• Energy Research

The physical significance of the Fractal fractional derivative, one of the most fascinating and modern analytical techniques, to the thermal flow is described in this paper. Free convection, which is the flow of an erratic, incompressible viscous fluid on a vertically inclined plate, has been considered in this work. Two types of base fluids, namely water and carboxymethyl cellulose, are used in the presence of graphene oxide (GO) and molybdenum disulfide (MoS2) nanoparticles. The flow is subject to slip possessions due to the inclined surface. The non-dimensional leading equations for thermal and momentum, under Boussinseq's approximation, can be solved by employing a Laplace transformation scheme, the fractal fractional derivative, and a more recent and improved definition of a fractional mathematical term. The thermal expressions are modeled using the Laplace transformation. The effect and comparison of various parameters are then visually and quantitatively analyzed after this activity. We, therefore, proposed that a water-based nanofluid's thermal profile and velocity are marginally higher than those of a hybrid nanofluid based on carboxymethyl cellulose. The momentum profile additionally illustrates the dual behavior of the flowing hybrid nanofluid as the fluid parameter of the Brinkman type increases.

Transport of heat in combustion engines, burners and consumption of energy via nuclear explosions is remarkably effected by magnetize nanofluid and radiation. Present attempt is relevant to the current Engineering applications; as design of heat exchangers, systems of renewable energy, and Nanotechnology. Therefore, main concern of the study is explored the radiative flux in Micropolar nanofluid flow under the Lorentz force and gravity modulation. The impacts of cross diffusion is also included in flow field. The mathematical model governing the flow are transformed into ODEs via similarity variables. The Keller box approach is utilized for numerical outcomes. A comprehensive analysis of the physical parameters is carried out, and numerical outcomes are displayed in graphical and tabular form. Obtained outcomes are compared with results that have already been published and found a good match. It has been found that temperature profile and concentration profile have a direct relation against Soret and Dufour respectively. Temperature profile and concentration profile has a direct relation against Dufour and Soret effects. Thermal field grows by enhancing radiation, Brownian motion and thermophoresis parameter. Furthermore, the skin friction.increases as the inclination factor grows up, but Nusselt and Sherwood numbers decline.

A number of thermal devices might benefit from the usage of nanofluids in solar power. In this research, the idea of MHD mixed convective hybrid nanofluids including grapheme oxide (GO) and molybdenum disulfide (MoS2) nanoparticles with water (H2O) and Carboxymethyl Cellulose (CMC) as base fluids in a perpendicular channel to analyze the heat transfer of the flowing fluid with the help of recent definition of fractional derivatives namely Fractal fractional derivative. The problem is expressed as PDEs with beginning and boundary conditions, and it is analyzed analytically using the Laplace transform method. The velocity, temperature, and concentration measurements are also shown in series for their appropriate Laplace inverse. Delays in parameters like nanoparticle volume sharing rate have a significant influence on these techniques. Skin friction, Nusselt, and Sherwood numbers are computed for the longitudinal channel's left and right walls, and the necessary numerical results are presented in tabular format. As a result, it is discovered that the rate of heat transfer reduces as the volume percentage of nanoparticles and the Fractal time fractional value rise. Furthermore, when comparing nanofluids, water-based (H2O + GO + MoS2) hybrid nanofluids have a greater influence on governed model than (CMC + GO + MoS2)-based hybrid nanofluids.

Nanofluids can be used in different solar thermal systems. Solar energy devices utilized in industries and nanofluids as a source of solar energy in thermal engineering are two other sources of solar energy, according to the article. This work inspects a viscous, incompressible nanofluid made of different (graphene oxide (GO) and molybdenum disulfide (MoS2)) nanoparticles suspended in carboxymethyl cellulose (CMC). The governed model also considers permeability and angled magnetic effects. Due to memory effects, classical derivatives cannot explore and estimate the physical significance of several fluid limitations. We have addressed the issues with nanofluid suspension using the Prabhakar fractional derivative definition, the quickest and latest modern fractional technique. First, the governed leading equations are transferred to a fractional version using the integral transform technique and Laplace transform, and then it is resolved with various numerical approaches. Each constraint visual impact and significance are analyzed by varying their considered values. The numerical influences of the heat and flow rate are observed at multiple time values. Therefore, we deduce that the momentum and heat profiles are slowed as the Prabhakar fractional restraints increase. While with the increment in the radiation parameter, the velocity profile shows an increasing behavior. Furthermore, the impact of graphene oxide-based suspension is more significant than molybdenum disulfide nanofluid on all governed equations due to the physical features of the considered nanoparticles.

This study investigates the complex behavior of Jeffrey nanofluid flow in a porous oscillating microchannel under the influence of magnetohydrodynamic (MHD) effects. The research explores how magnetic field distortions lead to diverse accumulation patterns of nanofluid particles, a phenomenon attributed to homogeneous magnetization in fluid dynamics. Nanoparticles ranging from 0.25 % to 0.5 % (low and inexpensive concentrations) are remarkably consistent for best results in most machining procedures. Different concentrations of various nanomaterial's is utilized (φ1 = φ2 = 0.01, 0.02, 0.03, 0.04) to make the simple nanfluid and hybrid nanofluid suspensions. By employing fractal-fractional derivatives governed by power law, a mathematical model developed to describe the time-varying, compressible MHD flow of Jeffrey nanofluid. The model incorporates the effects of heat transfer, pressure, and magnetic fields on the fluid dynamics. A novel fractional approach utilizing the Laplace transform is applied to solve the fractal MHD hybrid-fluid model integrated into a porous medium. The study reveals velocity flow decrease with increasing Reynolds numbers but increase with channel inclination. Additionally, both the Darcy number and magnetic field orientation enhance heat transfer rates. In addition, the velocity profile enhanced by the hybrid nanofluid suspension as compared to simple nanofluid flow. The research validates its findings by demonstrating the convergence of fractional and numerical solution methods. Furthermore, the study compares the performance of different hybrid nanofluids, concluding that water-based (H2O + GO + MoS2) hybrid fluids exhibit slightly superior characteristics compared to (CMC + GO + MoS2) hybrid nanofluids.

This study investigates the impact of coupled heat and mass transfer on the peristaltic migration of a magnetohydrodynamic (MHD) stress-strain Jeffery-type hybrid nanofluid flowing through an inclined asymmetric micro-channel with a porous medium. The fundamental two-dimensional momentum and energy transport equations are simplified under the assumptions of long wavelength and low Reynolds number. To solve the momentum and heat transfer problems, two advanced fractional derivative approaches are employed: the fractal integral and the Prabhakar fractional derivative. The pressure difference is determined using numerical integration techniques, such as the Stehfest and Tzou's algorithms. The results are presented through graphs and tables, which illustrate the effects of various parameters on the velocity, heat transfer, and trapping phenomena. As a result, we concluded that, pressure gradients grow with higher Reynolds numbers and channel-inclined angles. The heat transfer rate is observed to decrease as the Darcy number and the orientation of the electromagnetic field increase. When comparing the fractional derivative approaches, the fractal operator exhibits a more significant impact on the momentum profiles compared to the Prabhakar fractional operator. This difference is attributed to the distinct characteristics of the integral kernels associated with each fractional derivative definition. Furthermore, when comparing hybrid nanofluids, water-based (H2O + Ag + TiO2) hybrid fluids have a somewhat more significant effect than (C6H9NaO7 + Ag + TiO2) hybrid nanofluids.

Engineers have recently become attracted to electrically conducting nanofluids (NFs) due to various applications in several applied science and engineering disciplines. They have been employed in magnetic refrigeration, cancer treatment (hyperthermia), medicine, and magnetic resonance imaging, among other things. Considering the importance of electrically conducting NFs, in this article, we have proposed a fractionalized MHD (Magnetohydrodynamics) and thermal transmission of a Brinkman-type tri-hybrid nanofluid over an infinite plate saturated through a porous medium with generalized velocity and ramped conditions. For the solution of the governed fractional model, we have utilized a recent definition of fractional derivatives, known as Atangana-Baleanu (AB) fractional derivative and Laplace transformation. The computational results are exhibited for tri-hybrid (TiO2-Al2O3-CuO/H2O) NF and described through graphical diagrams and tables to discover the physics of numerous relevant flow parameters on temperature and velocity profiles. It is detected that both thermal transmission and momentum profile for tri-hybrid NF is a better technique as compared to hybrid NF and NF for both graphical and numerical comparisons.

The photosynthetic activity of phytoplankton in the seas is responsible for an estimated 50–80 % of the world's oxygen generation. Both phytoplankton and zooplankton require some of this synthesized oxygen for cellular respiration. This study aims to better understand how the oxygen-phytoplankton dynamics are altered due to the Allee effect in phytoplankton development, particularly when considering the time-dependent oxygen generation rate. The dynamic analysis of the model is dedicated to finding the possible equilibrium points. The analysis reveals that three equilibrium points can be obtained. The stability study demonstrates that one of the equilibrium points is always stable. The remaining equilibrium points are stable under specific conditions. We also identify bifurcations originating from these equilibrium points, including transcritical, pitchfork, and Hopf bifurcation. We derive conditions for stable limit cycles (supercritical Hopf bifurcation) and, in some cases, establish the non-existence of solutions. Numerical simulations are performed to validate our theoretical findings. Furthermore, it is noted that the Allee threshold for the phytoplankton population (k0) significantly influences the overall dynamics of the system. When k0≤0.001, the population of plankton is at risk of extinction. On the other hand, when 0.001

In this paper, we propose an effective numerical method to solve the one- and two-dimensional time-fractional convection-diffusion equations based on the Caputo derivative. The presented approach employs a hybrid method that combines Lucas and Fibonacci polynomials with the Caputo derivative definition. The main objective is to transform the problem into a time-discrete form utilizing the Caputo derivative technique and then approximate the function's derivative using Fibonacci polynomials. To evaluate the efficiency and accuracy of the proposed technique, we apply it to one- and two-dimensional problems and compare the results with the exact as well as with existing methods in recent literature. The comparison demonstrates that the proposed approach is highly efficient, accurate and ease to implement.