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This article presents a comprehensive study on the thermal behavior of a three dimensional viscoelastic micropolar nanofluid under the inspiration of Cattaneo-Christov heat conduction model. The nanofluid is subject to an exponentially stretchable sheet and the flow is characterized by Darcy-Forchheimer formulation. Similarity variables are used to convert viscoelastic nanofluids PDEs into ODEs. MATLAB platform with bvp4c command is used to solve resulting ODE. The impact of involving parameters such that velocity ratio, Schmidt number, Prandtl number, Peclet number, Forchheimer number, buoyancy ratio parameter, Brownian motion, Heat source, Magnetic parameter on velocity profiles, rotation, temperature concentration and density profiles via graphs and tables. Temperature curve is improved up for magnetic parameters, temperature exponent parameter and thermopherosis parameter while significance loss is noted for increasing value of Prandtl number Pr and relaxation time λT. This research bears significance in applications related to advanced heat exchangers, microfluidic systems, and other emerging technologies where the interplay of nanofluids, viscoelasticity, and non-local heat conduction is of paramount importance.

Tangent hyperbolic nanofluid enhances heat transfer in various applications, such as cooling systems and electronics, due to its improved thermal conductivity and stability. Therefore current analysis explore the inspiration of joule heating and activation energy on Tangent hyperbolic nanofluid in the existence of motile microorganism. For motivation the impact of Riga plate, variable thermal conductivity, thermal radiation and heat source are the part of this investigation. The appropriate similarity variable are assumed to transformed the set of governing partial differential equations considering the influential effects of Joule heating and activation energy into ordinary differential equations. MATLAB via bvp5c tool is engaged to solve resulting system. The effects of dimensionless parameters like Weissenberg number We, Power-law index Power-law index n, Hartmann number M, thermal radiation Rd, Brownian motion Nb, Prandtl number Pr, Peclet number Pe and thermophoresis Nt on velocity f′(η) temperature θ(η), volumetric concentration of nano particles φ(η) and density profile χ(η) are displayed in graphical and tabulated form. It is noted that improving the Weissenberg number We, Hartmann number M and Power-law index n, the speed of flow decreased. By increasing value of Prandtl number Pr the temperature curve reduced, inverse relation is observed for growing value of Rd.

The need for a consistent and reliable energy supply to improve productivity is steadily increasing both in industrial and residential settings. The fulfillment of this requirement can be effectively achieved by implementing quadratic thermal radiation, such as utilizing an appropriate thermoelectric generator to supply power and optimizing the optical heat process. This research investigates the three different thermal radiation models, namely linear, quadratic, and nonlinear thermal radiation on the two-phase boundary layer flow of a dusty nanofluid across a vertically moving flat plate. The nanofluid is composed of aluminum oxide (Al203) and nanoparticles suspended in water (H20) based fluid. Furthermore, quadratic Boussinesq approximation and Prandtl's boundary layer approximation are utilized. The Chebyshev collocation spectral method is employed to address the non-linear problem. The effect of different parameters, such as thermal Grashof number, momentum dust, magnetic field parameter on the fluid flow, and temperature profiles are considered to visualize the findings. The findings show that linear thermal radiation exhibits the lowest thermal transport, followed by quadratic thermal radiation, with nonlinear thermal radiation demonstrating the highest thermal transport. The velocity of the dusty nanoliquid is decreased when a transverse magnetic field is present. Additionally, it is observed that the existence of aluminum oxide nanoparticles of 3% volume concentration in particulate H20 effectively increases the thermal transfer of the fluid system.

A coupled system of fractional order Gross-Pitaevskii equations is under consideration in which the time-fractional derivative is given in Caputo sense and the spatial fractional order derivative is of Riesz type. This kind of model may shed light on some time-evolution properties of the rotating two-component Bose¢ Einstein condensates. An unconditional convergent high-order scheme is proposed based on L2-$ 1_{\sigma} $ finite difference approximation in the time direction and Galerkin Legendre spectral approximation in the space direction. This combined scheme is designed in an easy algorithmic style. Based on ideas of discrete fractional Grönwall inequalities, we can prove the convergence theory of the scheme. Accordingly, a second order of convergence and a spectral convergence order in time and space, respectively, without any constraints on temporal meshes and the specified degree of Legendre polynomials $ N $. Some numerical experiments are proposed to support the theoretical results.

The Cattaneo-Christov heat and mass flux theory extends classic models to provide more accurate predictions in situations with instantaneous heat and mass transfer. Herein, an enhancement of heat and mass transfer in Carreau-Yasuda (CY) tri-nanofluid (TNF) over a stretched surface is modeled and studied via generalized conservation laws subjected to Cattaneo-Christov heat and mass flux theory. Silicon carbide (SiC), Aluminum Oxide (Al2O3), and Silver (Ag) are recruited as active nanoparticles in ethylene glycol (C2H6O2), and hired as CY fluid. Based on Finite Element Method (FEM), the code is created and validated for the formulated problems by comparing the current results to the published benchmarks. The computational findings showed that the thickness of the thermal and diffusion boundary layer decreases by increasing the thermal (δ) and diffusion relaxation (δc) parameters. The numerical analysis showed that CY-TNF exerts the largest shear stress on the wall compared to CY mono nanofluid (NF), and CY hybrid nanofluid (HNF). If CY-TNF has to flow over the specific surface, then adequate surface strength must be ensured. Moreover, comparing enhancement in thermal properties of CY-NF, CY-HNF, and CY-TNF revealed that the CY-TNF performs better than CY-HNF and CY-NF. Owing to the highest heat and mass flux, CY-TNF has an optimized ability to transport heat and mass, thus proving to be an efficient fluid for all processes requiring optimized heat and mass flux.

In this paper, numerical simulation for the two-dimensional flow of tangent hyperbolic fluid in the manifestation of nanoparticles, heat source and joule heating is considered. For motivation of problem, the role of Riga plate is investigated. Chemical reaction and Brownian motion are the parts of the analysis. The set of PDEs of Tangent hyperbolic nanofluids with swimming germs is converted in to couple of ODEs by employing well-known approach namely shooting scheme. The resulting highly nonlinear and coupled ODEs are solved by using ND solve tool of Wolfram Mathematica 11. Numerical outcome of involving parameters of interest like Lewis number Le, Prandtl number Pr, Chemical diffusion k, Peclet number Pe, Weissenberg number We, Bioconvection Lewis number Lb, nonlinear radiation, Biot number Bi, modified Hartmann number Q and magnetic parameter M on tangent hyperbolic nanofluids velocity f″, temperature θ, concentration φ and density of germs distribution are discussed in the form of graphical trend and tables. We professed that the speed of fluid degenerated for the increasing value of power-law index n and magnetic parameter M. The Nusselt number growths for growing values of the thermophoresis parameter Nt, Biot number Bi and radiation parameter Nr.

The exploration of electroosmotic peristaltic flow in asymmetric channels using hybrid non-Newtonian nanofluids holds significant promise across multiple domains. From microfluidics and electronics cooling to energy systems and biomedical applications, its implications are vast. By leveraging the distinctive attributes of nanofluids and the precision offered by electroosmotic and peristaltic flow, this research has the potential to drive the development of more efficient and innovative designs in these diverse fields. The current investigation reveals an analysis of heat transfer concerning hybrid nano liquid based on water. This nano liquid is influenced by both electroosmosis and peristalsis, operating simultaneously. Within this water-based hybrid nanofluid, there are nanoparticles composed of copper and iron oxide (Fe2O3−Cu/H2O). The study investigates into characteristics of flow and heat transport processes, considering key factors such as the applied electric and magnetic fields, thermal conductivity, mixed convection, shape of nanoparticles, variable viscosity, and assumptions related to Ohmic heating. Thermal and velocity slip boundary conditions are considered. To handle the analysis, the Poisson-Boltzmann equation is approximated using the Debye-Hückel approximation. The governing equations are then simplified using lubrication approximation. To solve the resulting system of dimensionless differential equations, NDSolve build in command of computational package Mathematica is employed. The outcomes of study affirm that inclusion of nanomaterials plays a vital role in enhancing heat transfer processes. Specifically, an increase in Joule heating and electromagnetic parameters contributes to a higher heat transfer rate at the boundary. Additionally, the incorporation of nanomaterials leads to a decrease in the flow rate of the nanofluid due to an increase in Helmholtz-Smoluchowski velocity. Furthermore, the heat transfer rate at wall diminishes as the Hartman number and Helmholtz-Smoluchowski velocity are increased. Showcasing the potential to enhance heat transfer, microfluidic devices, and various systems by harnessing the distinctive characteristics of hybrid nanofluids and regulating flow through peristaltic and electroosmotic methods. Providing insights into potential applications and industries that could profit from these findings, including microfluidics, electronics cooling, biomedical devices, and energy systems.

The growing need for reliable energy supply to enhance productivity in industrial and residential sectors underscores the importance of conserving solar energy. This can be achieved through measures such as optimizing solar collector coatings and optical heat processes. The environmental risks posed by fossil fuels, like coal and diesel, for electricity generation, further highlight the urgency of seeking alternative solutions. Solar energy has emerged as a highly promising option, capturing global attention for its potential to improve productivity and sustainability. The study focuses on examining aluminum alloy-titanium alloy/ethylene glycol hybrid nanofluid in the flow of non-Newtonian Oldroyd-B through a parabolic trough surface collector located in the solar water pumps (SWP). The Galerkin weighted residual method was utilized to solve the group of equations that describe momentum, energy, and entropy generation. The findings show that the hybrid nanofluid leads to better thermal radiative performance compared to the ordinary nanofluid. Therefore, the implications of these findings are substantial, particularly in the fields of thermal engineering and renewable energy. By offering insights into the efficient utilization of solar energy in water pumping systems and the reduction of entropy generation, this research has the potential to drive innovations that enhance the sustainability and performance of such systems.

This study examines the impact of solar-powered tractor on agricultural productivity and energy efficiency. The implementation of solar energy in tractors has the potential to reduce dependence on non-renewable energy sources, minimize carbon emissions, and promote sustainable farming practices. This research investigates the reduction of energy consumption and enhancement of productivity by evaluating magnetohydrodynamic (MHD) entropy production through the flow of nanofluids containing copper-engine oil (Cu-EO) and silver-engine oil (Ag-EO). The study also evaluates the effectiveness of thermal transport in solar-powered tractors through several properties such as solar thermal radiation, viscous dissipation, slippery velocity, and porous media. The investigation analyzed the thermodynamics of entropy generation in a non-Newtonian Williamson nanofluid, with the aim of assessing its energy equilibrium and the effects of diverse physical parameters. In order to enable numerical investigation, similarity variables were implemented to transform partial differential equations into ordinary differential equations, and the Chebyshev collocation spectral method was applied to solve the governing equations. It has been revealed that the Ag−EO Williamson nanofluid have a smoother flow compared to the Cu−EO mixture fluid. Furthermore, Williamson-nanofluid demonstrate superior thermal conductivity and heat transfer characteristics compared to the base fluid, making them appropriate for utilization in cooling systems and heat exchangers in various industries. The boundary layer exhibits the maximum temperature while employing lamina-shaped particles, whilst the lowest temperature is shown when utilizing spherical-shaped nanoparticles. The Ag-EO nanofluid an efficiency rate of approximately 2.64 % with a minimum efficiency rate of 3.22 %. The findings will help develop eco-friendly agricultural methods that promote economic development while mitigating harm to the environment.

This paper explores the new soliton solutions of the evolution equations named as truncated M-fractional (1+1)-dimensional non-linear Kaup-Boussinesq system by utilizing the expa function, modified simplest equation and Sardar sub-equation techniques. This system is used in the analysis of long waves in shallow water. The attained results involving trigonometric, hyperbolic and exponential functions. The effect of fractional order derivative is also discussed. Obtained results are very close to the approximate results due to the use of M-fractional derivative. Achieved results are verified by Mathematica tool. Few of the gained results are also explained through 2-D, 3-D and contour graphs. At the end, these techniques are straight forward, useful and effective to deal with non-linear FPDEs.

The distinction between homogeneous and heterogeneous chemical reactions is crucial because many chemically reactive systems, such as hydrometallurgical processes, cooling towers, biological systems, fog dispersion, catalysis, etc., involve both types of reactions. Thus, this study analyzes the heat transmission (HT) characteristics in an MHD stagnant flow of power-law fluid caused by a spinning disk that is stretched and saturated in a porous medium. The study considers homogeneous-heterogeneous (HH) reactions and nonlinear thermal radiation subject to no-slip and convection boundary conditions. The leading equations are switched into ordinary differential equations (ODEs) employing similarity variables. The study focuses on the dimensionless concentration, velocity, temperature, Nusselt number, and skin friction coefficient, which are discussed in detail in the results and discussion section. The study observes that for power-law fluids with an index value less than 1, the skin friction coefficient decays as the power-law index grows. It also notes that the dimensionless skin friction of power-law fluids decreases as the velocity ratio increases. The dimensionless concentration increases with Schmidt and modified Prandtl numbers for both power-law fluids over a stretching spinning porous disk. The HH reaction parameters decline the concentration of power-law fluids.

In this work, the modified auxiliary equation method (MAEM) and the Riccati–Bernoulli sub-ODE method (RBM) are used to investigate the soliton solutions of the fractional complex coupled maccari system (FCCMS). Nonlinear partial differential equations (NLPDEs) can be transformed into a collection of algebraic equations by utilizing a travelling wave transformation, the MAEM, and the RBM. As a result, solutions to hyperbolic, trigonometric and rational functions with unconstrained parameters are obtained. The travelling wave solutions can also be used to generate the solitary wave solutions when the parameters are given particular values. There are several solutions that are modelled for different parameter combinations. We have developed a number of novel solutions, such as the kink, periodic, M-waved, W-shaped, bright soliton, dark soliton, and singular soliton solution. We simulate our figures in Mathematica and provide many 2D and 3D graphs to show how the beta derivative, M-truncated derivative and conformable derivative impacts the analytical solutions of the FCCMS.The results show how effectively the MAEM and RBM work together to extract solitons for fractional-order nonlinear evolution equations in science, technology, and engineering.