Asian Research Journal of Mathematics

MHD Carreau Fluid Flow Past a Melting Stretching Cylinder with Quadratic Thermal Radiation and Joule Heating

K. B. Vidya — 2026-10-23

The present study investigates the steady, axisymmetric magnetohydrodynamic (MHD) flow of a Carreau fluid over a stretching cylinder with melting heat transfer, incorporating quadratic thermal radiation and Joule heating. The governing equations for continuity, momentum, and energy are formulated under the boundary-layer approximation. The Rosseland diffusion approximation, together with a quadratic temperature expansion, is employed to describe radiative heat transfer under significant temperature differences. Appropriate similarity transformations are applied to reduce the governing partial differential equations to a coupled system of nonlinear ordinary differential equations, which is solved numerically using the MATLAB bvp4c solver. The effects of the magnetic parameter, melting parameter, Weissenberg number, curvature parameter, quadratic radiation parameter, and Eckert number on the velocity and temperature profiles are systematically analyzed. The skin friction coefficient and local Nusselt number are also evaluated to characterize the momentum and heat transfer rates. The results indicate that an increase in the magnetic parameter reduces the fluid velocity owing to the enhanced Lorentz force, while the associated Joule heating elevates the fluid temperature and increases the thermal boundary-layer thickness. The melting parameter generally reduces both velocity and temperature distributions. In contrast, an increase in the quadratic radiation parameter enhances the temperature field by intensifying radiative heat transfer. The Eckert number also contributes to temperature enhancement through viscous dissipation and Joule heating effects, whereas variations in the Weissenberg number and curvature parameter influence the flow and thermal characteristics according to the non-Newtonian rheology and cylindrical geometry. The computed skin friction and Nusselt number reveal the combined effects of magnetic forces, melting, fluid elasticity, curvature, and thermal transport mechanisms on the surface shear stress and heat transfer rate. Furthermore, the numerical results are compared with previously published results for limiting cases, demonstrating good agreement and supporting the accuracy of the proposed numerical approach. The findings provide useful insights into the coupled influence of non-Newtonian fluid behavior, electromagnetic effects, melting, and nonlinear thermal radiation in cylindrical heat-transfer applications.

Central \(\sigma\)-Symmetric Rings and Their Structural Properties

Manjuri Dutta — 2026-10-26

For an associative ring \(R\) with identity and an endomorphism \(\sigma\), the central \(\sigma\)-symmetric condition requires that \(a b c=0\) imply both \(a c \sigma(b)\) and \(\sigma(b) a c\) belong to the centre of \(R\). This condition was considered by Dutta and Singh (2022) in connection with \(\sigma\)-symmetric rings. We examine the distinction between its one-sided forms using explicit triangular-matrix examples, describe its relationship with \(\sigma\)-compatibility, symmetric rings, and skew central reversibility, and establish structural criteria for subrings, isomorphic images, quotients, diagonal matrix rings, central localizations, and direct products. The distinction between unital and nonunital endomorphisms is made explicit. In particular, \(\sigma\)-compatibility together with ordinary symmetry yields the stronger \(\sigma\)-symmetric property, whereas central \(\sigma\)-symmetry need not imply \(\sigma\)-symmetry. The arguments describe the precise hypotheses under which these implications and constructions hold.

Spectral Properties of Fused Graphs of Paths

S. B. Reeja — 2026-10-27

This study examines the spectral properties of graphs formed by identifying two distinct vertices of a path, with particular emphasis on the singularity and nullity of the adjacency matrix. The analysis considers paths of even and odd order and distinguishes between pendant and non-pendant vertices, as well as core and noncore vertices where these classifications apply. Established results on the adjacency spectra of cycles and paths, vertex null spread, and the characteristic polynomial of graph coalescence are used to determine the effect of vertex identification. For even-order paths, the results classify the fused graphs according to whether the resulting cycle has even or odd length and, in relevant cases, according to the distance between the fused vertex and its nearest pendant vertex. For odd-order paths, the classification depends on whether the identified vertices are both core vertices, both noncore vertices, or one of each. The stated theorems distinguish nonsingular fused graphs from those with nullity one or two under these configurations. Illustrative constructions involving paths of orders eight and nine accompany the theoretical arguments and show how the conditions apply to specified vertex pairs. Overall, the analysis provides a case-based description of how vertex selection and cycle length govern the occurrence and multiplicity of the zero-adjacency eigenvalue in fused graphs of paths.