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When materials are processed in the form of sheets that are stretched, cooling is often required. Coolants have been developed to maximize the rate of heat transfer away from the sheet, including by adding nanoparticles and microorganisms to control the physical properties of the fluid. Such coolants perform well, but the interaction between them and the sheet is not yet fully understood. Most of the articles found in the literature have used similarity models to solve the set of governing equations. In this method, the governing equations can be mapped into a set of 1-D equations and solved easily. However, care should be taken when using this method as the validity of this method is ensured only in the fully developed region, far away enough from the extrusion slit. The present study, therefore, aims to explore the reliability of a similarity model by comparing it with a full computational fluid dynamics (CFD) approach. In this work, the boundary layer flow of a nanoliquid comprising gyrotactic microorganisms in both the developed and undeveloped regions of a stretching sheet is studied using computational fluid dynamics with the finite difference approach, implemented using FORTRAN. The results of the CFD method are compared against the similarity analysis results for the length of the developed and undeveloped regions. This study, for the first time, distinguishes between the undeveloped and fully developed regions and finds the region in which the similarity analysis is valid. The numerical results show that the critical Reynolds numbers for the boundary layers of the concentration of the nano-additives and of density of the microorganisms are equal. To achieve an agreement between the CFD and the similarity model within 5%, the Grashof number for the hydrodynamic boundary layer must be &lt;4 × 104. Increasing the bioconvection Rayleigh number leads to a decrease in the skin friction coefficient. The length of the region in which the microorganism’s density is not fully developed remains approximately constant for 103 &lt; Gr &lt; 105. Nonetheless, this length reduces significantly when the Grashof number increases from 105 to 106. The reduced Nusselt number, Nur, increases when the density difference of the microorganisms increases.

mathematics

A Fully Resolved Computational Fluid Dynamics Study of the Boundary Layer Flow of an Aqueous Nanoliquid Comprising Gyrotactic Microorganisms over a Stretching Sheet: The Validity of Conventional Similarity Models