Statistical and Numerical Analysis of Conjugate Heat and Momentum Transfer in an Open Cavity With a Thick Wall Using Cu–Water Nanofluid

ABSTRACT Although open cavity configurations are common in modern electronic and solar applications, limited attention has been given to thick‐walled hollow cavity designs, particularly in the context of comprehensive sensitivity analysis. To address this gap, the study provides a detailed statistical and numerical investigation of conjugate heat and momentum transfer in a thick‐walled open cavity, with specific emphasis on the bottom‐mounted thick wall configuration that demonstrates strong potential for enhanced thermal regulation. A Cu–water nanofluid is used as the working fluid, and the flow is subjected to mixed convection while the effect of magnetohydrodynamics is also considered. A set of governing two‐dimensional equations with the accompanying boundary conditions in nondimensional form is solved using the finite element approach based on Galerkin weighted residual formulation. A statistical sensitivity analysis is done using the statistical response surface methodology (RSM) to find a best‐fitted correlation between input factors and response function. Simulations are carried out for varying solid volume fractions ( ϕ = 0.01, 0.05, 0.1, and 0.15), Hartmann number ( Ha = 0, 5, 15, and 20) and Reynolds numbers ( Re = 50, 150, 300, and 500). The empirical results are presented in terms of streamlines, isotherms, heat transfer rate, and average fluid temperature. The findings show that the heat transfer rate Nu av is higher for higher values of Re and ϕ , but significantly lower for higher values of Ha . Particularly, increasing Re from 50 to 150, 300, and 500 leads to a reduction in average fluid temperatures of 10%, 14%, and 35%, respectively, at any particular time. Also, the regression model is statistically appropriate to build an appropriate correlation between the independent factors ( Re , ϕ , and Ha ) and output function.