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Muzamal Hussain,Saima Akram,Mohamed A. Khadimallah,Madeeha Tahir,Shabir Ahmad,Mohammed Alsaigh,Abdelouahed Tounsi 국제구조공학회 2023 Steel and Composite Structures, An International J Vol.48 No.6
This work considered an optimal control formulation in the sense of Caputo derivatives. The optimality of the fractional optimal control problem. The tumor immune interaction in fractional form provides an excellent tool for the description of memory and hereditary properties of inter and intra cells. So the interaction between effector-cells, tumor cells and are modeled by using the definition of Caputo fractional order derivative that provides the system with long-time memory and gives extra degree of freedom. In addiltion, existence and local stability of fixed points are investigated for discrete model. Moreover, in order to achieve more efficient computational results of fractional-order system, a discretization process is performed to obtain its discrete counterpart. Our technique likewise allows the advancement of results, such as return time to baseline that are unrealistic with current model solvers.
Lubrication phenomenon in the stagnation point flow of Walters-B nanofluid
Muhammad Taj,Manzoor Ahmad,Mohamed A. Khadimallah,Saima Akram,Muzamal Hussain,Madeeha Tahir,Faisal Mehmood Butt,Abdelouahed Tounsi Techno-Press 2023 Advances in concrete construction Vol.15 No.5
The present study investigates the effects of Cattaneo-Christov thermal effects of stagnation point in Walters-B nanofluid flow through lubrication of power-law fluid by taking the slip at the interfacial condition. For the solution, the governing partial differential equation is transformed into a series of non-linear ordinary differential equations. With the help of hybrid homotopy analysis method; that consists of both the homotopy analysis and shooting method these equations can be solved. The influence of different involved constraints on quantities of interest are sketched and discussed. The viscoelastic parameter, slip parameters on velocity component and temperature are analyzed. The velocity varies by increase in viscoelastic parameter in the presence of slip parameter. The slip on the surface has major effect and mask the effect of stagnation point for whole slip condition and throughout the surface velocity remained same. Matched the present solution with previously published data and observed good agreement. It can be seen that the slip effects dominates the effects of free stream and for the large values of viscoelastic parameter the temperature as well as the concentration profile both decreases.