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Nanoparticles have gained recognition for significantly improving convective heat transfer efficiency near boundary layer flows. The characteristics of both momentum and thermal boundary layers are significantly influenced by the Prandtl number, which holds a crucial role. In this vein, the current study conducted a detailed computational analysis of the mixed convection flow of $\gamma$Al$_2$O$_3$-H$_2$O and $\gamma$Al$_2$O$_3$-C$_2$H$_6$O$_2$nanofluids over a stretching surface. This research integrates an effective Prandtl number, utilizing viscosity and thermal conductivity models based on empirical findings. Additionally, a unique double-fractional constitutive model is debuted to accurately evaluate the effective Prandtl number’s function in the boundary layer. The equations were solved using a numerical technique that combined the finite-difference method with the L$_1$algorithm. This investigation presents numerical findings related to the velocity, temperature distributions, wall shear stress coefficient, and heat transfer coefficient, contrasting scenarios with and without the effective Prandtl number. The research shows that integrating nanoparticles into the base fluids reduces the temperature of the nanofluid with an effective Prandtl number while enhancing the heat transfer rate irrespective of its presence. Nonetheless, the introduction of a fractional parameter reduced the heat transfer efficiency within the system. Notably, the $\gamma$Al$_2$O$_3$-C$_2$H$_6$O$_2$nanofluid demonstrates superior heat transfer enhancement capabilities compared to its $\gamma$Al$_2$O$_3$-H$_2$O counterpart but also exacerbates the drag coefficient more significantly. Many practical applications of this study include electronics cooling, industrial process heat exchangers, and rotating and stationary gas turbines in power plants, and efficient heat exchangers in aircraft.Graphical Abstract

The immediate shift in the environment leads to many challenges in pursuit-evasion studies. Existing techniques need help to handle these unexpected changing scenarios. To address these situations, we proposed a hybrid solution called BINNQN. Hybrid Bio-Inspired Neural Network combined with the advantage of Deep Q-Network (DQN) to improve the performance of multi-robot evasion in unpredictable environments. Here, the BINN features help to simulate neurodynamic activities that approach a pursuit-evasion scenario. It also allows the immediate, real-time development of collision-free evasive paths. On the other hand, the DQN component provides continuous knowledge improvement to address the local minimal concerns and help adapt it to complex, unexpected risks. Additionally, DQN learns from the reward system to evaluate and select the best evasive actions based on continuous feedback from the environment; this helps the system increase the evasion time and decrease the risks of capture and collision. This hybrid approach involves the BINN-based quick response ability combined with the adaptive learning and decision-making ability of DQN. The existing studies implement their proposed approach with real-world mobile robots. Still, in contrast, this study creates an app to test the proposed hybrid BINNQN scenario, which provides a safe and cost-effective platform for testing and visualizing complex multi-robot evasion techniques without the risks of real-world hardware involvement. To encourage the user’s accessibility and their interaction knowledge with the model, we planned to execute the proposed model using the mobile app. Combining the advanced techniques of BINN and DQN, the proposed BINNQN model works well and effectively contributes to this field. The existing BINN achieves the stable value of 21.2, whereas the proposed hybrid achieves a stable state of 23.4, which is a promising approach for real-time evasion in complex multi-robot systems environments.

The finite element scheme is proposed and analyzed for the solution of an acid-mediated tumor invasion model. The reaction–diffusion equation shows the evolution in the tumor cell density, H + ions concentration, and healthy tissue density over time. The coupled non-linear partial differential equations are discretized in time with the implicit Euler method and in space with standard Galerkin finite element. To solve the non-linear and coupled terms of the system a fixed point iteration scheme is presented. Moreover, a mass-lumped scheme is adopted to reduce the computation cost. The cut-off method is used to compute the bounded solutions of the PDEs. Finally, The effects of proliferation rate and healthy tissue degradation rate are investigated. We aim to address the following research questions in our study, • How can a finite element algorithm be developed to simulate the tumor cell dynamics? • What key components should be considered to accurately represent tumor invasion? • How does acidity affect cell proliferation, and extracellular matrix remodeling? • How does the spatial and temporal heterogeneity contribute to variations in tumor invasion? • Can the finite element algorithm provide insights into the impact of heterogeneity on tumor invasion? [ABSTRACT FROM AUTHOR]

This study looks into the steady heat transfer issue of a flow of an incompressible Carreau fluid. Carreau fluid exhibits the shear thinning and thickening characteristics at low, moderate, and high shear rates. At the tubule wall, the fluid absorption is used as a function of pressure gradient and wall permeability through the tubule wall. Supposing the tubule radius considerably small in comparison to its length, the governing equations are considerably simplified. Significant quantities of interest are computed analytically by using perturbation, and the influence of emergent parameters is discussed through graphical results. The comparisons of results with existing data are set up to be good agreement.

Purpose:The goal of this study is to investigate the entropy optimization of Jeffrey nanofluid flow with the homogeneous and heterogeneous reaction by stretching the rotating disk. The impact of Hall current is also being considered. The process of heat transmission is carried out. For heat transfer coefficient, temperature, concentration, velocity, Bejan number, and entropy generation rate and relevant equations are computed. The implications of various characteristics are investigated. The effect of emerging parameters of nanofluid flow is discussed and represented by a graph. To reduce partial differential equations into ordinary differential equations by using effective similarity transformation. The achieved non-linear system is resolved by the Homotopy analysis technique (HAM) to found the convergent solution of the designated flow problem. The impact of various pertinent parameters, i.e thermal radiations parameter, Brinkman number, Reynolds number, magnetic parameter, Hall Effects parameter, Jeffrey nanofluid parameters are discussed and presented by the graph. Engineering quantities such as Nusselt number and skin friction are also taken into account.