Impact of induced magnetic field on Darcy-Forchheimer nanofluid flows comprising carbon nanotubes with homogeneous-heterogeneous reactions.

The appealing traits of carbon nanotubes (CNTs) encompassing mechanical and chemical steadiness, exceptional electrical and thermal conductivities, lightweight, and physiochemical reliability make them desired materials in engineering gadgets. Considering such stimulating characteristics of carbon nanotubes, our goal in the current study is to scrutinize the comparative analysis of Darcy-Forchheimer nanofluid flows containing CNTs of both types of multi and single-wall carbon nanotubes (MWCNTs, SWCNTs) immersed into two different base fluids over a stretched surface. The originality of the model being presented is the implementation of the induced magnetic field that triggers the electric conductivity of carbon nanotubes. Moreover, the envisioned model is also analyzed with homogeneous-heterogeneous (h-h) chemical reactions and heat source/sink. The second-order slip constraint is assumed at the boundary of the surface. The transmuted high-nonlinearity ordinary differential equations (ODEs) are attained from the governing set of equations via similarity transformations. The bvp4c scheme is engaged to get the numerical results. The influence of different parameters is depicted via graphs. For both CNTs, the rate of heat flux and the surface drag coefficient are calculated using tables. It is highlighted that an increase in liquid velocity is witnessed for a varied counts volume fraction of nanoparticles. Also, Single-wall water-based carbon nanotube fluid has comparatively stronger effects on concentration than the multi-walled carbon nanotubes in water-based liquid. The analysis also indicates that the rate of heat flux and the surface drag coefficient are augmented for both SWCNTs and MWCNTs for different physical parameters. The said model is also validated by comparing it with a published result.

Analysis of Liquid Chromatography Considering a Linear Single-Component Heterogeneous-Type Reactive General Rate Model.

This paper elaborates on the significance of liquid chromatography for a single-component reactive linear general rate model. The model equations consist of a set of two coupled partial differential equations, which include diffusion, interfacial mass transfer, axial dispersion, external and intraparticle pore diffusivity, and heterogeneous chemical reaction of the first order with two sets of boundary conditions. The model equations are solved by the Laplace transformation. The actual time domain solution is obtained by numerical Laplace inversion, as analytical inversion cannot be obtained. The graphical sketch of different physical parameters is presented to analyze the dynamics of the elution profiles. The result indicates that the chromatographic reactor works more efficiently on increasing the value of the heterogeneous-type first-order reaction. To check the analytical results, a second-order high-resolution finite volume scheme is used. Both results are in good agreement and indicate the correctness of the numerical scheme. The current work is also compared with the previously available numerical schemes, which shows that the proposed numerical scheme is better for elaborating the chromatographic reactor performance. A comparison table is also presented to compute error analysis and computational run time for analyzing the efficiency of the reactor. A graphical sketch of the numerical temporal moment analysis is also presented, which gives significant information about the performance and the shape of the concentration profiles.

Magnetic Dipole and Thermophoretic Particle Deposition Impact on Bioconvective Oldroyd-B Fluid Flow over a Stretching Surface with Cattaneo-Christov Heat Flux.

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.

Analyzing the impact of induced magnetic flux and Fourier's and Fick's theories on the Carreau-Yasuda nanofluid flow.

The current study analyzes the effects of modified Fourier and Fick's theories on the Carreau-Yasuda nanofluid flow over a stretched surface accompanying activation energy with binary chemical reaction. Mechanism of heat transfer is observed in the occurrence of heat source/sink and Newtonian heating. The induced magnetic field is incorporated to boost the electric conductivity of nanofluid. The formulation of the model consists of nonlinear coupled partial differential equations that are transmuted into coupled ordinary differential equations with high nonlinearity by applying boundary layer approximation. The numerical solution of this coupled system is carried out by implementing the MATLAB solver bvp4c package. Also, to verify the accuracy of the numerical scheme grid-free analysis for the Nusselt number is presented. The influence of different parameters, for example, reciprocal magnetic Prandtl number, stretching ratio parameter, Brownian motion, thermophoresis, and Schmidt number on the physical quantities like velocity, temperature distribution, and concentration distribution are addressed with graphs. The Skin friction coefficient and local Nusselt number for different parameters are estimated through Tables. The analysis shows that the concentration of nanoparticles increases on increasing the chemical reaction with activation energy and also Brownian motion efficiency and thermophoresis parameter increases the nanoparticle concentration. Opposite behavior of velocity profile and the Skin friction coefficient is observed for increasing the stretching ratio parameter. In order to validate the present results, a comparison with previously published results is presented. Also, Factors of thermal and solutal relaxation time effectively contribute to optimizing the process of stretchable surface chilling, which is important in many industrial applications.