Numerous researchers have been drawn to the rheology of non-Newtonian fluids because of their diverse uses in the engineering and manufacturing fields, such as lubrication, plastic processing, and mining. Additionally, the characteristics of magnetohydrodynamics non-Newtonian fluids permit its widespread application in computer hard drives, loudspeakers, magnetic resonance imaging, the administration of magnetic medicines, and magnetic hyperthermia. The novelty of present study is the use of fourier’s and fick’s laws. The current work is focused on the analysis of heat and mass transfer in a magnetohydrodynamics Maxwell nanofluid flows across an inclined vertical plate because of these possible uses. The values of angle of inclination is chosen in the range 0 to \(\frac{\pi }{3}\) . From Table 1, the values of nanoparticles lies in the range of 0.012–0.18. Using suitable non-dimensional variables, ordinary differential equations are created from the modeling equations, and the Laplace transform method is used to solve these equations. Semi-analytical solutions for temperature, concentration, Bio-Convection, and velocity are found after employing the Laplace transform approach to address the issue. The study highlights several key outcomes likes velocity of fluid is increased with increasing values of Gr but decreased with increasing values of Pr, M, and maxwell parameter. The effect of increasing values of parameters R, \(L_{1}\) , and \(N_{1}\) are seen to suppress the concentration profile. The bioconvection concentration profile increases with \(\Phi \) but reduced with increasing values of L2. Furthermore, the comparison between ordinary and fractionalized maxwell fluid has been drawn. The application of the unsteady flow of nanofluid over a plate with the CPC operator has the potential to impact a wide range of solar energy-related technologies and innovations, leading to increased efficiency, sustainability, and the advancement of renewable energy solutions.
