Analysis of bio-convective heat transfer over an unsteady curved stretching sheet using the shifted Legendre collocation method

Bio-convection is used in many ecologically beneficial applications, including pharmaceuticals, biological polymer production, and other eco-friendly uses. Several of these applications, such as the production of plastic films and polymer sheets, rely on stretching surface technology because the heat transfer rate determines the ultimate product quality at the stretching surface. Therefore, this study examines the bio-convective heat transfer caused by the swimming of gyrotactic micro-organisms in a nanofluid flowing over an unsteady curved stretched sheet. Local similarity transformations are utilized to alter the nonlinear partial differential equations. The resulting nonlinear system of ordinary differential equations is solved using the shifted Legendre collocation method. The effects of many influential parameters on motile micro-organism concentration and temperature, velocity, and nanoparticle concentration profiles are plotted and discussed. The velocity field is reduced when the slip parameter increases. According to this focused study's results, the concentration of motile bacteria drops dramatically when the curvature parameter increases. The Brownian motion parameter, thermophoresis parameter, and Peclet number reduce the motile micro-organism number. Motile micro-organism dispersal improves with an increase in bio-convective Schmidt number.