Humaira Yasmin

Nanofluids are considered as an effective way to enhance the thermal conductivity of heat transfer fluids. Additionally, the involvement of micro-organisms makes the liquid more stable, which is important in nanotechnology, bio-nano cooling systems, and bio-microsystems. Therefore, the current investigation focused on the examination of the thermodynamic and mass transfer of a Carreau–Yasuda magnetic bionanomaterial with gyrotactic micro-organisms, which is facilitated by radiative peristaltic transport. A compliant/elastic symmetric channel subject to partial slip constraints was chosen. The features of viscous dissipation and ohmic heating were incorporated into thermal transport. We use the Brownian and thermophoretic movement characteristics of the Buongiorno nanofluid model in this study. A set of nonlinear ordinary differential equations are created from the partial differential equations that control fluid flow. The governing system of differential equations is solved numerically via the shooting technique. The results of pertinent parameters are examined through velocity, temperature, motile micro-organisms, concentration, and heat transfer rate.

This article is related to the fractional-order analysis of one- and two-dimensional nonlinear systems of third-order KdV equations and coupled Burgers equations, applying modified analytical methods. The proposed problems will be solved with the Caputo–Fabrizio fractional derivative operator and the Yang transform. The results we obtained by implementing the suggested methods are compared with the exact solution. The convergence of the method is successfully presented and mathematically proved. To show the effectiveness of the proposed methods, we compared exact and analytical results with the help of graphs and tables, which are in strong agreement with each other. Also, the results obtained by implementing the suggested methods at various fractional orders are compared, confirming that solution gets closer to exact solution as the value tends from fractional order towards integer order. Moreover, the proposed methods are attractive, easy, and highly accurate, which confirms that these methods are suitable methods for solving partial differential equations or systems of partial differential equations.