Application of fractional derivatives in a Darcy medium natural convection flow of MHD nanofluid

Nanofluid thermophysical characteristics are critical for predicting heat transfer behavior. This attempt provides a computational assessment of boundary layer flow and heat transfer behavior of fractional Maxwell viscoelastic nanofluid and their hybrids over a permeable vertical surface. The effects of Lorents and buoyancy forces are also considered in the flow region. The flow problem is modeled with novel distributed order time fractional derivatives to achieve control of the flow and heat transfer. Mid-point quadrature approach is used to process the distributed order integrals, whereas nonlinear cou-pled time fractional derivatives are discretized through the finite difference method along withL1- algo- rithm.The results shows that heat transfer rate enhanced 56:51% by enhancing the thermal Grashof number. Further, increase in nanoparticles volume fraction causes enhancement in thermal conductivity. More effects of the flow characteristic on velocity and temperature fields are shown graphically and ana-lyzed in detail. The involvement of novel distributed fractional order derivatives, and nanoparticles enhanced the importance of the simulated results, which can be helpful to effectively control related thermal engineering issues, like temperature management in internal combustion engines, cooling devices, and heat exchangers. (c) 2022 THE AUTHORS. Published by Elsevier BV on behalf of Faculty of Engineering, Ain Shams Uni-versity. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/ by-nc-nd/4.0/).