Abstract In the present study, free convection in a cavity with a corrugated partition which have different fluids on different parts of the partition was numerically examined. In one of the domains carbon nanotube (CNT)-water nanofluid with an inclined uniform magnetic field is considered. A triangular wave form of conductive corrugated partition is used. The numerical simulation was performed with Galerkin weighted residual finite element method. Various values of pertinent parameters of current thermal configuration such as Rayleigh number (between 104 and 106), Hartmann number (between 0 and 50), magnetic inclination angle (between 0° and 90°), solid particle volume fraction (between 0 and 0.03), number of triangular waves (between 1 and 40), height of triangular waves (between 0.01H and 0.2H) and thermal conductivity ratio (between 0.1 and 100) and their influence on the hydro-thermal behavior were examined. It was observed that significant enhancements in the Nusselt number is obtained with CNTs. The average heat transfer decreases for higher values of Hartmann number but slightly varies as the value of magnetic inclination angle changes. As the number and height of the triangular waves increase, the average heat transfer reduce which are 32 % and 27 % for the highest values of number and height of triangular waves both for water and nanofluid. For forecasting the average heat transfer coefficient of the current thermal system, a novel method based on Proper Orthogonal Decomposition (POD) and Adaptive-Network-Based Fuzzy Inference System (ANFIS) is used which yields highly accurate results that are computationally inexpensive.