Application of Fractional Derivative Without Singular and Local Kernel to Enhanced Heat Transfer in CNTs Nanofluid Over an Inclined Plate

Abstract

Nanofluids are a novel class of heat transfer fluid that plays a vital role in industries. In mathematical investigations, these fluids are modeled in terms of traditional integer-order partial differential equations (PDEs). It is recognized that traditional PDEs cannot decode the complex behavior of physical flow parameters and memory effects. Therefore, this article intends to study the mixed convection heat transfer in nanofluid over an inclined vertical plate via fractional derivatives approach. The problem in hand is modeled in connection with Atangana–Baleanu fractional derivatives without singular and local kernel with a strong memory. Human blood is considered as base fluid and carbon nanotube (CNTs) (single-wall carbon nanotubes (SWCNTs) and multi-wall carbon nanotubes (MWCNTs)) are dispersed into it to form blood-CNTs nanofluid. The nanofluid is considered to flow in a saturated porous medium under the influence of an applied magnetic field. The exact analytical expressions for velocity and temperature profiles are acquired using the Laplace transform technique and plotted in various graphs. The empirical results indicate that the memory effect decreases with increasing fractional parameters in the case of both temperature and velocity profiles. Moreover, the temperature profile is higher for blood SWCNTs because of higher thermal conductivity whereas this trend is found opposite in the case of velocity profile due to densities difference.

A Numerical Study of Chemical Reaction in a Nanofluid Flow Due to Rotating Disk in the Presence of Magnetic Field

“…The value of +1 is determined with the help of Simpson's rule. Where +1 , +1 and ζ +1 are used to find the value of , ζ in equations (19) - (22) to obtain the solution of equation (13).…”

“…Osalusi [13] with the help of shooting techniques. Due to the rotating disk the analytical modeling for heat transfer of the couple stress and unsteady MHD flow is pointed out by Khan et al [14] and also Runge -Kutta method with shooting technique was hired for the solution of their model numerically and also explain the variation of physical [19][20][21][22][23][24][25][26][27][28][29][30][31] In aforementioned studies and a comprehensive literature review, it is disclosed that no such study has been carried out and is currently available to examine the heat transfer and magnetically driven nanofluid flow over the rotating disk in the occurrence of chemical reaction was examined. The partial differential equation of the model can be converted into an ordinary differential equation with the help of similarity transformation and solved these ordinary differential equations by using finite difference method.…”

Heat and Mass Transfer Impact on Differential Type Nanofluid with Carbon Nanotubes: A Study of Fractional Order System

“…Abro et al [11] applied a fractional derivative with non-singular and non-local kernel on a nano-fluid under magnetism. Saqib et al [12] highlighted the strong memory effect of the Atangana-Baleanu fractional model of CNT's nano-fluid. The abeyance of nanoparticles in fluid airing notable enhancement of their properties at reticent nano-particle concentrations are known as nano-fluids [13].…”

Study of Heat Transfer under the Impact of Thermal Radiation, Ramped Velocity, and Ramped Temperature on the MHD Oldroyd-B Fluid Subject to Noninteger Differentiable Operators

“…As compared to classical models, the memory effect is much stronger in fractional derivatives. From the past to the present, modeling of different processes is handled through various types of fractional derivatives and fractal-fractional differential operators, such as Caputo (power law), Atangana-Baleanu (Mittag-Leffler law), Caputo-Fabrizio (exponential law), Riemann-Liouville, and modified Riemann-Liouville (power law with boundaries) [5][6][7][8][9][10][11][12][13][14][15][16]. Ramped wall velocity and temperature with MHD fluid flow are gaining attention of many researchers.…”