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This study investigates the intricate interplay among various factors, including melting heat, Brownian motion, activation energy, and thermophoresis in the Maxwell fluid along a stretching sheet. To model these complex phenomena, we have formulated mathematical equations that are subsequently transformed into a set of partial differential equations. Through a similarity renovation, these equations are transformed into ordinary differential equations, and we solve the resulting boundary value problem using numerical techniques, specifically the BVP4C method, known for its fourth-order accuracy. Utilizing the numerical capabilities of BVP4C, we delve into the influence of different parameters, including thermophoresis, melting effect, Brownian motion, and activation energy, on critical flow characteristics. These characteristics encompass the concentration profile and the Sherwood number profile. Our work has been validated against previously published research, showing good matching. The primary objective of this work is to provide plots depicting Nusselt number, skin friction, and Sherwood number profiles for different parameters. This examination aims to shed light on the interconnected effects of these complex phenomena, which have direct relevance across numerous industrial and engineering applications, spanning areas such as metallurgy, nanotechnology, and chemical processing. The primary finding from this research underscores that both the melting heat effect and activation energy contribute to an increase in the concentration profile.
Sudarmozhi et al. (Fri,) studied this question.