Partial Differential Equations in Applied Mathematics (Sep 2024)
Enhancement of heat transfer through alloys and nanoparticle over a melted sheet: A Koo and Kleinstreuer (K-K) model
Abstract
Alloys are used in a wide variety of contexts, including aircraft building, the military, industry, medicine, and manufacturing. Alloys including tools, equipment, cars, and structures. Furniture, shipping containers, and medical supply storage containers are among products that benefit from the usage of aluminium alloys. To further enhance simultaneous heat transmission, scientists have developed nano-fluids, which are essentially nano-particle suspensions in a regular fluid. Ferric Sulfate may be added to soil to improve its quality and is also used to clean water. Iron (3+) sulphate is an iron (III) and sulfate (III) combination with a 3:2 ratio of iron (III) to sulfate (III) ions. As a catalyst, mordant, and astringent, it serves several purposes. It is a sulphate of a metal and a molecule of iron. Due of these purposes, we employ the K-K model to study how alloys and nanoparticles affect surface flow and heat transfer. By making use of the boundary layer approach and the flow assumptions, the partial differential equations (PDEs) were generated by approximating the Navier-Stokes equation. This system is transformed into ordinary differential equations (ODE's) using similarity transformations. Using the BVP4C method, a system with non-dimensions is defined. Mathematical and pictorial explanations are provided for the consequences of the key physical variables. It is founded that the magnitude of the temperature field is directly proportional to the R value; a higher value indicates more heat conduction to the liquid. Additionally, the velocity of the fluid lessened by the impact of melting effect.