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The present problem is offered for the visualization of the MHD flow of non-Newtonian Cross-hybrid nanoliquid with the application of Darcy–Forchheimer through the porous medium toward the moving thin needle. Further, the present work described the engineering applications of the non-Newtonian fluids. Commonly, the non-Newtonian liquids are useful for lubricating purposes including greases and Engine oil (EO), etc. Additionally, the computations for Hall current and viscous dissipation are deliberated for the enhancement of flow behavior. The heat transmission phenomenon is discussed under the Cattaneo–Christov heat flux theory instead of Fourier's law. Engineering applications of the homogeneous and heterogeneous chemical reactions are analyzed in the current analysis. EO has an enormous application in the engineering fields, and therefore in the present work EO is used as a base liquid and molybdenum disulfide MoS 2 and graphene oxide GO are the nanoparticles. The hybrid nanofluid showed more satisfactory results in the enhancement of the heat transport in the engineering fields as compared to the nanofluids and regular fluids; therefore the MoS 2 and GO are mix-ups in the EO. The present model is developed in the form of PDEs which can be altered into ODEs through the execution of suitable similarity transformations. A homotopic analysis scheme is adopted for the analytic simulation of the transformed ODEs. The velocity, energy, and mass curves are computed against different flow parameters in a pictorial form. Skin friction and Nusselt in contour graphs are discussed. Key findings from this inspection are that both nanoparticle volume fractions declined the velocity profile but augmented the temperature of the hybrid nanoliquid. Further, it is noted that boosting the Schmidt has significantly reduced the hybrid nanofluid concentration. [ABSTRACT FROM AUTHOR]

Phenomena such as black hole (BH) growth, Hawking radiation and gravitational waves are captivating not only in changing spacetime's curvature but also in affecting the thermodynamics characteristics of the sources with respect to time. The current study aims at exploring the effects of time and quintessential dark energy on the thermodynamical properties of the perturbed Sch. BH spacetime. A technique, based on the introduction of general time conformal factor, i.e., e ϵ μ (t) , is employed, which allows us to rescale the energy context of spacetime. Employing the Lagrangian to the perturbed spacetime, the Noether symmetry equation is acquired, which subsequently yields a set of 19 partial differential equations (PDEs). By solving these PDEs, we get the required perturbed Sch. BH spacetime with their Noether and approximated Noether symmetries along with their conservation laws. Additionally, calculation of the spacetime event horizon as a function of time t is worked out. Meanwhile, the same effect is studied as well as graphically analyzed on pressure, surface gravity, Hawking temperature, and volume of time conformal quintessential Sch. BH. [ABSTRACT FROM AUTHOR]