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

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...

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Bibliographic Details
Published in:PloS one 2022-03, Vol.17 (3), p.e0261860
Main Authors: Zubair, Tamour, Usman, Muhammad, Sooppy Nisar, Kottakkaran, Khan, Ilyas, Ghamkhar, Madiha, Ahmad, Muhammad
Format: Article
Language:English
Subjects:
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
Nanofluids
Nanoparticles
Numerical analysis
Partial differential equations
Physical Sciences
Porous materials
Silver
Temperature profiles
Velocity
Viscoelasticity
Viscosity
Viscous fluids
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Summary: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.
ISSN:1932-6203
1932-6203
DOI:10.1371/journal.pone.0261860