This study emphasizes the performance of two-dimensional electrically non-conducting Oldroyd-B fluid flowing across a stretching sheet with thermophoretic particle deposition. The heat and mass transfer mechanisms are elaborated in the presence of a magnetic dipole, which acts as an external magnetic field. The fluid possesses magnetic characteristics due to the presence of ferrite particles. The gyrotactic microorganisms are considered to keep the suspended ferromagnetic particles stable. Cattaneo–Christov heat flux is cogitated instead of the conventional Fourier law. Further, to strengthen the heat transfer and mass transfer processes, thermal stratification and chemical reaction are employed. Appropriate similarity transformations are applied to convert highly nonlinear coupled partial differential equations into non-linear ordinary differential equations (ODEs). To numerically solve these ODEs, an excellent MATLAB bvp4c approach is used. The physical behavior of important parameters and their graphical representations are thoroughly examined. The tables are presented to address the thermophoretic particle velocity deposition, rate of heat flux, and motile microorganisms’ density number. The results show that the rate of heat transfer decreases as the value of the thermal relaxation time parameter surges. Furthermore, when the thermophoretic coefficient increases, the velocity of thermophoretic deposition decreases.

High-temperature heat transfer mechanisms seen in many systems are significantly influenced by thermal radiation. When there are significant temperature fluctuations within the thermal boundary layer, radiative heat transport is often inadequately captured by conventional linear radiation models. To overcome this constraint and provide a more accurate depiction of radiative heat transport, the quadratic thermal radiation model is used. Given these appealing features, the present study investigates the aqueous-based hybrid nanofluid over an extending surface with variable thickness influenced by quadratic thermal radiation. The hybrid nanofluid comprises carbide nanoparticles (SiC, TiC) suspended in water. The novelty of the proposed model lies in considering both homogeneous and heterogeneous reactions under convective boundary conditions at the surface. Analytical solutions are derived for the anticipated model using the optimal homotopy asymptotic method (OHAM). The trends of velocity and temperature distributions are analyzed via graphs against distinct parameters. The outcomes show that fluid velocity declines by approximately 52% as the volume fraction of carbide nanoparticles increases from 0.01 to 0.07. Also, the temperature increases by approximately 57% as quadratic thermal radiation increases from 0.1 to 3.1. Tabular results indicate that the carbide nanoparticle volume fraction ranges from 0.01 to 0.05, enhancing the heat transfer rate by approximately 37.5%. These results demonstrate that nonlinear radiation modeling and carbide-based hybrid nanofluids can greatly enhance heat transport. As a result, this study’s findings could offer valuable theoretical guidance for the development and improvement of advanced thermal systems across fields such as fluid mechanics, thermal management, and chemical processing technologies. The model’s trustworthiness is confirmed by comparing it with existing published work.

A two-component model of reactive liquid chromatography is presented consid?ering M ? N type reaction. The model incorporates surface and pore diffusions in the adsorbates, axial dispersion, interfacial mass transfer, first order chemical reactions in the liquid and particle phases, and two sets of boundary conditions. The model contains a system of four coupled PDE describing the dynamics of reactants and products in both phases. The Laplace transformation and eigen-decomposition technique are jointly applied to solve the model equations analytically. An efficient and accurate numerical Laplace inversion technique is utilized to retrieve back solutions in the original time domain. The developed semi-analytical results are verified against the numerical results of a high resolution finite volume scheme. A good agreement between the solutions not only confirms the accuracy of semi-analytical results but also validates the accuracy of proposed numerical scheme. This study extends and generalizes our previous analysis on heterogeneous reactions in the liquid chromatography. In order to analyze the behavior of a chromatographic reactor, different case studies are presented showing the effects of model parameters on the process.

This study investigates unsteady hybrid nanofluid flow between concentric stretched cylinders, incorporating homogeneous-heterogeneous (h–h) reactions. The SWCNTs/MWCNTs are selected as hybrid nanoparticles in a base fluid engine oil, with Newtonian heating at the inner wall. The shape factors of the nanoparticles were also considered, as they are important in the heat transfer rate of the system. Uniquely, in order to better explain the heat transfer phenomenon, the Hamilton-Crosser model and the Einstein model are used, which explain the variable temperature-dependent viscosity and variable temperature-dependent thermal conductivity in the present study. The presumed model is represented by Partial differential equations. The governing equations are transformed into nonlinear ODEs by similarity transformation and then solved numerically using the bvp4c method. Key findings reveal that radial velocity increases with the unsteadiness parameter, whereas axial velocity near the outer cylinder decreases. Rising variable viscosity reduces radial velocity, while variable thermal conductivity enhances temperature profiles. Wall friction at the outer cylinder increases with unsteadiness, but decreases at the inner cylinder, and the Nusselt number drops on both walls, signifying reduced heat transfer. Model validation is also included, endorsing the proposed framework. This analysis with an annular geometries model provides critical insights for optimizing thermal systems in many engineering applications where precise flow control is essential.