We introduce a new polynomial for knot diagrams. The coefficients of this polynomial are dependent on thenumber of the arcs on the regions of the knot diagrams. A relation between the sum of the coefficients andthe number of crossing of the knot diagram is developed. Some other properties of the developed regionbased polynomial are explained. The behaviour of the polynomial against Reidemeister moves is also examined.

This study investigates the heat and mass transfer of magnetohydrodynamic nanofluids via the Riga plate subjected to convective boundary conditions, including the thermal radiation parameter. Utilizing variable thermal conductivity and mixed convection effects, the heat transfer process is investigated. The peculiarity of the flow model enables us to investigate the importance of thermophoresis and Brownian motion to the kinetics of Newtonian fluids. The governing partial differential equations are converted into non-dimensional ordinary differential equations using proper similarity transformations and numerically solved using bvp4c in Matlab. The graphs explore the effects of pertinent parameters on the transference of heat, mass and velocity profiles. As the Biot number [Formula: see text] increases, so does the thermal boundary layer. The Nusselt number intensifies with radiation parameter but decreases with intensifying magnetic field parameter [Formula: see text], Eckert number [Formula: see text] and Brownian motion parameter [Formula: see text]. The influence of several physical quantities is illustrated and displayed through graphs and tables. Furthermore, it is observed that the thickness of the temperature profile is increased by combining the Biot number, the thermal radiation parameter, the thermal conductivity parameter and the modified Hartmann number.