scholarly journals Unsteady/Steady Free Convective Couette Flow of Reactive Viscous Fluid in a Vertical Channel Formed by Two Vertical Porous Plates

2012 ◽  
Vol 2012 ◽  
pp. 1-10 ◽  
Author(s):  
Basant K. Jha ◽  
Ahmad K. Samaila ◽  
Abiodun O. Ajibade
Keyword(s):  
Steady State ◽  
Free Convection ◽  
Viscous Fluid ◽  
Couette Flow ◽  
Perturbation Technique ◽  
Equations Of Motion ◽  
Vertical Channel ◽  
Regular Perturbation ◽  
Transient Solutions ◽  
Steady State Problem

This paper presents unsteady as well as steady-state free convection Couette flow of reactive viscous fluid in a vertical channel formed by two infinite vertical parallel porous plates. The motion of the fluid is induced due to free convection caused by the reactive nature of viscous fluid as well as the impulsive motion of one of the porous plates. The Boussinesq assumption is applied, and the nonlinear governing equations of motion and energy are developed. The time-dependent problem is solved using implicit finite difference method, and steady-state problem is solved by applying regular perturbation technique. During the course of computation, an excellent agreement was found between the well-known steady-state solutions and transient solutions at large value of time.

scholarly journals Computational Modelling of Thermal Stability in a Reactive Slab with Reactant Consumption

2012 ◽  
Vol 2012 ◽  
pp. 1-13
Author(s):  
O. D. Makinde
Keyword(s):  
Steady State ◽  
Perturbation Technique ◽  
Nonlinear Partial Differential Equation ◽  
Exothermic Reaction ◽  
Computational Modelling ◽  
Reaction Diffusion ◽  
Lower Surface ◽  
Diffusion Problem ◽  
One Step ◽  
Steady State Problem

This paper investigates both the transient and the steady state of a one-stepnth-order oxidation exothermic reaction in a slab of combustible material with an insulated lower surface and an isothermal upper surface, taking into consideration reactant consumption. The nonlinear partial differential equation governing the transient reaction-diffusion problem is solved numerically using a semidiscretization finite difference technique. The steady-state problem is solved using a perturbation technique together with a special type of the Hermite-Padé approximants. Graphical results are presented and discussed quantitatively with respect to various embedded parameters controlling the systems. The crucial roles played by the boundary conditions in determining the thermal ignition criticality are demonstrated.

Member Initial Curvature Effects on the Elastic Slider-Crank Mechanism Response

1982 ◽  
Vol 104 (1) ◽  
pp. 159-167 ◽  
Author(s):  
M. Badlani ◽  
A. Midha
Keyword(s):  
Steady State ◽  
Natural Frequency ◽  
Equations Of Motion ◽  
Excitation Frequency ◽  
Beam Theory ◽  
Connecting Rod ◽  
Initial Curvature ◽  
Curvature Effects ◽  
Transient Solutions ◽  
Crank Mechanism

Parametric vibration of initially curved columns loaded by axial-periodic loads has received considerable attention, concluding that regions of instability exist and that excitation frequencies less than the natural frequency of the principal resonance may occur. Recent publications have cautioned against the use of curved members in machines designed for precise operation, suggesting a detrimental coupling of the longitudinal and transverse deformations. In this work, the dynamic behavior of a slider-crank mechanism with an initially curved connecting rod is investigated. Governing equations of motion are developed using the Euler-Bernoulli beam theory. Both steady-state and transient solutions are determined, and compared with those obtained for the mechanism possessing a geometrically perfect (straight) connecting rod. A very small initial curvature is shown to cause a significantly greater steady-state response. The magnification in its transient response is shown to be even greater than that due to a straight connecting rod. Additionally, an excitation frequency less than the natural frequency is also shown to occur.

Component Mode Analysis of Nonlinear, Nonconservative Systems

1983 ◽  
Vol 50 (1) ◽  
pp. 204-209 ◽  
Author(s):  
B. H. Tongue ◽  
E. H. Dowell
Keyword(s):  
Steady State ◽  
Equations Of Motion ◽  
Nonlinear Problems ◽  
Mode Analysis ◽  
Nonlinear Constraints ◽  
Nonconservative Systems ◽  
Transient Solutions

In this paper a method for attacking coupled linear-nonlinear problems is developed. This method allows one to express the equations of motion with a number of equations proportional to the number of nonlinear constraints on the system rather than to the number of linear modes of the system. Both steady state and transient solutions are investigated for a system possessing cubic nonlinearities.

Sign in / Sign up

Export Citation Format

Share Document