Application of fractional derivative on nanofluid with magnetic field

The study investigates the combined impact of heat and mass transfer on a vertical plate, considering factors such as an applied magnetic field, thermal radiation, heat absorption, and a first-order chemical reaction. The fluid under examination is assumed to be an electrically conducting Cu-nanofluid based on water. Thermophysical properties are derived from Table 1 for both the base fluid (water) and nanoparticles (Cu), with the nanoparticle volume fraction chosen within the range of 0.01 to 0.02. A novel aspect of this study involves considering both passive and active control of the Maxwell nanofluid. The governing equations are solved using the Laplace transform technique to obtain uniform closed-form solutions. Graphical representations illustrate the velocity, temperature, concentration, and Bio-Convection profiles under various flow parameters. Remarkably, the velocity profile exhibits consistent behavior for both stationary η = 0 and moving η = 1 plates, as depicted in Figures 2–10. The obtained semi-analytical solutions successfully fulfill all initial and boundary conditions. Moreover, manipulating the nanoparticle volume fraction demonstrates significant control over the flow and heat transfer characteristics.