In this work, an attempt has been made to explore numerically the thermo-fluidic transport process in a novel M-shaped enclosure filled with permeable material along with Al₂O₃-Cu hybrid nanoparticles suspended in water under the influence of a horizontal magnetizing field. To exercise the influence of geometric parameters, a classical trapezoidal cavity is modified with an inverted triangle at the top to construct an M-shaped cavity. The cavity is heated isothermally from the bottom and cooled from the top, whereas the inclined sidewalls are insulated. The role of geometric parameters on the thermal performance is scrutinized thoroughly by changing the sidewall inclination, number, and height of the top inverted triangular undulation under similar boundary conditions. The governing equations transformed into dimensionless form are solved by using a computing code written in the finite volume approach. The analysis is conducted by considering a wide range of parametric influences like sidewall angles (γ), number (n), and height (δ) of the top triangular undulations, modified Rayleigh number (Ra_m), Darcy number (Da), Hartmann number (Ha), and hybrid nanoparticle concentrations (φ). Furthermore, the artificial neural network (ANN) technique is implemented and tested to predict the overall thermal behavior of the novel cavity to predict new cases. The results revealed that the design of sidewall inclination (γ) is an important parameter for modulating the thermo-flow physics. The M-shaped cavity (compared to trapezoidal) reveals either a rise or drop in the fluid circulation strength depending upon the magnitude of δ, but the heat transfer rate always increases due to an increase in the cooling length. The heat transfer increment is ∼61.01% as δ increases. Single undulation with higher depth is the optimum choice for achieving improved heat transfer (which may go up to ∼355.75% for $\delta$ = 0.5 and γ = 45°). A decrease in Da or Ha causes a drop in the flow strength, which consequently leads to a drop in the heat transfer rate. Furthermore, the concepts of ANN will help researchers predict the behavior for such complicated cavity shapes with a multiphysics approach. This will save efforts as well as computing time for exploring the thermal behavior of any range of a dataset.

The high demand for compact heat exchangers has led researchers to develop high-quality and energy-efficient heat exchangers at a lower cost than conventional ones. To address this requirement, the present study focuses on improvements to the tube/shell heat exchanger to maximize the efficiency either by altering the tube’s geometrical shape and/or by adding nanoparticles in its heat transfer fluid. Water-based Al₂O₃-MWCNT hybrid nanofluid is utilized here as a heat transfer fluid. The fluid flows at a high temperature and constant velocity, and the tubes are maintained at a low temperature with various shapes of the tube. The involved transport equations are solved numerically by the finite-element-based computing tool. The results are presented using the streamlines, isotherms, entropy generation contours, and Nusselt number profiles for various nanoparticles volume fraction 0.01 ≤ φ ≤ 0.04 and Reynolds numbers 2400 ≤ Re ≤ 2700 for the different shaped tubes of the heat exchanger. The results indicate that the heat exchange rate is a growing function of the increasing nanoparticle concentration and velocity of the heat transfer fluid. The diamond-shaped tubes show a better geometric shape for obtaining the superior heat transfer of the heat exchanger. Heat transfer is further enhanced by using the hybrid nanofluid, and the enhancement goes up to 103.07% with a particle concentration of 2%. The corresponding entropy generation is also minimal with the diamond-shaped tubes. The outcome of the study is very significant in the industrial field and can solve many heat transfer problems.