Heat transfer is a critical function in many technical, industrial, home, and commercial structures. As a result, the purpose of this study is to investigate the effects of slip velocity and variable fluid characteristics on Casson bionanofluid flow across a stretching sheet that has been saturated by gyrotactic microorganisms. The suggested system will be converted to a computationally tractable form using the Galerkin method. The shifted Vieta-Lucas polynomials are then used as basis functions on the provided domain to solve the nonlinear system of ordinary differential equations that has been constructed (ODEs). The results are presented in the form of graphs and tables to assess the impact of the problem’s governing parameters. The estimated solutions produced by using the proposed techniques were physically acceptable and accurate. The current outcomes are confirmed by comparing them to the available literature. It appears that the temperature distribution is enhanced whereas the velocity distribution declines, caused by rising values of the magnetic parameter, slip parameter, and Casson parameter. Also, the local Nusselt number escalates with the strength of the viscosity parameter while the friction drag decays with the same parameter. In addition, the effectiveness and accuracy of the proposed method are satisfied by computing and the residual error function.
In this paper, an efficient numerical treatment for magnetohydrodynamic flow and heat transfer calculations is presented, based on the differential transformation method (DTM), and the finite element method (FEM). This numerical treatment is obtained for the ordinary differential equation (ODE) which describes physically the boundary layer flow due to a permeable shrinking sheet. The DTM and FEM are utilized in this study because of their capacity to solve linear and nonlinear systems of ODEs, as well as their accuracy and convenience of use. These methods are approximate analytical that can usually get the solution in a series form. These numerical procedures are effective for this type of physical problem of varying degrees of complexity. The numerical calculations yield that the dimensionless velocity enhances when the wall mass suction for the flow is increased after the magnetic field is imposed. Also, the dimensionless velocity was found to increase for the large value of the magnetic parameter.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.