Exploring the impact of Prabhakar fractional operator and heat transfer on flow of fluid with applications in solar energy

Abstract
This research investigates the unsteady, incompressible, one-dimensional flow of a fluid over an infinitely vertical moving plate, emphasizing novel thermal and mass stratification effects relevant to industrial engineering and heat transfer systems. Employing the Prabhakar-fractional derivative framework, the model incorporates the combined buoyant forces due to mass and heat transfer, offering a generalized perspective on transient behavior in complex fluid systems. Using the Laplace method, analytical equations for heat flux, velocity, bioconvection, and are generated to simplify the analysis, assuming different values for the nanoparticles, MHD, Schmidt and Prandtl numbers. The range of nanoparticles lies from 0.012 to 0.18. Comparative assessments between long-term steady-state and unsteady-state solutions are conducted, highlighting dynamic transitions. The effects of significant dimensionless variables on solutal and thermal transfer are thoroughly evaluated. Graphical results for mass, energy, bioconvection and speed of fluid provide insights into boundary layer characteristics. The findings demonstrate that both thermal and mass stratifications significantly alter the flow dynamics, underlining their importance in the design, optimization, and performance analysis of industrial engineering applications involving fluid flow and heat exchange, such as chemical reactors, thermal regulation units, and energy conversion systems.

Author
Dana Mohammad Khidhir

DOI
https://doi.org/10.1080/10420150.2025.2509217

ISSN
1042-0150

Publish Date: 2025-06-03