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The two-field thermal conditions of local thermal nonequilibrium (LTNE) were used to investigate linear stability of thermal convection in a liquid-saturated, porous layer via the extended Brinkman–Darcy model for different non-uniform basic thermal gradients. The critical values were numerically computed by the Galerkin method for rigid isothermal boundaries. The impact of LTNE and different forms of non-uniform basic temperature gradients on the onset of porous convection was examined. The porosity modified conductivity ratio has no influence on system stability at a small inter-phase heat transport coefficient limit. However, for higher values of the inter-phase heat transport coefficient, an increase in the porosity modified conductivity ratio hastens the onset of convection. An increase in the Darcy number delays the convective motions. The results for different basic temperature profiles are symmetric qualitatively. In addition, the possibility of control of convection by a basic temperature profile was studied in detail. [ABSTRACT FROM AUTHOR]

In the present article, we investigate the free convective flow of a ternary hybrid nanofluid in a two-phase inclined channel saturated with a porous medium. The flow has been propelled using the pressure gradient, thermal radiation, and buoyancy force. The flow model's governing equations are resolved using the regular perturbation approach. The governing equations are solved with the help of the regular perturbation method. Polyethylene glycol and water (at a ratio of 50%:50%) fill up Region I, while a ternary hybrid nanofluid based on zirconium dioxide, magnesium oxide, and carbon nanotubes occupies Region II. The ternary hybrid nanofluids are defined with a mixture model in which three different shapes of nanoparticles, namely spherical, platelet, and cylindrical, are incorporated. The consequences of the most significant variables have been examined using both visual and tabular data. The main finding of this work is that utilising a ternary hybrid nanofluid at the plate y = 1 increases the rate of heat transfers by 753%, demonstrating the potential thermal efficiency. The overall heat and volume flow rates are amplified by buoyant forces and viscous dissipations and dampened by the thermal radiation parameter. The optimum enhancement of temperature is achieved by the influence of buoyancy forces. A ternary nanofluid region experiences the maximum temperature increase compared to a clear fluid region. To ensure the study's efficiency, we validated it with prior studies. [ABSTRACT FROM AUTHOR]

The impact of convection and radiation on the thermal distribution of the wavy porous fin is examined in the present study. A hybrid model that combines the differential evolution (DE) algorithm with an artificial neural network (ANN) is proposed for predicting the heat transfer of the wavy porous fin. The equation representing the thermal variation in the wavy porous fin is reduced to its dimensionless arrangement and is numerically solved using Rung, e-Kutta-Fehlberg's fourth-fifth order method (RKF-45). The study demonstrates the effectiveness of this hybrid model, and the results indicate that the proposed approach outperforms the ANN model with parameters obtained through grid search (GS), showcasing the superiority of the hybrid DE-ANN model in terms of accuracy and performance. This research highlights the potential of utilizing DE with ANN for improved predictive modeling in the heat transfer sector. The originality of this study is that it addresses the heat transfer problem by optimizing the selection of parameters for the ANN model using the DE algorithm. [ABSTRACT FROM AUTHOR]