Crank Nicholson scheme to examine the fractional-order unsteady nanofluid flow of free convection of viscous fluids

• Published in: PloS one Vol. 17; no. 3; p. e0261860
• Main Authors: Zubair, Tamour, Usman, Muhammad, Sooppy Nisar, Kottakkaran, Khan, Ilyas, Ghamkhar, Madiha, Ahmad, Muhammad
• Format: Journal Article
• Language: English
• Published: United States Public Library of Science 01.03.2022; Public Library of Science (PLoS)
• Subjects: Algorithms; Calculi; Calculus; Chemical reactions; Chemical speciation; Complex fluids; Convection; Copper; Crank-Nicholson method; Differential equations; Evaluation; Flow equations; Fluid dynamics; Fluid flow; Fluids; Fractional calculus; Free convection; Heat conductivity; Heat transfer; Hydrodynamics; Incompressible flow; Mathematical models; Mathematics; Mechanical properties; Methods; Models, Theoretical; Nanofluids; Nanoparticles; Nanotechnology - methods; Numerical analysis; Partial differential equations; Physical Sciences; Porous materials; Silver; Temperature; Temperature profiles; Velocity; Viscoelasticity; Viscosity; Viscous fluids; Writers; Pakistan; Saudi Arabia
• ISSN: 1932-6203; 1932-6203
• DOI: 10.1371/journal.pone.0261860

Fractional fluid models are usually difficult to solve analytically due to complicated mathematical calculations. This difficulty in considering fractional model further increases when one considers nth order chemical reaction. Therefore, in this work an incompressible nanofluid flow as well as the benefits of free convection across an isothermal vertical sheet is examined numerically. An nth order chemical reaction is considered in the chemical species model. The specified velocity (wall's) is time-based, and its motion is translational into mathematical form. The fractional differential equations are used to express the governing flow equations (FDEs). The non-dimensional controlling system is given appropriate transformations. A Crank Nicholson method is used to find solutions for temperature, solute concentration, and velocity. Variation in concentration, velocity, and temperature profiles is produced as a result of changes in discussed parameters for both Ag-based and Cu-based nanofluid values. Water is taken as base fluid. The fractional-order time evaluation has opened the new gateways to study the problem into a new direction and it also increased the choices due to the extended version. It records the hidden figures of the problem between the defined domain of the time evaluation. The suggested technique has good accuracy, dependability, effectiveness and it also cover the better physics of the problem specially with concepts of fractional calculus.