Fractional study of radiative Brinkman-type nanofluid flow across a vertical plate with the effect of Lorentz force and Newtonian heating

Contaminant removal from water is accomplished using a variety of technologies, with adsorption being the simplest, successful, cost-effective, and long-term solution. Nanocomposites made from clay minerals and polymers have developed as a new method for cleaning contaminated water in recent years. Therefore, in this paper, clay-based water nanoliquid has been analyzed across a vertical sheet. For flow analysis, Brinkman-type fluid model has been considered along with the consequences of first-order chemical reaction and heat generation/heat absorption. Conditions for Slippage velocity and Newtonian heating also have been taken into account. Using relative constitutive equations, a mathematical model for the flow analysis has been formulated in terms of coupled partial differential equations and then generalized by using constant proportional caputo fractional derivative. The fractional Laplace transform approach was used to solve the problem for exact analytical solutions. The physics of several essential flow constraints vs velocity, thermal energy, and concentration propagation have been addressed graphically using the exact solutions. To check the validity and correctness, the obtained solution is evaluated with the published work. It is worth mentioning that the heat transition rate in the fluid increases by 8.7671% by the accumulation of clay nanoparticulates, while the rate of mass transmission increases by 11.830%.