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This paper aims to study the effect of concentric hot circular cylinder inside egg-cavity porous-copper nanofluid on natural convection phenomena.

The finite element method–based Galerkin approach is applied to solve numerically the set of governing equations with appropriate boundary conditions.

The effects of different range parameters, such as Darcy number (10–3 = Da = 10–1), Rayleigh number (103 = Ra = 106), nanoparticle volume fraction (0 = ϑ = 0.06) and eccentricity (−0.3 = e = 0.1) on the fluid flow represent by stream function and heat transfer represent by temperature distribution, local and average Nusselt numbers.

A comparison between oval shape and concentric circular concentric cylinder was investigated.

In the current numerical study, heat transfer by natural convection was identified inside the new design of egg-shaped cavity as a result of the presence of a circular inside it supported by a porous medium filled with a nanofluid. After reviewing previous studies and considering the importance of heat transfer by free convection inside tubes for many applications, to the best of the authors’ knowledge, the current work is the first study that deals with a study and comparison between the common shape (concentric circular tubes) and the new shape (egg-shaped cavity).

This paper aims to present a numerical study that investigates the flow of MgO-Al₂O₃/water hybrid nanofluid inside a porous elliptical-shaped cavity, in which we aim to examine the performance of this thermal system when exposed to a magnetic field via heat transfer features and entropy generation.

The configuration consists of the hybrid nanofluid out layered by a cold ellipse while it surrounds a non-square heated obstacle; the thermal structure is under the influence of a horizontal magnetic field. This problem is implemented in COMSOL multiphysics, which solves the related equations described by the “Darcy-Forchheimer-Brinkman” model through the finite element method.

The results illustrated as streamlines, isotherms and average Nusselt number, along with the entropy production, are given as functions of: the volume fraction, and shape factor to assess the behaviour of the properties of the nanoparticles. Darcy number and porosity to designate the impact of the porous features of the enclosure, and finally the strength of the magnetic induction described as Hartmann number. The outcomes show the increased pattern of the thermal and dynamical behaviour of the hybrid nanofluid when augmenting the concentration, shape factor, porosity and Darcy number; however, it also engenders increased formations of irreversibilities in the system that were revealed to enhance with the permeability and the great properties of the nanofluid. Nevertheless, this thermal enhanced pattern is shown to degrade with strong Hartmann values, which also reduced both thermal and viscous entropies. Therefore, it is advised to minimize the magnetic influence to promote better heat exchange.

The investigation of irreversibilities in nanofluids heat transfer is an important topic of research with practical implications for the design and optimization of heat transfer systems. The study’s findings can help improve the performance and efficiency of these systems, as well as contribute to the development of sustainable energy technologies. The study also offers an intriguing approach that evaluates entropy growth in this unusual configuration with several parameters, which has the potential to transform our understanding of complicated fluid dynamics and thermodynamic processes, and at the end obtain the best thermal configuration possible.