A comparative analysis of fractal and fractionalized thermal non-equilibrium model for chaotic convection saturated by porous medium

• A thermal non-equilibrium model is proposed for fractal porous subject to chaotic convection. • A chaos control is focused between fractal porous and fractional porous with uncertainty quantification for the flow in heterogeneous media • To approximate the propagation of chaos, chaotic attractors through fractal and fractional approaches have been investigated. • The fractional and fractal effects caused by interactions between uncertain parameters have disclosed the microstructures on the permeability of porous media. The convective heat transfer is one of the most important mechanism of heat transference for controlling the chaotic characteristics in porous media. A comparative study of thermal non-equilibrium model is proposed for fractal porous under the consideration of chaotic convection. A novel chaos control is focused between fractal porous and fractional porous by means of newly proposed differential and integral techniques. The sensitivity analysis for chaos expansion and uncertainty quantification for the flow in heterogeneous media have been perceived to the problem of chaotic convection through numerical simulations. In order to approximate the propagation of chaos, two types of simulations have been carried out in terms of chaotic attractors through fractal and fractional approaches. For examining a variety of chaos under the numerical simulations in which fractal domain is varied and fractional domain is fixed, fractal domain is fixed and fractional domain is varied, and both fractal as well as fractional domain are varied. Finally, it is observed that the fractional and fractal memory effects have caused by interactions between uncertain parameters and disclosed the microstructures on the permeability of porous media.