Revisiting the Mixed Problem for Equations of Compound and Hyperbolic Types of Order Four

Author(s):  
Adakhimzhan Sopuev ◽  
Sayfullo Babaev ◽  
Zamirbek M. Bekmamatov
Keyword(s):  
2019 ◽  
Vol 484 (1) ◽  
pp. 18-20
Author(s):  
A. P. Khromov ◽  
V. V. Kornev

This study follows A.N. Krylov’s recommendations on accelerating the convergence of the Fourier series, to obtain explicit expressions of the classical mixed problem–solution for a non-homogeneous equation and explicit expressions of the generalized solution in the case of arbitrary summable functions q(x), ϕ(x), y(x), f(x, t).


2019 ◽  
Vol 8 (3) ◽  
pp. 5795-5802 ◽  

The main objective of this paper is to focus on a numerical study of viscous dissipation effect on the steady state flow of MHD Williamson nanofluid. A mathematical modeled which resembles the physical flow problem has been developed. By using an appropriate transformation, we converted the system of dimensional PDEs (nonlinear) into coupled dimensionless ODEs. The numerical solution of these modeled ordinary differential equations (ODEs) is achieved by utilizing shooting technique together with Adams-Bashforth Moulton method of order four. Finally, the results of discussed for different parameters through graphs and tables.


2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Muhammad Bilal ◽  
Hamna Arshad ◽  
Muhammad Ramzan ◽  
Zahir Shah ◽  
Poom Kumam

AbstractThe key objective of the present research is to examine the hybrid magnetohydrodynamics (MHD) nanofluid (Carbon-nanotubes and ferrous oxide–water) CNT–Fe3O4/H2 flow into a horizontal parallel channel with thermal radiation through squeezing and dilating porous walls. The parting motion is triggered by the porous walls of the channel. The fluid flow is time-dependent and laminar. The channel is asymmetric and the upper and lower walls are distinct in temperature and are porous. With the combination of nanoparticles of Fe3O4 and single and multi-wall carbon nanotubes, the hybrid nanofluid principle is exploited. By using the similarity transformation, the set of partial differential equations (PDEs) of this mathematical model, governed by momentum and energy equations, is reduced to corresponding ordinary differential equations (ODEs). A very simple numerical approach called the Runge–Kutta system of order four along with the shooting technique is used to achieve the solutions for regulating ODEs. MATLAB computing software is used to create temperature and velocity profile graphs for various emerging parameters. At the end of the manuscript, the main conclusions are summarized. Through different graphs, it is observed that hybrid-nanofluid has more prominent thermal enhancement than simple nanofluid. Further, the single-wall nanotubes have dominated impact on temperature than the multi-wall carbon nanotubes. From the calculations, it is also noted that Fe2O3–MWCNT–water has an average of 4.84% more rate of heat transfer than the Fe2O3–SWCNT–water. On the other hand, 8.27% more heat flow observed in Fe2O3–SWCNT–water than the simple nanofluid. Such study is very important in coolant circulation, inter-body fluid transportation, aerospace engineering, and industrial cleaning procedures, etc.


Sign in / Sign up

Export Citation Format

Share Document