Due to rapid development in science and technology, the nanoparticles got a great importance in field of science and technology. Basically, nanoparticles are used in manufacturing of makeup cream, soaps, as a coolant in automobile engine and many other electronic devices. Non-renewable energy resources damage the ecosystem badly so the present research discusses the importance of renewable resources of energy like solar energy. In the last century, researches have made a comprehensive study of literature to overview the importance of renewable energy resources. In the present research we have analyzed the entropy generation by virtue of 2nd law of thermodynamics. Basic intention of under consideration exploration is to investigate the effects of convective boundary condition with stratification on two-dimensional Williamson liquid with MHD flow. A mathematical technique bvp4c is used to solve the problem by using software MATLAB. For different parameters, moreover graphs are plotted to discuss the effects on temperature, concentration, microorganism and entropy profile. As the numeric value of the Brownian movement parameters along thermophoresis parameter grows up the temperature gradient of nanofluids shows increasing trend while the temperature declines for increasing the numeric value of Prandtl number. On the other hand, concentration profile has reverse behavior for thermophoresis parameter and Brownian movement parameter i.e. concentration declined for growing value of Brownian motion parameter while increases up for raising numeric value of thermophoresis parameter. Additionally, AI neural networks and a unique BP-LMA are used to tackle numerical issues. A range of performance indicators, including Mean Squared Error, Fitness State of Function including Training State of Function, graphs for Regression Analysis along the Error Histograms is utilized to evaluate the efficacy of the projected NNs of AI employing BP-LMA. The influence of primary elements on profiles of Micro-organisms along Temperature and Concentration are also carefully examined. As (The Magnetic field parameter) rises, the Temperature profile rises, and as (The Prandtl number) rises, the Temperature profile falls. Graphical results revealed that fluids concentration Profile has declining behavior as (Brownian motion parameter) increases. The Microorganism profile decreases when (Peclet number) increases.
Abbasi et al. (Wed,) studied this question.