This research investigates the influence of the Cattaneo-Christov double diffusive flow of ferromagnetic hybrid nanofluids, taking into account heterogeneous-homogeneous chemical reactions, heat radiative flux, and the Soret-Dufour effect. The mathematical modeling of the system of equations results in the formulation of partial differential equations (PDEs). These PDEs were subsequently transformed into total differential equations (ODEs) via the application of similarity transformation. The resultant modified ODEs were addressed utilizing an innovative approach known as the spectral relaxation method (SRM). This methodology was employed to solve the system of ODEs in an iterative manner, following the Gauss-Seidel procedure. The findings of this investigation indicate that the heterogeneous-homogeneous chemical reaction significantly influences the fluid concentration, leading to a reduction in the concentration profile. An elevated level of thermal radiation was found to enhance both the fluid temperature and the velocity contour. Conversely, an increase in the magnetic field strength was noted to diminish the velocity contour. The current analysis was compared with previous studies and was found to exhibit a strong correlation.
In this paper, by using a new identity we establish some trapezoidal type inequalities for functions whose modulus of the first derivatives are \( \left( s,m\right)\)-preinvex via Caputo fractional derivatives.
This review provides a comprehensive overview of the synthesis process of nanoscale materials and highlights key characterization methods used for nanomaterials and biomaterials. It emphasizes the importance of effective techniques for investigating materials at the nanoscale, as these are too small for the human eye to detect. The review also explores various approaches to producing nanoscale materials and offers insights into the application, development, advantages, and limitations of different experimental methods for nanoparticle characterization. A particular focus is placed on advanced characterization techniques and their role in data interpretation, aiming to guide novice researchers in the field of nanoscience and nanotechnology.
