Optimizing Heat Transfer in Radiative MHD Flow in Vertical Superhydrophobic Microchannel

Superhydrophobic microchannels have an extensive range of applications in the field of engineering, including energy-efficient heat exchangers, lab-on-a-chip systems, medical devices, and electronics cooling systems. Moreover, microchannels increase heat transfer efficiency by minimising drag effects by incorporating MHD effect. Grey Relational Analysis (GRA) is employed for maximizing Heat Transfer ( HT ) in radiative MHD flow through vertical superhydrophobic microchannels. This analysis examines two surface conditions: no-slip (Case 2) and superhydrophobic (Case 1). We formed a mathematical representation of the suggested paradigm. Governing higher order differential equations were converted into one dimensional differential equations (ODE) with the help of similarity transformation. Resultant ODEs were solved numerically by bvp4c, which is the built-in routine in Matlab. From the study, it revealed that the ideal level for improved heat transfer is R = 0, H = 3, S = 1, and γ = 1 based on the integrated GRA-PCA optimization. This integrated approach creates a strong base for getting the most out of thermal performance for radiative MHD flow in vertical superhydrophobic microchannels. It also gives useful information for advanced heat transfer and microfluidics uses. Moreover, ANOVA indicates that R , S , H and γ contributed 33.90%, 31.41%, 2.84%, and 31.84% of the total responses, respectively.