Abstract
Purpose: The purpose of the current framework is to scrutinize the two-dimensional flow and heat transfer of Casson nanofluid over cylinder/plate along with impacts of thermophore-sis and Brownian motion effects. Also, the effects of exponential thermal sink/source, bioconvec-tion, and motile microorganisms are taken.Methodology/Approach: The resulting non-linear equations (PDEs) are reformed into nonlinear ODEs by using appropriate similarity variables. The resultant non-linear (ODEs) were numerically evaluated by the use of the Bvp4c package in the mathematical solver MATLAB.Findings: The numerical and graphical illustration regarding outcomes represents the perfor-mance of flow-involved physical parameters on velocity, temperature, concentration, and microor-ganism profiles. Additionally, the skin friction coefficient, local Nusselt number, local Sherwood number, and local microorganism density number are computed numerically for the current pre-sented system. We noted that the velocity profile diminishes for the rising estimations of magnetic and mixed convection parameters. The Prandtl number corresponds with the declining performance of the temperature profile observed. The enhancement in the values of the Solutal Biot number and Brownian motion parameter increased in the concentration profile.Originality: In specific, this framework focuses on the rising heat transfer of Casson nanofluid with bioconvection by using a shooting mathematical model. The novel approach of the presented study is the use of motile microorganisms with exponential thermal sink/source in a Casson nano -fluid through a cylinder/plate. A presented study performed first time in the author's opinion. Understanding the flow characteristics and behaviors of these nanofluids is crucial for the scientific community in the developing subject of nanofluids.(c) 2023 The Authors. Published by Elsevier B.V. on behalf of King Saud University. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).