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Thermal energy storage systems use thermal energy to elevate the temperature of a storage substance, enabling the release of energy during a discharge cycle. The storage or retrieval of energy occurs through the heating or cooling of either a liquid or a solid, without undergoing a phase change, within a sensible heat storage system. In a sensible packed bed thermal energy storage system, the structure comprises porous media that form the packed solid material, while fluid occupies the voids. Thus, a cavity, partially filled with a fluid layer and partially with a saturated porous layer, has become important in the investigation of natural convection heat transfer, carrying significant relevance within thermal energy storage systems. Motivated by these insights, the current investigation delves into the convection heat transfer driven by buoyancy and entropy generation within a partially porous cavity that is differentially heated, vertically layered and filled with a hybrid nanofluid.

The investigation encompasses two distinct scenarios. In the first instance, the porous layer is positioned next to the heated wall, while the opposite region consists of a fluid layer. In the second case, the layers switch places, with the fluid layer adjacent to the heated wall. The system of equations for fluid and porous media, along with appropriate initial and boundary conditions, is addressed using the finite difference method. The Tiwari–Das model is used in this investigation, and the viscosity and thermal conductivity are determined using correlations specific to spherical nanoparticles.

Comprehensive numerical simulations have been performed, considering controlling factors such as the Darcy number, nanoparticle volume fraction, Rayleigh number, bottom slit position and Hartmann number. The visual representation of the numerical findings includes streamlines, isotherms and entropy lines, as well as plots illustrating average entropy generation and the average Nusselt number. These representations aim to provide insight into the influence of these parameters across a spectrum of scenarios.

The computational outcomes indicate that with an increase in the Darcy number, the addition of 2.5% magnetite nanoparticles to the GO nanofluid results in an enhanced heat transfer rate, showing increases of 0.567% in Case 1 and 3.894% in Case 2. Compared with Case 2, Case 1 exhibits a 59.90% enhancement in heat transfer within the enclosure. Positioning the porous layer next to the partially cooled wall significantly boosts the average total entropy production, showing a substantial increase of 11.36% at an elevated Rayleigh number value. Positioning the hot slit near the bottom wall leads to a reduction in total entropy generation by 33.20% compared to its placement at the center and by 33.32% in comparison to its proximity to the top wall.

The need for precise synthesis of customized designs has resulted in the development of advanced coating processes for modern nanomaterials. Achieving accuracy in these processes requires a deep understanding of thermophysical behavior, rheology and complex chemical reactions. The manufacturing flow processes for these coatings are intricate and involve heat and mass transfer phenomena. Magnetic nanoparticles are being used to create intelligent coatings that can be externally manipulated, making them highly desirable. In this study, a Keller box calculation is used to investigate the flow of a coating nanofluid containing a viscoelastic polymer over a circular cylinder.

The rheology of the coating polymer nanofluid is described using the viscoelastic model, while the effects of nanoscale are accounted for by using Buongiorno’s two-component model. The nonlinear PDEs are transformed into dimensionless PDEs via a nonsimilar transformation. The dimensionless PDEs are then solved using the Keller box method.

The transport phenomena are analyzed through a comprehensive parametric study that investigates the effects of various emerging parameters, including thermal radiation, Biot number, Eckert number, Brownian motion, magnetic field and thermophoresis. The results of the numerical analysis, such as the physical variables and flow field, are presented graphically. The momentum boundary layer thickness of the viscoelastic polymer nanofluid decreases as fluid parameter increases. An increase in mixed convection parameter leads to a rise in the Nusselt number. The enhancement of the Brinkman number and Biot number results in an increase in the total entropy generation of the viscoelastic polymer nanofluid.

Intelligent materials rely heavily on the critical characteristic of viscoelasticity, which displays both viscous and elastic effects. Viscoelastic models provide a comprehensive framework for capturing a range of polymeric characteristics, such as stress relaxation, retardation, stretching and molecular reorientation. Consequently, they are a valuable tool in smart coating technologies, as well as in various applications like supercapacitor electrodes, solar collector receivers and power generation. This study has practical applications in the field of coating engineering components that use smart magnetic nanofluids. The results of this research can be used to analyze the dimensions of velocity profiles, heat and mass transfer, which are important factors in coating engineering. The study is a valuable contribution to the literature because it takes into account Joule heating, nonlinear convection and viscous dissipation effects, which have a significant impact on the thermofluid transport characteristics of the coating.

The momentum boundary layer thickness of the viscoelastic polymer nanofluid decreases as the fluid parameter increases. An increase in the mixed convection parameter leads to a rise in the Nusselt number. The enhancement of the Brinkman number and Biot number results in an increase in the total entropy generation of the viscoelastic polymer nanofluid. Increasing the strength of the magnetic field promotes an increase in the density of the streamlines. An increase in the mixed convection parameter results in a decrease in the isotherms and isoconcentration.