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In this article, we analyze the dynamics of the non-linear tumor-immune delayed (TID) model illustrating the interaction among tumor cells and the immune system (cytotoxic T lymphocytes, T helper cells), where the delays portray the times required for molecule formation, cell growth, segregation, and transportation, among other factors by exploiting the knacks of soft computing paradigm utilizing neural networks with back propagation Levenberg Marquardt approach (NNLMA). The governing differential delayed system of non-linear TID, which comprised the densities of the tumor population, cytotoxic T lymphocytes and T helper cells, is represented by non-linear delay ordinary differential equations with three classes. The baseline data is formulated by exploiting the explicit Runge-Kutta method (RKM) by diverting the transmutation rate of Tc to Th of the Tc population, transmutation rate of Tc to Th of the Th population, eradication of tumor cells through Tc cells, eradication of tumor cells through Th cells, Tc cells' natural mortality rate, Th cells' natural mortality rate as well as time delay. The approximated solution of the non-linear TID model is determined by randomly subdividing the formulated data samples for training, testing, as well as validation sets in the network formulation and learning procedures. The strength, reliability, and efficacy of the designed NNLMA for solving non-linear TID model are endorsed by small/negligible absolute errors, error histogram studies, mean squared errors based convergence and close to optimal modeling index for regression measurements. [ABSTRACT FROM AUTHOR]

Entropy generation with activation energy has garnered worldwide attention from researchers due to its extensive applications in thermodynamic design, chemical engineering, and optimization processes. One of the primary reasons for focusing on entropy is the global energy crisis, driven by massive consumption against limited resources. This study elucidates the double diffusion process in the dynamics of a viscous fluid over a stretching cylinder, incorporating considerations of entropy generation and activation energy. The non‐Fourier heat flux model is employed to describe the thermodynamics of the thermal system, while non‐Fick's law is used to elucidate the mass diffusion process. The unsteady phases of axisymmetric flow of the viscous fluid are thoroughly discussed. Transport equations in cylindrical configuration are transformed into ordinary differential equations, and an efficient mathematical method (i.e., homotopy analysis method) is applied to solve the transformed system. The graphical examination reveals the impact of flow parameters on velocity configuration, entropy configuration, temperature configurations, and concentration configurations. Additionally, a comparative benchmark is established with the results from previously published work for authentication and validation purposes. It is noted that concentration and temperature configurations are directly related to the unsteady stretching parameter. Entropy generation exhibits an inverse relationship with the unsteady stretching parameter when close to the stretching cylinder, whereas it shows a direct relationship when the fluid is flowing away from the surface. [ABSTRACT FROM AUTHOR]

In this study, a novel neuro heuristic approach is designed to investigate the flow properties of magnetohydrodynamic (MHD) nanofluid along an exponentially extending sheet with a permeable medium with the impact of radiation as well as fluctuating heat source/sink. The designed scheme to handle the suggested problem is established through the well‐known biologically inspired neural networks (BINNs) by exploiting the inverse multiquadric kernel (IMQK), that is, BINNs‐IMQK which is quite a new approach. The partial differential equations (PDEs) which govern the fluidic flow are reformed into a nonlinear system of ordinary differential equations (ODEs) using the most fitted similarity transformations rules and numerically solved by varying the parametric values including unsteady parameter, Brownian motion parameter, suction/injection parameter, radiation parameter, Schmidt number together with Prandtl number to visualize the velocity, thermal gradient, and mass transfer in the suggested fluid problem. It is noticed that nanofluid temperature hikes by uplifting the value of the Brownian motion parameter but this effect is reversed in case of unsteady parameter. The obtained numerical results are verified through reference solution using the well‐known Adams method and the efficacy of the suggested solver is endorsed using a variety of statistical operators. [ABSTRACT FROM AUTHOR]

Purpose: The present study aims to encompass the bidirectional magnetized flowing of a hybrid-nanofluid over an unsteady stretching device with the inclusion of thermal radiation and entropy generation. Brick-shaped nanoparticles (zinc-oxide and ceria) are suspended in water, serving as the base-fluid to observe the performance of the hybrid mixture. The Maxwell thermal conductivity relation is employed to link the thermophysical attributes of the hybrid mixture with the host liquid. Additionally, a heat source/sink term is incorporated in the energy balance to enhance the impact of the investigation. Both prescribed-surface-temperature (PST) and prescribed-heat-flux (PHF) conditions are applied to inspect the thermal performance of the hybrid nanofluid. Design/methodology/approach: The transport equations in Cartesian configuration are transformed into ordinary differential equations (ODEs), and an efficient method, namely the Keller-Box method (KBM), is utilized to solve the transformed system. Postprocessing is conducted to visually represent the velocity profile, thermal distribution, skin-friction coefficients, Bejan number, Nusselt number and entropy generation function against the variations of the involved parameters. Findings: It is observed that more entropy is generated due to the increases in temperature difference and radiation parameters. The Bejan number initially declines but then improves with higher estimations of unsteadiness and Hartmann number. Overall, the thermal performance of the system is developed for the PST scenario than the PHF scenario for different estimations of the involved constraints. Originality/value: To the best of the authors' knowledge, no investigation has been reported yet that explains the bidirectional flow of a CeO2-ZnO/water hybrid nanofluid with the combined effects of prescribed thermal aspects (PST and PHF) and entropy generation. [ABSTRACT FROM AUTHOR]