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The limitation of intermittent and irregular supply of the solar energy systems can be compensated through utilization of thermal energy storage systems. The design of an efficient latent heat thermal energy storage system plays a huge role in determining the overall performance. Therefore, this study aims to investigate the effect of geometric parameters such as thermal charger interspacing and inclination angle on the charging performance of a PCM (phase change material) inside a semi-circular enclosure with two charging sources (renewable heat sources). A numerical analysis is performed using the enthalpy-porosity method. The system performance is assessed in terms of dimensionless flow parameters such as Fourier number, Rayleigh number, and Stefan number. The study shows that the variation of Rayleigh number significantly influences the natural convection in the fluid zone of a PCM. An increase of Rayleigh number from 1e4 to 5e5 reduced the overall melting time by more than half. In addition, the thermal charger interspacing and inclination angle both showed considerable effect on the flow physics which can cause significant expedition/delay of the melting process.

Convective heat transport in permeable media has been widely modeled using the local thermal non-equilibrium (LTNE) model. The majority of earlier LTNE-based models take temperature interactions between the fluid and solid phases into consideration. The present investigation delves into the intricate dynamics of Darcy–Rayleigh–Bènard (DRB) convection occurring within a liquid layer situated above a porous layer, wherein thermal gradients and heat generation play a pivotal role. This research examines the effects of many types of thermal gradients, including parabolic, step function (SF), linear, piecewise linear heated from below (PLHB), inverted parabolic, and piecewise linear cooled from above (PLCA). A fluid layer sits on top of a porous layer in the composite layer that makes up the system. The porous medium has achieved complete saturation with the identical fluid. The observed system demonstrates the manifestation of LTNE phenomena. Furthermore, the composite layer is constrained horizontally due to the presence of adiabatic stiff peripheries. The explanation to the aforementioned issue is obtained by employing the perturbation approach via analytical methodologies. The ongoing research is focused on exploring various physical parameters in order to examine the underlying physical implications that uphold the phenomenon of LTNE, employing the utilization of diagrammatic representation. A juxtaposition is drawn between the results derived from manipulating various constraints, including the temperature expansion ratio of the liquid phase, the corrected internal Rayleigh numbers, the thermal ratio, the diffusivity ratio of the liquid layer, and the permeable layer, within the framework of the LTNE configuration, and those obtained within the Local Thermal Equilibrium (LTE) regime. The depth ratio is a key factor in the onset of DRB convection, and higher depth ratio values which indicate porous layers that predominate in composite layered systems have a noticeable impact on all variables under investigation.

One of the practical methods for examining the stability and dynamical behaviour of non-linear systems is weakly non-linear stability analysis. Time-varying gravitational acceleration and triple-diffusive convection play a significant role in the formation of acceleration, inducing some dynamics in the industry. With an emphasis on the natural Rayleigh–Bernard convection, more is needed on the significance of a modulated gravitational field on the heat and mass transfer due to triple convection focusing on weakly non-linear stability analysis. The Newtonian fluid layers were heated, salted and saturated from below, causing the bottom plate’s temperature and concentration to be greater than the top plate’s. In this study, the acceleration due to gravity was assumed to be time-dependent and comprised of a constant gravity term and a time-dependent gravitational oscillation. More so, the amplitude of the modulated gravitational field was considered infinitesimal. The case in which the fluid layer is infinitely expanded in the x-direction and between two concurrent plates at z=0 and z=d was considered. The asymptotic expansion technique was used to retrieve the solution of the Ginzburg–Landau differential equation (i.e., a system of non-autonomous partial differential equations) using the software MATHEMATICA 12. Decreasing the amplitude of modulation, Lewis number, Rayleigh number and frequency of modulation has no significant effect on the Nusselt number proportional to heat-transfer rates (Nu), Sherwood number proportional to mass transfer of solute 1 (Sh1) and Sherwood number proportional to mass transfer of solute 2 (Sh2) at the initial time. The crucial Rayleigh number rises in value in the presence of a third diffusive component. The third diffusive component is essential in delaying the onset of convection.

This study investigates time-dependent free convection heat transfer and buoyancy-assisted flow over a horizontal heated plate within a vertical channel for two distinct scenarios: one stand alone and second involving tilted plates and varying plate positions. The temperature difference between the plate and air induces buoyant airflow. The study explores the impact of plate tilt angles and positions on time-dependent heat transfer coefficients due to varying buoyant airflow. The primary focus of the research for both classes of study is on the effects of the tilt angles (which control the change in flow blockage ratio) and positions of the heated plate on the time-dependent heat transfer coefficients due to the time-dependent buoyant airflow. As the blockage ratio increases and the positions of the heated plate in the vertical channel decreases, the influence of time-dependent buoyancy on the time-dependent Nusselt number weakens. The time-dependent Richardson's number varied from 7.4 to 9.6 throughout the tests. Based on the experimental data gathered from corresponding flux geometries and test conditions, the CFD model was validated. We have also developed a set of empirical correlations for predicting time-dependent Nusselt numbers for a time-dependent Rayleigh number range of 2000 < Ra < 7500, the dimensionless height of the heated plate from 0.507 ≤  ϕ  ≤ 0.551, and a flow blockage ratio of 0.08 ≤  χ  ≤ 0.024. At orientations where γ  = π/2 and γ  = π/4 , it has been observed that the heat transfer at position ∅ 1 is higher, whereas at γ  = 0 orientation, ∅ 1 heat transfer value is lower compared to the others. When the time required for the heated plate at all positions ( ∅ ) to reach thermal equilibrium with the ambient environment is compared with respect to orientation angles, it has been observed that the γ  = π/2 orientation angle reaches thermal equilibrium in the shortest time compared to the γ  = π/0 and γ  = π/4 orientation angles.

This study examines the thermal and entropic behaviors of magnetohydrodynamic natural convection in a permeable medium after considering various thermal boundary spacings and Rayleigh numbers. It explored the combined effects of buoyancy-driven convection, electromagnetic forces, and the properties of the porous medium to analyze heat transfer and entropy generation mechanism. A numerical method had been utilized, applying the Darcy–Brinkman model for fluid flow through the porous medium, along with the energy equations to incorporate the effect of magnetic force. The parametric analysis addressed a broad spectrum of Rayleigh numbers and spacing distance evaluating their effects on flow patterns, temperature distributions, and rates of entropy production. The results have shown significant transitions in flow regimes with increasing Rayleigh numbers, shifting from conduction to convection-dominated behaviors with magnetic forces influencing the intensity and configuration of these regimes. The spacing distance is critical in shaping the flow dynamics. Smaller spacings obstruct convective motion because of an increase in viscous damping, whereas larger spacings have helped in promoting stronger convection. The analysis of entropy has revealed the competing impact of heat transfer irreversibility, fluid friction together with magnetic effects gaining better results at a higher magnetic field strength.

The convective phenomenon in non-Newtonian nanofluids utilizing a more physically realistic model, based on considering zero nanoparticle flux on the boundaries has worth in the areas of oil extraction from underground reservoirs and geophysics. In connection with this, we have studied linear and nonlinear stability analysis of Oldroyd-B nanofluid with no nanoparticle flux at the boundaries. Linear stability analysis is studied using a one-term Galerkin scheme, while nonlinear analysis for the stability has been considered using a minimal representation of the Fourier series. The governing ODEs are numerically solved using NDSolve in Mathematica. Interestingly, due to viscoelasticity of the Oldroyd fluid, oscillatory motions come into existence which were non-existent in the case of Newtonian base fluid with nanoparticles. Results reveal that the oscillatory convection comes to an end as the value of strain retardation parameter exceeds or equals stress relaxation parameter and it turns out to be stationary as strain retardation parameter surpasses a certain threshold value.

The joint influences of variable heat source patterns and temperature-reliant viscosity on the onset of convective motion in porous beds in the presence of gravity varian ce have been investigated. The linear analysis is performed using normal mode analysis and the Galerkin technique is applied to analyze the impact of variable heating and changeable gravity field on the behavior of system stability. The exponential temperature-dependent viscosity is considered. We examined three different types of heat source and gravity variance function combinations: Convection is accelerated by increases in viscosity and the gravity variance parameter, but decelerated by increases in the heat source strength. It has been shown that the configuration is more stable when the gravity variance and heat source functions are combined in instance case (ii), but less stable when they are combined in case (i) and case (iii).

In this paper, we carried out a series of linear analyses on the onset of thermal convection of highly compressible fluids whose physical properties strongly vary in space in convecting vessels either of a three-dimensional spherical shell or a two-dimensional spherical annulus geometry. The variations in thermodynamic properties (thermal expansivity and reference density) with depth are taken to be relevant for the super-Earths with ten times the Earth’s mass, while the thermal conductivity and viscosity are assumed to exponentially depend on depth and temperature, respectively. Our analysis showed that, for the cases with strong temperature dependence in viscosity and strong depth dependence in thermal conductivity, the critical Rayleigh number is on the order of 108–109, implying that the mantle convection of massive super-Earths is most likely to fall in the stagnant-lid regime very close to the critical condition, if the properties of their mantle materials are quite similar to the Earth’s. Our analysis also demonstrated that the structures of incipient flows of stagnant-lid convection in the presence of strong adiabatic compression are significantly affected by the depth dependence in thermal conductivity and the geometries of convecting vessels, through the changes in the static stability of thermal stratification of the reference state. When the increase in thermal conductivity with depth is sufficiently large, the thermal stratification can be greatly stabilized at depth, further inducing regions of insignificant fluid motions above the bottom hot boundaries in addition to the stagnant lids along the top cold surfaces. We can therefore speculate that the stagnant-lid convection in the mantles of massive super-Earths is accompanied by another motionless regions at the base of the mantles if the thermal conductivity strongly increases with depth (or pressure), even though their occurrence is hindered by the effects the spherical geometries of convecting vessels.

To provide insights into the challenging problem of turbulent convection, Jack Herring used a greatly truncated version of the complete Boussinesq equations containing only one horizontal wavenumber. In light of later observations of a robust large-scale circulation sweeping through convecting enclosures at high Rayleigh numbers, it is perhaps not an implausible point of view from which to reexamine high-Rayleigh-number data. Here we compare past experimental data on convective heat transport at high Rayleigh numbers with predictions from Herring’s model and, in fact, find excellent agreement. The model has only one unknown parameter compared to the two free parameters present in the lowest-order least-squares power-law fit. We discuss why the underlying simplistic physical picture, meant to work at Rayleigh numbers slightly past the critical value of a few thousand, is consistent with the data when the single free parameter in it is revised, over some eleven decades of the Rayleigh number—stretching from about a million to about 1017.

The effect of a heat source and temperature gradient on Brinkman–Bènard Triple-Diffusive magneto-Marangoni (BBTDMM) convection in a two-layer system is investigated. The two-layer system is horizontally infinite and is surrounded on all sides by adiabatic boundaries. It is exposed to basic uniform and non-uniform temperature profiles and heat sources. The appropriate eigenvalues and thermal Marangoni numbers (TMNs), which depend on temperature and concentration, are obtained for the temperature profiles (TPs) for lower rigid and higher free boundaries with surface tension. The transformed system of ordinary differential equations is solved by using an exact technique. For all three TPs, the impact of significant relevant parameters on these eigenvalues, and hence on BBTDMM convection, are investigated versus the thermal ratio. It is observed that, by increasing the values of the modified internal Rayleigh number for the fluid layer and the solute Marangoni numbers, the Darcy number, and the viscosity ratio for the set of physical parameters chosen in the study, one can postpone BBTDMM convection. Higher values of the modified internal Rayleigh numbers for the porous layer augment BBTDMM convection.