A fractional model was developed for presenting the thermal assessment of nanoparticles in an inclined moving surface. Water was used as a base fluid, while the nanofluid utilized copper oxide and silver nanoparticles. The modification of the thermal model was further supported by mixed convection, magnetic force, and porous saturated space. Slip effects to the porous surface were also introduced. The fluctuation in temperature at different times was assumed by following the ramped thermal constraints. The fractional computations for the set of flow problems were performed with implementations of the Atangana–Baleanu (AB) and Caputo–Fabrizio (CF) analytical techniques. The integration process for such computations was achieved using the Laplace transformation. The comparative velocity and thermal analysis for the water and kerosene-oil-based nanofluid model is presented. The declining change in the velocity was observed due to the increase in the volume fraction of nanoparticles. It was observed that the increment in the temperature profile was more progressive for the kerosene oil and silver nanoparticle suspension.

With efficient thermal activities, nanofluids have a novel role in different scientific engineering fields due to their unique and numerous applications. For example, these fluids can be used in magnetic resonance imaging (MRI), magnetic refrigeration (MR), cancer treatment (hyperthermia), and drug delivery. By inspiriting these applications and the significance of electrically conducting nanofluids, in this article, we have studied blood-based nanofluid containing carbon nanotubes (CNTs). The Brinkman type nanofluid modal is established in terms of an efficient mathematical fractional technique namely Prabhakar fractional derivative with ramped temperature and sinusoidal oscillations conditions and for the generalized solutions of temperature and velocity profile, Laplace transformation scheme is utilized. For the heat transfer of nanofluids, the Prabhakar fractional derivative which is based on generalized Fourier’s law of thermal flux is determined. The physical behavior of different parameters is examined by graphical illustrations. As a result, we have concluded that the velocity profile is a bit higher for multi-walled carbon nanotubes (MWCNTs) as compared to single-walled carbon nanotubes (SWCNTs). Furthermore, velocity and temperature fields represent decaying behavior by varying the values of fractional parameters.

The functional implications of substances, such as retardation and relaxation, can be studied for magnetized diffusion coefficient based on the relative increase throughout magnetization is a well-known realization. In this context, we have explored the Oldroyd-B hybrid nanofluid flowing through a pored oscillating plate along with an inclined applied magnetics effect. The slipping effect and sinusoidal heating conditions are also supposed to be under consideration. An innovative and current classification of fractional derivatives, i.e., Prabhakar fractional derivative and Laplace transform, are implemented for the result of transformed leading equations. The graphical representation is also described to understand the physical implementation of all effecting parameters. In order to justify and physically examine the considered problem, some limiting cases, the rate of heat and mass transfer, and friction factors are also analyzed. As a result, we have concluded that the thermal enhancement can be improved more progressively with the interaction of silver-water-based nanofluid suspension compared to copper-nanoparticles mixed nanofluid. Furthermore, It has examined the impact of both parameters, i.e., time relaxation ${\mathsf{\Omega }}_1$ and retardation ${\mathsf{\Omega }}_2$ is opposite of the momentum field.

This paper aims to investigate free convection heat transmission in hybrid nanofluids across an inclined pours plate, which characterizes an asymmetrical hybrid nanofluid flow and heat transfer behavior. With an angled magnetic field applied, sliding on the border of walls is also considered with sinusoidal heat transfer boundary conditions. The non-dimensional leading equations are converted into a fractional model using an effective mathematical fractional approach known as the Prabhakar time fractional derivative. Silver (Ag) and titanium dioxide (TiO₂) are both considered nanoparticles, with water (H₂O) and sodium alginate (C₆H₉NaO₇) serving as the base fluids. The solution of the momentum, concentration, and energy equation is found by utilizing the Laplace scheme, and different numerical algorithms are considered for the inverse of Laplace, i.e., Stehfest and Tzou’s. The graphical analysis investigates the impact and symmetry of significant physical and fractional parameters. Consequently, we surmise that water-based hybrid nanofluid has a somewhat higher velocity than sodium alginate-based hybrid nanofluid. Furthermore, the Casson parameter has a dual effect on the momentum profile. Furthermore, the memory effect reduces as fractional restriction increases for both the velocity and temperature layers. The results demonstrate that increasing the heat transmission in the solid nanoparticle volume fractions enhanced the heat transmission. In addition, the numerical assessment examined the increase in mass and heat transmission, while shear stress was increased with an increase in the Prabhakar fractional parameter α.

The prime objective of the present article is to investigate the heat and mass transfer impact on the viscous chemically reacting transient fluid flow past an upright surface analytically by employing Prabhakar fractional model. The fractional model has been developed for investigating the transient viscous fluid flow in the presence of inclined magnetic force subject to Newtonian surface heating. The integer order computation techniques for the governing partial differential equations for the formulated flow problem fail to determine the physical behavior of flow parameters with memory effects. To this end, the present model presents the fractional approach based on the Prabhakar fractional derivative. The problem modeled in terms of dimensionless expressions is first transformed into fractional model and later on simulations are performed with Laplace technique. The inverse Laplace transform of the flow characteristics is computed by adopting Stehfest and Tzou’s algorithms. For fractional parameters, the increasing trend in the velocity and temperature profiles has been observed. The increasing behavior of velocity subject to increasing values of heat Grashof number and mass Grashof number is observed.