Heat and mass transfer with Eckert number on flow of nanofluid

• Published in: International journal of applied and computational mathematics Vol. 11; no. 4
• Main Authors: AL Garalleh, Hakim, Ramzan, Muhammad, Amir, Muhammad, Abbas, Shajar, Abduvalieva, Dilsora, Alawaideh, Yazeen M., Bamashmus, Hassan Najeeb
• Format: Journal Article
• Language: English
• Published: New Delhi Springer India 01.08.2025; Springer Nature B.V
• Subjects: Applications of Mathematics; Atomic properties; Biomedical engineering; Chemical reactions; Clay; Computational Science and Engineering; Derivatives; Fluid flow; Fractals; Heat transfer; Magnetohydrodynamic flow; Mass transfer; Mathematical and Computational Physics; Mathematical Modeling and Industrial Mathematics; Mathematics; Mathematics and Statistics; Nanofluids; Nanoparticles; Nuclear Energy; Operations Research/Decision Theory; Operators (mathematics); Original Paper; Parameters; Partial differential equations; Power law; Prandtl number; Schmidt number; Theoretical; Velocity distribution; Heat generation; Chemical reaction; Nanofluid; Free convection; Magnetic field
• ISSN: 2349-5103; 2199-5796
• DOI: 10.1007/s40819-025-01959-x

The fractal fractional derivative is a new class of fractional derivative with power law kernel which has many applications in real world problems. This operator is used for the first time in such kind of fluid flow. The big advantage of this operator is that one can formulate models describing much better the systems with memory effects. Furthermore, in real world there are many problems where it is necessary to know that how much information the system carries. To explain the memory in a system fractal-fractional operators with power law kernel is analyzed in the present work. Keeping these motivation in mind in the present paper, new concept of fractal-fractional operator for the modelling of nanofluid with combined effect of heat and mass transfer have been used. The MHD flow is taken in a channel with Eckert number and chemical reaction in the presence of solutal buoyancy forces. The clay and water are used for nanoparticles. Clay nanoparticles with Casson fluid are discussed in different areas, such as biomedical, engineering, and industries. The addition of nanoparticles to transformer oil increased its efficiency by 15.37%. The governing equations in the present flow model are partial differential equations, which are solved numerically by using Crank-Nicolson technique to obtain the solutions for concentration, temperature, and velocity fields. In additions the physical aspects of flow and material parameters like as Prandtl number, Schmidt number, Grashof thermal number, Grashof mass number, especially the fractional parameters are discussed by sketching the graphs of field of interest.