The Effect of First- and Second-Order Slip Condition on Oscillatory Flows: Several Exact Solutions

2014 ◽  
Author(s):  
Zheming Zhang ◽  
Ramesh K. Agarwal
Keyword(s):  
Exact Solutions ◽  
Second Order ◽  
Slip Condition ◽  
Oscillatory Flows

On Exact Solutions for Oscillatory Flows in a Generalized Burgers Fluid with Slip Condition

2010 ◽  
Vol 65 (5) ◽  
pp. 381-391 ◽  
Author(s):  
Tasawar Hayat ◽  
Saher Najam ◽  
Muhammad Sajid ◽  
Muhammad Ayub ◽  
Said Mesloub
Keyword(s):  
Resonant Frequency ◽  
Exact Solutions ◽  
Slip Condition ◽  
Darcy Law ◽  
Porous Space ◽  
Oscillatory Flows ◽  
Flow Modelling ◽  
Slip Effects ◽  
Burgers Fluid

An analysis is performed for the slip effects on the exact solutions of flows in a generalized Burgers fluid. The flow modelling is based upon the magnetohydrodynamic (MHD) nature of the fluid and modified Darcy law in a porous space. Two illustrative examples of oscillatory flows are considered. The results obtained are compared with several limiting cases. It has been shown here that the derived results hold for all values of frequencies including the resonant frequency.

scholarly journals A Partial Lagrangian Approach to Mathematical Models of Epidemiology

2015 ◽  
Vol 2015 ◽  
pp. 1-11 ◽  
Author(s):  
R. Naz ◽  
I. Naeem ◽  
F. M. Mahomed
Keyword(s):  
Mathematical Models ◽  
Exact Solutions ◽  
Numerical Solutions ◽  
First Integrals ◽  
Order Equation ◽  
Second Order ◽  
Lagrangian Approach ◽  
Hiv Model ◽  
First Order ◽  
Partial Lagrangian

This paper analyzes the first integrals and exact solutions of mathematical models of epidemiology via the partial Lagrangian approach by replacing the three first-order nonlinear ordinary differential equations by an equivalent system containing one second-order equation and a first-order equation. The partial Lagrangian approach is then utilized for the second-order ODE to construct the first integrals of the underlying system. We investigate the SIR and HIV models. We obtain two first integrals for the SIR model with and without demographic growth. For the HIV model without demography, five first integrals are established and two first integrals are deduced for the HIV model with demography. Then we utilize the derived first integrals to construct exact solutions to the models under investigation. The dynamic properties of these models are studied too. Numerical solutions are derived for SIR models by finite difference method and are compared with exact solutions.

Pressure Drop and Flow Development in the Entrance Region of Microchannels With Second-Order Velocity Slip Condition and the Requirement for Development Length

2020 ◽  
Vol 142 (4) ◽  
Author(s):  
Baibhab Ray ◽  
Franz Durst ◽  
Subhashis Ray
Keyword(s):  
Shear Stress ◽  
Pressure Drop ◽  
Parallel Plate ◽  
Velocity Slip ◽  
Second Order ◽  
Entrance Region ◽  
Slip Condition ◽  
Local Velocity ◽  
Flow Development ◽  
Developing Region

Abstract In this investigation, Lfd* and Δp in the entrance region of circular and parallel plate microchannels have been determined for 10−2≤Re≤104 and 10−4≤Kn≤0.2, employing the second-order velocity slip condition at the wall with C1=1 and 0≤C2≤0.5. Results indicate that although local velocity slip at the wall is always higher than that for the fully developed section, local wall shear stress for higher Kn and C2 could be lower than its fully developed value, which is also more prominent for lower Re. Therefore, depending upon the operating condition, K(x) and Kfd could assume negative values, implying that pressure gradient in the developing region could even be less than that in the fully developed section. It has been further observed that both Lfd* and Kfd are characterized by the low and the high Re asymptotes, using which extremely accurate correlations have been proposed for both geometries.

Symmetries, ansätze and exact solutions of nonlinear second-order evolution equations with convection terms, II

2006 ◽  
Vol 17 (5) ◽  
pp. 597-605 ◽  
Author(s):  
ROMAN CHERNIHA ◽  
MYKOLA SEROV
Keyword(s):  
Exact Solutions ◽  
Evolution Equations ◽  
Applied Mathematics ◽  
Reaction Diffusion ◽  
Second Order ◽  
Lie Symmetries ◽  
Nonlinear Reaction ◽  
Diffusion Convection ◽  
Natural Way

New results concerning Lie symmetries of nonlinear reaction-diffusion-convection equations, which supplement in a natural way the results published in the European Journal of Applied Mathematics (9(1998) 527–542) are presented.

scholarly journals Cauchy Problems for Evolutionary Pseudodifferential Equations overp-Adic Field

2014 ◽  
Vol 2014 ◽  
pp. 1-7
Author(s):  
Bo Wu ◽  
Yin Li ◽  
Weiyi Su
Keyword(s):  
Exact Solutions ◽  
Pseudodifferential Operator ◽  
Second Order ◽  
Cauchy Problems ◽  
Pseudodifferential Equations ◽  
Mixed Classes

We study a class of evolutionary pseudodifferential equations of the second order int,  (∂2u(t,x)/∂t2+2a2Tα/2(∂u(t,x)/∂t)+b2Tαu(t,x)+c2u(t,x)=q(t,x)), wheret∈(0,z]andTαis pseudodifferential operator inx∈Qp, which defined by Weiyi Su in 1992. We obtained the exact solutions to the equations which belong to mixed classes of real andp-adic functions.

EXACT SOLUTIONS OF THE DIRAC EQUATION WITH A COULOMB PLUS SCALAR POTENTIAL IN 2 + 1 DIMENSIONS

2002 ◽  
Vol 11 (06) ◽  
pp. 483-489 ◽  
Author(s):  
SHI-HAI DONG ◽  
XIAO-YAN GU ◽  
ZHONG-QI MA ◽  
SHISHAN DONG
Keyword(s):  
Dirac Equation ◽  
Differential Equations ◽  
Exact Solutions ◽  
Coulomb Potential ◽  
Scalar Potential ◽  
Second Order ◽  
First Order ◽  
Second Order Differential Equations

The exact solutions of the (2+1)-dimensional Dirac equation with a Coulomb potential and a scalar one are analytically presented by studying the second-order differential equations obtained from a pair of coupled first-order ones. The eigenvalues are studied in some detail.

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