Browsing by Author "Waheed, Asif"

Now showing 1 - 5 of 5

Analysis of Homotopy Perturbation Method for Solving Fractional Order Differential Equations
(MDPI, 2019) Baleanu, Dumitru; Baleanu, Dumitru; Waheed, Asif; Khan, Mansoor Shaukat; Affan, Hira; 56389
The analysis of Homotopy PerturbationMethod (HPM) for the solution of fractional partial differential equations (FPDEs) is presented. A unified convergence theorem is given. In order to validate the theory, the solution of fractional-order Burger-Poisson (FBP) equation is obtained. Furthermore, this work presents the method to find the solution of FPDEs, while the same partial differential equation (PDE) with ordinary derivative i.e., for alpha = 1, is not defined in the given domain. Moreover, HPM is applied to a complicated obstacle boundary value problem (BVP) of fractional order.
Exact solutions of fractional mBBM equation and coupled system of fractional Boussinesq-Burgers
(Elsevier Science BV, 2018) Baleanu, Dumitru; Saif, Summaya; Waheed, Asif; Baleanu, Dumitru; 56389
The new exact solutions of nonlinear fractional partial differential equations (FPDEs) are established by adopting first integral method (FIM). The Riemann-Liouville (R-L) derivative and the local conformable derivative definitions are used to deal with the fractional order derivatives. The proposed method is applied to get exact solutions for space-time fractional modified Benjamin-Bona-Mahony (mBBM) equation and coupled time-fractional Boussinesq-Burgers equation. The suggested technique is easily applicable and effectual which can be implemented successfully to obtain the solutions for different types of nonlinear FPDEs.
Investigation Of Electroosmosis Flow Of Copper Nanoparticles With Heat Transfer Due To Metachronal Rhythm
(2021) Baleanu, Dumitru; Waheed, Asif; Javeed, Shumaila; Baleanu, Dumitru; Zeb, Muhammad; Ahmad, Sohail; 56389
A mathematical model is explored to establish the electroosmotic flow for Cu-wa-ter nanoliquids within a ciliated symmetric micro-channel, the flow is established with aid of ciliary motion and axial pressure gradient. Nanofluid comprise of Cu as a nanofluid particles and water as base fluid. Maxwell-Garnelt model is exploited for viscosity and thermal conductivity of nanoliquid. Magnetic field is applied in the transverse direction and external electric field is enforced in the axial direction. Equations of motion are simplified for nanofluid flow in the micro-channel by employing low Reynolds number and long wavelength approximation theory. Crucial exact analytical expression are gathered for electric potential, temperature profile, axial velocity, volume flux, pressure gradient, stream function, and result for pressure rise per wavelength explored numerically. The influence of crucial flow parameters on, flow behaviour, pumping phenomena, and temperature profile are thoroughly investigated. © 2021. Society of Thermal Engineers of Serbia. Published by the Vinča Institute of Nuclear Sciences, Belgrade, Serbia. This is an open access article distributed under the CC BY-NC-ND 4.0 terms and conditions.
Soliton Solutions of Mathematical Physics Models Using the Exponential Function Technique
(2020) Baleanu, Dumitru; Alimgeer, Khurram Saleem; Nawaz, Sidra; Waheed, Asif; Suleman, Muhammad; Baleanu, Dumitru; Atif, M.; 56389
This paper is based on finding the exact solutions for Burger's equation, Zakharov-Kuznetsov (ZK) equation and Kortewegde vries (KdV) equation by utilizing exponential function method that depends on the series of exponential functions. The exponential function method utilizes the homogeneous balancing principle to find the solutions of nonlinear equations. This method is simple, wide-reaching and helpful for finding the exact solution of nonlinear conformable PDEs.
Study Of Electro-Osmotıc Nanofluid Transport For Scraped Surface Heat Exchanger With Heat Transfer Phenomenon
(2021) Baleanu, Dumitru; Imran, Ali; Javeed, Shumaila; Baleanu, Dumitru; Zeb, Muhammad; Ahmad, Sohail; 56389
In this study a novel mathematical model for electroosmotic flow for Cu-water based nanofluid with heat transfer phenomenon is reported for scraped-surface heat exchanger. The flow is initiated due to motion of lower wall of the channel and axial pressure gradient. The flow is modelled with aid of low Reynolds number and lubrication approximation theory. Exact analytical expressions are gathered for axial velocity, and stream functions for various stations of scraped-surface heat exchanger. Physical phenomenon of electro osmotic parameter are investigated on velocity profile, velocity distribution and pressure rise at edge of the blades. It is reported that electro-osmotic parameter mainly works as dragging force, it can be used to control the flow. This controlling mechanism may be helpful in mixing different materials in scraped-surface heat exchanger. Pressure rise at edge of the blades mainly rises below the blades with electro-osmotic, whereas, this profiles is suppressed for region above the blades and between the blades.