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In contemporary times, there has been a significant focus among researchers on hybrid nanofluids derived from oils, owing to their remarkable and substantial utility in the domains of engineering, mechanics, and industrial applications. The aim of this research is to determine the impact of incorporating tantalum and nickel nanoparticles in mineral oil on thermal characteristics and flow patterns, with the objective of predicting possible improvements. The dependence of the role of both nanoparticles on their shapes is evaluated for column, platelet, lamina, cylinder, and tetrahedron-type shapes. This work analyzes the thermal performance of two different nanofluids individually made of tantalum and nickel nanoparticles while also examining the synergistic effects produced due to the simultaneous suspension of these particles. A profound understanding of the intricate flow dynamics and thermal energy transfer phenomena along a vertical surface holds paramount importance in the pursuit of optimizing heat exchange procedures, formulating effective cooling systems, and designing thermally efficient devices. Furthermore, it contributes to the advancement of climate modeling, the precision of weather forecasting, and the refinement of the operational effectiveness of solar thermal systems. The basic mathematical model is formulated subject to free convection, time-dependent flow and heat conditions, and thermal radiation. This governing system is made non-dimensional to lessen the intricacy and provide the basis for the utilization of fractional operators. In order to assess the effectiveness of fractional modeling techniques, constant proportional Caputo (CPC) and Atangana–Baleanu (ABC) derivatives are operated for the model generalization. Most of the time, solving fractional models via an analytic method are not a feasible technique because it produces extremely complex and implicit mathematical expressions. However, in this study, the Laplace transform is served as a solution procuring technique, and series and integral form exact solutions are extracted for CPC and ABC derivative-based models, respectively. To interpret modifications in thermal and velocity patterns arising from diverse physical phenomena, numerous graphical depictions of exact solutions are communicated. Moreover, the implications of varying a number of critical factors, including the fractional parameter, nanoparticles' shapes and proportions, and radiation term, on shear stress and thermal productivity of the hybrid nanofluid are discussed using the tabulated findings. On comparing shape effects and individual suspensions of considered nanoparticles, it is observed that lamina shape and nickel nanoparticles are relatively more effective regarding the improvement of thermal performance. The model based on the CPC derivative yields lower profiles of temperature and flow functions as compared to the ABC derivative-based model. The results indicate that introducing homogeneous proportions of tantalum and nickel nanoparticles into mineral oil raises its heat-transferring capacity by up to 47.60%. These findings suggest that the examined hybrid nanofluid performs extremely well as a lubricant and a cooling agent. [ABSTRACT FROM AUTHOR]

Engine Oil is a widely used fluid in engineering problems, particularly to enhance the rate of heat transfer when these working fluids play a fundamental role. We consider engine oil as a base fluid and the suspension of different shaped (Spherical cylindrical and platelet) nanoparticles dispersed uniformly in the base fluid to enhance the working capability of engine oil. The spherical shape CuO , platelet shape Al 2 O 3 and cylindrical shape TiO 2 nanoparticles are added in engine oil to constitute tri-hybrid nanofluid aiming at obtaining better thermal performance. Furthermore, we also analyze the Jeffery tri-hybrid nanofluid in a rotating frame over an infinite vertical plate. More precisely, the classical model of Jeffery tri-hybrid nanofluid is transformed into a time-fractional model by applying the newly developed constant proportional Caputo fractional derivatives. Sharp numerical results are obtained applying a Laplace transform steered approach. All the flow parameters are highlighted through graphs via MATHCAD. Furthermore, a comparative analysis between nanofluid, hybrid nanofluid and tri-hybrid nanofluid has been performed showing that tri-hybrid nanofluid has good thermal performance. The solutions of the constant proportional operator are discussed classically by taking fractional parameter α → 1. Moreover, some engineering quantities have been calculated and presented in tables. During the analysis we dispersing the mixture of nanoparticles in engine oil base fluid enhanced the heat transfer up-to18.72% which can efficiently improve the lubricity of the engine oil. [ABSTRACT FROM AUTHOR]

The core devotion of this study is to develop a generalized model by means of a recently proposed fractional technique in order to anticipate the enhancement in the thermal efficiency of engine oil because of the dispersion of graphene and magnesia nanoparticles. In addition to investigating the synergistic attributes of the foregoing particles, this work evaluates shape impacts for column, brick, tetrahedron, blade, and lamina-like shapes. In the primary model, the flow equation is coupled with concentration and energy functions. This classical system is transmuted into a fractional environment by generalizing mathematical expressions of thermal and diffusion fluxes by virtue of the Prabhakar fractional operator. In this study, ramped flow and temperature slip conditions are simultaneously applied for the first time to examine the behavior of a hybrid nanofluid. The mathematical analysis of this problem involves the incorporation of dimension-independent parameters into the model and the execution of the Laplace transform for the consequent equations. By doing so, exact solutions are derived in the form of Mittag–Leffler functions. Multiple illustrations are developed by dint of exact solutions to chew over all aspects of temperature variations and flow dynamics. For the preparation of these illustrations, the details of parametric ranges are as follows: 0.00 ≤ Υ ≤ 0.04 , 2.0 ≤ G r 1 ≤ 8.0 , 0.5 ≤ S c ≤ 2.0 , 0.1 ≤ τ ≤ 4.0 , 0.1 ≤ d ≤ 0.6 , 0.2 ≤ λ 1 ≤ 1.5 , and 1.0 ≤ G r 2 ≤ 7.0 . The contribution of differently shaped nanoparticles, volume proportions, and fractional parameters in boosting the heat-transferring attributes of engine oil is also anticipated. In this regard, results for Nusselt number are provided in tabular form. Additionally, a brief analysis of shear stress is carried out for fractional parameters and various combinations of magnesia, graphene, and engine oil. This investigation anticipates that engine oil's hybridization with magnesia and graphene would result in a 33% increase in its thermal performance, which evidently improves its industrial significance. The enhancement in Schmidt number yields an improvement in the mass transfer rate. An increment in collective volume fraction leads to raising the profile of the thermal field. However, the velocity indicates a decreasing behavior. Nusselt number reaches its highest value ( N u = 8.1363 ) for the lamina shape of considered particles. When the intensity of the buoyancy force augments, it causes the velocity to increase. [ABSTRACT FROM AUTHOR]

The researchers are continuously working on nanomaterials and exploring many multidisciplinary applications in thermal engineering, biomedical and industrial systems. In current problem, the analytical simulations for performed for thermos-migration flow of nanofluid subject to the thermal radiation and porous media. The moving wedge endorsed the flow pattern. The heat source effects are also utilized to improves the heat transfer rate. The applications of thermophoresis phenomenon are addressed. The formulated set of expressions are analytically treated with implementation of variational iteration method (VIM). The simulations are verified by making the comparison the numerical date with existing literature. The VIM analytical can effectively tackle the nonlinear coupled flow system effectively. The physical impact for flow regime due to different parameters is highlighted. Moreover, the numerical outcomes are listed for Nusselt number. [ABSTRACT FROM AUTHOR]

The study of thermo-physical characteristics is essential to observe the impact of several influential parameters on temperature and velocity fields. The transportation of heat in fluid flows and thermal instability/stability is a charming area of research due to their wider applications and physical significance because of their utilization in different engineering systems. This report is prepared to study thermal transportation in Maxwell hybrid nanofluid past over an infinite stretchable vertical porous sheet. An inclusion of hybrid nanofluid is performed to monitor the aspects of thermal transportation. Keeping in mind the advantages of thermal failure, non-Fourier theory for heat flux model is utilized. Aspects of external heat source are also considered. The mathematical formulation for the considered model with certain important physical aspects results in the form of coupled nonlinear PDEs system. The obtained system is reduced by engaging boundary layer approximation. Afterwards, transformations have been utilized to convert the modeled PDEs system into ODEs system. The converted nonlinear ODEs system is then handled via finite element method coded in symbolic computational package MAPLE 18.0. Grid independent survey is presented for the validation of used approach and the comparative analysis has been done to confirm the reliability of obtained solution. The obtained solution is discussed and physical aspects have been explored and recorded against numerous involved influential variables. Motion into hybrid nanoparticles and nanoparticles becomes slow down versus higher values of Forchheimer and Darcy's porous numbers. Thermal growth is enhanced for the case of hybrid nano-structures rather than for case of nanofluid. Thickness regarding momentum layer is dominated for hybrid nanoparticles rather than case of nanoparticles. [ABSTRACT FROM AUTHOR]

Fractal-fractional derivative is a new class of fractional derivative with power Law kernel which has many applications in real world problems. This operator is used for the first time in such kind of fluid flow. The big advantage of this operator is that one can formulate models describing much better the systems with memory effects. Furthermore, in real world there are many problems where it is necessary to know that how much information the system carries. To explain the memory in a system fractal-fractional derivatives with power law kernel is analyzed in the present work. Keeping these motivation in mind in the present paper new concept of fractal-fractional derivative for the modeling of couple stress fluid (CSF) with the combined effect of heat and mass transfer have been used. The magnetohydrodynamics (MHD) flow of CSF is taken in channel with porous media in the presence of external pressure. The constant motion of the left plate generates the CSF motion while the right plate is kept stationary. The non-dimensional fractal-fractional model of couple stress fluid in Riemann–Liouville sense with power law is solved numerically by using the implicit finite difference method. The obtained solutions for the present problem have been shown through graphs. The effects of various parameters are shown through graphs on velocity, temperature and concentration fields. The velocity, temperature and concentration profiles of the MHD CSF in channel with porous media decreases for the greater values of both fractional parameter α and fractal parameter β respectively. From the graphical results it can be noticed that the fractal-fractional solutions are more general as compared to classical and fractional solutions of CSF motion in channel. Furthermore, the fractal-fractional model of CSF explains good memory effect on the dynamics of couple stress fluid in channel as compared to fractional model of CSF. Finally, the skin friction, Nusselt number and Sherwood number are evaluated and presented in tabular form. [ABSTRACT FROM AUTHOR]

Involvement of hybrid nanoparticles a vital role to improve the efficiency of thermal systems. This report covers the utilization of different nanoparticles mixed in Carreau Yasuda material for the improvement of thermal performance. The configuration of flow situation is considered over a rotating porous cone by considering the Hall and Ion slip forces. Transport of momentum is considered to be in a rotating cone under generalized ohm's law and heat transfer is presented by considering viscous dissipation, Joule heating and heat generation. Rheology of considered model is derived by engaging the theory proposed by Prandtl. Modeled complex PDEs are reduced into ODEs under similarity transformation. To study the physics behind this phenomenon, solution is essential. Here, FEM (Finite Element Method) is adopted to compute the solution. Furthermore, the grid independent study is reported with several graphs and tables which are prepared to note the influence of involved parameters on thermal and velocity fields. It is worth mentioning that heat transport is controlled via higher radiation parameter and it upsurges for Eckert number. Moreover, Hall and ion slip parameters are considered significant parameters to produce the enhancement in motion of fluid particles but speed of nano and hybrid nanoparticles becomes slow down versus large values of Forchheimer and Weissenberg numbers. Additionally, an enhancement in production of heat energy is addressed via large values of heat generation number and Eckert number while reduction in heat energy is occurred due to positive values of thermal radiation and Hall and ion slip parameters. [ABSTRACT FROM AUTHOR]

In this study, the effects of variable characteristics amalgamated with chemical reaction and Arrhenius activation energy are analyzed on a two-dimensional (2D) electrically conducting radiative Casson nanoliquid flow past a deformable cylinder embedded in a porous medium. The surface of the cylinder is deformable in the radial direction i.e., the z-axis. The impression of Soret and Dufour's effects boosts the transmission of heat and mass. The flow is analyzed numerically with the combined impacts of momentum slip, convective heat, and mass conditions. A numerical solution for the system of the differential equations is attained by employing the bvp4c function in MATLAB. The dimensionless protuberant parameters are graphically illustrated and discussed for the involved profiles. It is perceived that on escalating the velocity slip parameter and porosity parameter velocity field depreciates. Also, on escalating the radiation parameter and heat transfer Biot number a prominent difference is noticed in an upsurge of the thermal field. For growing values of Brownian motion and thermophoretic parameters, temperature field augments. On escalating the curvature parameter and porosity parameter, drag force coefficient upsurges. The outcome of the Soret number, mass transfer Biot number, and activation energy parameter is quite eminent on the concentration distribution for the sheet in comparison to the deformable cylinder. A comparative analysis of the present investigation with an already published work is also added to substantiate the envisioned problem. [ABSTRACT FROM AUTHOR]