Sumant Kumar

A numerical study focuses on the temporal evolution of fractional-order convective nanofluid flow along with entropy generation characteristics within a wavy square porous enclosure containing a circular cylinder. The application of fractional derivatives facilitates a more accurate representation of fluid flow dynamics, thermal transport, and entropy production. The governing equations are formulated as fractional partial differential equations, with momentum transport modeled using the Darcy–Brinkman–Forchheimer approach. The complete mathematical framework is solved using a robust numerical technique that integrates the implicit finite difference scheme (L1-scheme) for temporal discretization and the penalty finite element method for spatial discretization. The numerical investigation is carried out for various emerging parameters, including fractional-order parameters (α), Rayleigh number (Ra), Darcy number (Da), and porosity (ε). The results are displayed through contour plots of streamlines, isotherms, and local entropy generation, along with graphical plots of the mean Nusselt number, Bejan number, and total entropy generation. These findings offer valuable insights into the interplay between fractional-order parameter and flow parameters in influencing flow dynamics, thermal transport, and entropy generation. The study reveals that the fractional-order parameter (α) plays a pivotal role in governing the system's temporal evolution, with higher values of α significantly accelerating the rate of evolution.

The following corrections are required in the original published paper:1 The operator ∂ α ∂ t α given in Eqs. (2)–(4) is replaced by C ̃ diff ∂ α ∂ t α for the

The present numerical work examines the effect of fractional order parameter on heat transfer and entropy generation for a thermo-magnetic convective flow of nanofluid (Cu-water) in a square porous enclosure that contains semi-circular bottom wall. The Darcy–Brinkmann–Forchheimer model is utilized to evaluate the momentum transfer in porous media, and the Caputo-time fractional derivative term is introduced in momentum as well as in the energy equation. Further, non-dimensional governing equations are simulated through the penalty finite element method, and the Caputo time derivative is approximated by L1-scheme. The study is carried out for various parameters, including Rayleigh number (Ra), Darcy number (Da), radius of the semicircle (r), fractional order (α), and Hartmann number (Ha). The comprehensive results are presented by the contour variation of isotherms, streamlines, and total entropy generation at the selected range of parameters. In addition, thermal transport and irreversibilities due to heat transfer, fluid friction, and magnetic field have been accounted through the numerical variation of mean Nusselt number (Num) and Bejan number due to heat transfer (Beht), fluid friction (Beff), and magnetic field (Bemf), respectively. The key findings of the present study reveal that during the initial evolution period, the Num value increases as α→1. Additionally, time taken to achieve the steady state condition varies and depends on fractional order α. Furthermore, in the absence of Ha, the heat transfer and entropy generation intensifies with augmentation of Ra and Da for all α, while, the increasing value of Ha shows an adverse impact on the heat transfer rate.

This study presents a numerical investigation to examine the influence of Soret and Dufour parameters on the double-diffusive convective flow of a hybrid nanofluid within an inverted T-shaped porous enclosure. The thermophysical properties and numerical values of the hybrid nanofluid are adopted from experimentally published data. The mathematical model is formulated based on the generalized Darcy–Brinkmann–Forchheimer equation and subsequently simulated using the penalty finite element method. A parametric study is conducted, encompassing a wide range of parameters for Rayleigh number, Darcy number, porosity value, buoyancy ratio, Lewis number, Soret parameter, and Dufour parameter. The resulting flow patterns, temperature distribution (isotherms), and concentration distribution (isoconcentration plots) provide insights into the fluid flow, heat transfer, and mass transfer phenomena within the physical domain. Furthermore, the heat and mass transfer rates at the heated (concentrated) wall are quantitatively evaluated by the mean Nusselt number and mean Sherwood number, respectively, considering various combinations of flow parameters. As a key finding, it is observed that the smaller value of the Rayleigh number remains insignificant at convective flow of thermal and solute phenomena. Moreover, the higher value of Ra reinforces the convective strength of hybrid nanofluid, and it helps to identify the real impact of each parameter. Thus, at a higher Rayleigh number, it is observed that the increasing value of Darcy number, porosity value, Lewis number, and buoyancy ratio significantly influence the convective flow of heat and solute transport activity, whereas the impact of Soret and Dufour parameters shows a relatively less influence on the heat and mass transfer phenomena.