Abstract
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.
Highlights
Natural convection process is that type of flow situation in which a liquid such as water as an example of Newtonian fluid, in which the fluid motion is produced by an external source instead by some parts of the fluid being heavier than other parts
We developed a straightforward method for introducing fractional ordered derivatives into linear viscous models, which drew much attention to this area
The above literature shows that several investigations are done on convection heat transfer using classical/fractional models [43–47] and [48–53]. In all these models, those they are involved with fractional derivatives, no attention is given to nth order chemical reaction in species concentration and the free convection flow of viscous nanofluid using fractional derivatives
Summary
Natural convection process is that type of flow situation in which a liquid such as water as an example of Newtonian fluid, in which the fluid motion is produced by an external source instead by some parts of the fluid being heavier than other parts. The fractional calculus theory sparked widespread interest due to its wide range of applications in physics and engineering [10] This kind of research has made use of multidimensional dynamics such as wave, viscoelastic, and relaxation activities. Despite the fact that there is extensive research literature on fluid flows, numerous mathematical and fluid models are developed and effectively solved using the fractional calculus method; see, for example, some useful investigations in this direction [7,40–42]. The above literature shows that several investigations are done on convection heat transfer using classical/fractional models [43–47] and [48–53] In all these models, those they are involved with fractional derivatives, no attention is given to nth order chemical reaction in species concentration and the free convection flow of viscous nanofluid using fractional derivatives. The collected findings demonstrate the suggested technique’s accuracy, dependability, and effectiveness
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