Numerical and statistical analyses of three-dimensional non-axisymmetric Homann's stagnation-point flow of nanofluids over a shrinking surface

Nanofluids, which are known for their superior heat transfer properties, have become indispensable in real-world applications. This underscores the critical importance of comprehensive understanding, which forms the core of this study. The goal of this study is to scrutinize Homann's non-axisymmetric stagnation-point flow over a shrinking surface of various single-phase water-based nanofluids (water-copper, water-alumina, and water-titanium dioxide) in a three-dimensional (3D) system. The model formulations are derived into ordinary differential equations via sophisticated similarity variables that satisfy the continuity equation. A boundary value problem solver (bvp4c) with a finite difference method in MATLAB is adapted to carry out numerical calculations while the response surface methodology (RSM) in MINITAB is used to statistically analyze the solution. The opposing flow created by the shrinking surface within a certain degree of shrinkage leads to the formation of two distinct alternative solutions. The current study offers two alternative solutions for boundary layer flow control modeling. However, only the first solution is tested to be stable. The critical point for boundary layer bifurcation is identified, to efficiently manage the flow. Water-copper nanofluid has been proven to perform better in heat transfer than water-alumina and water-titanium dioxide nanofluids. The 2 % volume fraction of copper provides better heat transfer compared to 1 % volume fraction in the present configuration of the flow system. The response optimizer via RSM also validates that the heat transfer performance of copper nanofluid is maximized when the volume fraction of copper is set at a high level with a low shear-to-strain rate.

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