Advances in transport phenomena with nanoparticles and generalized thermal process for vertical plate

In this paper, a quantitative analysis is performed to investigate the convective flow of Maxwell fluid along with an erect heated plate via Prabhakar-like energy transport. The governing equations for this mathematical model are attained by Prabhakar fractional derivative. Laplace transform is applied to obtain the generalized results for dimensionless velocity and temperature profiles. By applying the conditions of nanofluid flow, we develop the constantly accelerated, variables accelerated, and non-uniform accelerated solution of the model, respectively. Prabhakar fractional derivative for Maxwell fluid based on generalized Fourier's thermal flux is determined for heat transfer. For volume fraction phi and fractional parameters alpha, beta, and gamma, different structures of graphs are obtained. Furthermore, fluid temperature and velocity can be increased by enhancing the fractional parameters' values. The comparison of nanoparticles Ag and nanoparticles Cu with water-based nanoparticles for velocity and temperature profile is also examined. The behavior of second grade and Maxwell fluid results to become a viscous fluid is justified.

Automated summary

This study quantitatively analyzes the convective flow of Maxwell fluid along an upright heated plate using a mathematical model based on Prabhakar-like energy transport. The governing equations are obtained through the Prabhakar fractional derivative. The model's solutions under various conditions are discussed, and the heat transfer and fluid parameters are analyzed and compared.