In this study, a mathematical model is developed to scrutinize the transient magnetic flow of Cross nanoliquid past a stretching sheet with thermal radiation effects. Binary chemical reactions and heat source/sink effects along with convective boundary condition are also taken into the consideration. Appropriate similarity transformations are utilized to transform partial differential equations (PDE’s) into ordinary ones and then numerically tackled by shooting method. The impacts of different emerging parameters on the thermal, concentration, velocity, and micro-rotation profiles are incorporated and discussed in detail by means of graphs. Results reveal that, the escalation in magnetic parameter and Rayleigh number slowdowns the velocity and momentum of the fluid. The increase in Biot number, radiation and heat sink/source parameters upsurges the thermal boundary but, converse trend is seen for escalating Prandtl number. The density number of motile microorganisms acts as a growing function of bioconvection Lewis number and declining function of bioconvection Peclet number.

The movement of microorganism cells in fluid influences various biotic processes, including septicity and marine life ecology. Many organic and medicinal applications need to look into the insight of mechanism in nanofluids containing a microbial suspension. The current paper concerns the bioconvection of a ternary hybrid nanofluid (Al₂O₃-Cu-CNT/water) flow containing motile gyrotactic microorganisms toward three different geometries (a flat plate, a wedge, and a cone) in the occurrence of natural convection, radiation, and heat source/sink. The Cattaneo–Christov theory is employed to develop the model. The equations are solved by using the “bvp4c function in MATLAB”. The influence of the crucial significant factors on the motile microorganisms’ density, velocity, temperature, nanoparticles’ concentration, microbe density gradient, and transmission rates of heat and mass is discussed. The results depict that the heat transmission rate is highest for the flow toward the cone, whereas the mass transmission rate and microbe density gradient are highest for the flow toward the wedge. In addition, the higher estimates of the thermal relaxation parameter corresponding to the Cattaneo–Christov theory act to enhance the rate of heat transmission. The results of the current study will be useful to many microbial-enhanced oil recovery systems, carriage processes, architectural design systems, medicinal fields that utilize nanofluids, and so on.

In this article, the iteration transform method is used to evaluate the solution of a fractional-order dark optical soliton, bright optical soliton, and periodic solution of the nonlinear Schrödinger equations. The Caputo operator describes the fractional-order derivatives. The solutions of some illustrative examples are presented to show the validity of the proposed technique without using any polynomials. The proposed method provides the series form solutions, which converge to the exact results. Using the present methodology, the solutions of fractional-order problems as well as integral-order problems are calculated. The present method has less computational costs and a higher rate of convergence. Therefore, the suggested algorithm is constructive to solve other fractional-order linear and nonlinear partial differential equations.

Nanofluids holding three distinct sorts of nanosized particles suspended in base fluid possess excellent thermal performance. In light of this novel use in coolant applications, the current work dealt with the optimal design and performance estimation of a ternary hybrid nanofluid, based on a modern machine learning prediction technique. The synthesis of $\left(Cu\right)$, $\left(Ti{O}_2\right)$, and $\left(Si{O}_2\right)$ ternary hybrid nanoparticles suspended in water over a symmetrically stretching sheet was scrutinized. The flow over a stretching sheet is the most noteworthy symmetry analysis for momentum and thermal boundary layers, due to the implications of heat transfer, and is applied in various industries and technological fields. The governing equations were transformed to a dimension-free series of ODEs, by handling similarity transformable with symmetry variables, after which, the series of ODEs were treated scientifically, with the help of the Wolfram Language tool. The precision of the current estimates was assessed by comparison to existing research. Moreover, the natures of the physical phenomena were forecast by designing a support vector machine algorithm with an emphasis on machine learning, which delivers a robust and efficient structure for every fluid application that infers physical influences. To validate the proposed research, some of the statistical metrics were taken for error assessment between true and anticipated values. It was revealed that the presented approach is the best strategy for predicting physical quantities. This investigation established that ternary hybrid nanofluid possesses excellent thermal performance, greater than that of hybrid nanofluid. The current optimization process delivers a new beneficial viewpoint on the production of polymer sheets, glass fiber, petroleum, plastic films, heat exchangers, and electronic devices. Hence, the obtained results are recommended for the development of industrial devices setups.