Zahra S. Hafed

The formulation of effective (true) static stress acting on a deformed surface is based on well-established principles of continuum mechanics. In this study, the solid is expected to be exposed to a uniform static uniaxial stress field. By accounting for second-order stress-strain interactions, a modified set of elastic motion equations is obtained, which incorporates the influence of static surface forces and body forces on elastic wave propagation in isotropic media. The thermal response is modelled using the generalized heat conduction equation within the modified Lord–Shulman magneto-thermoelastic framework, augmented by a higher-order time derivative of order N. The resulting coupled system of governing partial differential equations is explained by assuming harmonic wave forms and employing the method of separation of variables. This formulation enables a systematic examination of magnetothermoelastic wave propagation and the corresponding stress behaviour of the solid, with particular emphasis on the role of the operator order. A comprehensive numerical analysis is carried out to examine the spatial and temporal variations of temperature, displacements, dilatation, and stress components. The results demonstrate that operator order N has a pronounced influence on the thermoelastic response: larger values of N significantly reduce thermal oscillations and enhance the decay of thermal disturbances, while the limiting case N → ∞ produces the smoothest and most stable temperature distribution.

The optimization of thermal performance in star-shaped thermal energy storage (TES) units filled with nano-enhanced phase change materials (NEPCMs) is investigated in this study. Several geometric configurations of the irregular enclosure are considered by varying the undulation number. An inner rotating cylinder is placed within the domain, and unlike previous studies, a wide range of clockwise angular velocities is examined. Four operating cases are analyzed based on the heating mode and cylinder motion: (i) internal heating with rotation, (ii) internal heating with a stationary cylinder, (iii) external heating with rotation, and (iv) external heating with a stationary cylinder. The flow region is filled with a dual-energy permeable medium, where the host fluid is modeled as a red blood cell (RBC)-based suspension. To solve the governing equations within the irregular geometry, the control volume method is supported by a point-in-polygon determination test. Expressions for the total heat transfer rate are derived, and the Nusselt numbers of both the fluid and solid phases are optimized using the Response Surface Methodology (RSM). The major results indicate that at higher Rayleigh numbers, buoyancy dominates over rotation-induced circulation. Additionally, stronger rotation promotes mixing and reduces thermal stratification. Furthermore, in the case of external heating, the presence of internal clockwise rotation enhances flow activity by 44.7 % compared to a stationary cylinder. The novelty of this work appears in presenting an innovative numerical investigation of micropolar NEPCM flow in an irregular star-shaped porous TESS under LTNE conditions, providing new quantitative insights for optimizing advanced thermal energy storage designs.

Background: Inclined square cavities play a critical role in engineering applications, particularly in thermal management, energy storage and electronic cooling, where inclination angles influence convective heat transfer. This study examines conjugate convective heat transfer within an inclined square cavity filled with micropolar nanofluids under a tilted Lorentz force using a two-phase nanofluid model. The system includes a heat-generating porous medium under thermal nonequilibrium, introducing complex dynamics. Factors such as thermal buoyancy, fluid–solid heat transfer coefficient and micropolar fluid properties are analyzed for their impact on heat transfer efficiency. Methods: The study uses the finite difference method (FDM) to solve nonlinear equations governing convective flow and heat transfer. Physical parameters, including thermal buoyancy, micropolar properties and thickness of the solid walls, are incorporated. The setup features conductive horizontal walls and adiabatic vertical walls to simulate realistic thermal conditions. An artificial neural network (ANN) trained on FDM data predicts local Nusselt numbers, leveraging multiple input factors. This hybrid numerical-AI approach enhances efficiency, reducing computational time while maintaining accuracy. Significant findings: The inclination angle, buoyancy ratio and micropolar effects significantly influence heat transfer efficiency by driving convective behavior within the cavity and affecting the local Nusselt number distribution. The ANN demonstrates high prediction accuracy, providing a fast and reliable tool for analyzing heat transfer in complex systems. Increasing the thickness of the solid walls from 0.05 to 0.3 results in a 35.78% reduction in flow activity. Additionally, when the fluid type is changed from Newtonian ([ ]) to non-Newtonian ([ ]), the heat transfer rate decreases by 50.63%.

Vibrational double diffusion has gained increasing attention in recent studies due to its role in enhancing mixing, disrupting thermal boundary layers, and stabilizing convection structures, especially in nanofluids and porous media. This study focuses on the case of two-phase nanofluid flow in the presence of vibrational effects. The flow domain is a fined chamber that is filled with a non-Darcy porous medium. Two concentration formulations are proposed for the species concentration and nanoparticle concentration. The thermal radiation is in both the x- and y-directions, while the flow domain is considered to be inclined. The solution technique depends on an effective finite volume method. The periodic behaviors of the stream function, Nusselt numbers, and Sherwood numbers against the progressing time are presented and interpreted. From the major results, a significant reduction in harmonic behaviors of the stream function is obtained as the lengths of the fins are raised while the gradients of the temperature and concentration are improved. Also, a higher rate of heat and mass transfer is obtained when the vibration frequency is raised. Furthermore, for fixed values of the Rayleigh number and vibration frequency (Ra = 10⁴, σ = 500), the heat transfer coefficient improves by 27.2% as the fin length increases from 0.1 to 0.25.