Browsing by Author "Usman, Muhammad"

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Citation - WoS: 4
Citation - Scopus: 4
Magnetic Field Effect on Heat and Momentum of Fractional Maxwell Nanofluid within a Channel by Power Law Kernel Using Finite Difference Method
(Wiley-hindawi, 2022) Lashin, Maha M. A.; Jarad, Fahd; Usman, Muhammad; Asjad, Muhammad Imran; Ali, Arfan; Jarad, Fahd; Muhammad, Taseer; 234808
The mathematical model of physical problems interprets physical phenomena closely. This research work is focused on numerical solution of a nonlinear mathematical model of fractional Maxwell nanofluid with the finite difference element method. Addition of nanoparticles in base fluids such as water, sodium alginate, kerosene oil, and engine oil is observed, and velocity profile and heat transfer energy profile of solutions are investigated. The finite difference method involving the discretization of time and distance parameters is applied for numerical results by using the Caputo time fractional operator. These results are plotted against different physical parameters under the effects of magnetic field. These results depicts that a slight decrease occurs for velocity for a high value of Reynolds number, while a small value of Re provides more dominant effects on velocity and temperature profile. It is observed that fractional parameters alpha and beta show inverse behavior against u(y,t) and theta(y,t). An increase in volumetric fraction of nanoparticles in base fluids decreases the temperature profile of fractional Maxwell nanofluids. Using mathematical software of MAPLE, codes are developed and executed to obtain these results.
Citation - WoS: 4
Citation - Scopus: 4
Thermal Transport With Nanoparticles of Fractional Oldroyd-B Fluid Under the Effects of Magnetic Field, Radiations, and Viscous Dissipation: Entropy Generation; Via Finite Difference Method
(de Gruyter Poland Sp Z O O, 2022) Baleanu, Dumitru; Usman, Muhammad; Kaleem, Muhammad Madssar; Baleanu, Dumitru; Muhammad, Taseer
It is a well-known fact that functional effects like relaxation and retardation of materials, and heat transfer phenomena occur in a wide range of industrial and engineering problems. In this context, a mathematical model is developed in the view of Caputo fractional derivative for Oldroyd-B nano-fluid. Nano-sized particles of copper (Cu) are used to prepare nano-fluid taking water as the base fluid. The coupled non-linear governing equations of the problem are transformed into dimensionless form. Finite difference scheme is developed and applied successfully to get the numerical solutions of deliberated problem. Influence of different physical parameters on fluid velocity profile and temperature profile are analyzed briefly. It is observed that for increasing values of fractional parameter (alpha), fluid velocity increased, but opposite behavior was noticed for temperature profile. Nusselt number (Nu) decayed for advancement in values of heat source/sink parameter (Q(0)), radiation parameter (Nr), volume fraction parameter of nano-fluid (phi), and viscous dissipation parameter (Ec). Skin friction (C-f) boosts for the increase in the values of magnetic field parameter (Ha). It can also be noticed that the extended finite difference scheme is an efficient tool and gives the accurate results of discussed problem. It can be extended for more numerous type heat transfer problems arising in physical nature with complex geometry.