Mathematical Analysis of Thermal and Mass Diffusion Over a Plate Using Yang–Abel–Cattani Fractional Operator

ABSTRACT Studying the free convection flow of heat transfer with nanofluids over a plate offers insights crucial for optimizing heat transfer efficiency in engineering systems and advancing thermal management technologies. This article presents an analytical study of nanoparticles containing blood, gold, and zinc. Heat transfer in the flow of second‐grade fluid with multiple effects is taken into account. Innovative results in the current study are obtained by utilizing the combined effect of heat and mass transfer over a plate. The modeled partial differential equations are made nondimensional and then solved by using the Laplace transform method. The model is generalized by using Fick's and Fourier's laws. The model is fractionalized by using the Yang–Abel–Cattani fractional operator for order . To validate the accuracy of the results, a comparison is made using algorithms. The impact of different flow parameters, including the nanoparticles, chemical reaction, Prandtl number, fractional parameters, and Schmidt number, is analyzed graphically. The accelerating volume fraction of the nanoparticle enhances the Nusselt Number, showing improved convective transfer of heat consistent with experiment, which offers useful design insights for the next‐generation automotive cooling system. More specifically, in comparison to the models, the fractional model provides better flow behavior. The main outcomes of this study highlight that zinc is generally more reactive than iron.