◽  
N. Raveendra
Keyword(s):  
Heat Transfer ◽  
Thermal Conductivity ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Mhd Flow ◽  
Variable Thermal Conductivity ◽  
Partial Differential ◽  
Linear Ordinary Differential Equations ◽  
Linear Partial Differential Equations ◽  
Non Linear

In this paper an examination is completed to explore the influence of variable thickness and variable thermal conductivity on MHD stream. We have considered the governing stream and heat transfer conditions as partial differential equations. These non-linear partial differential equations are changed to non-linear ordinary differential equations at that point explained numerically utilizing fourth order RK strategy with shooting procedure. The influence of governing factors on velocity and temperature is concentrated through diagrams and numerical estimations of skin frictions and wall temperature inclination are determined, classified and examined.

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.

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