Ascertaining the existence of hidden objects in a complex system, objects that cannot be observed from the external world, not only is curiosity-driven but also has significant practical applications. Generally, uncovering a hidden node in a complex network requires successful identification of its neighboring nodes, but a challenge is to differentiate its effects from those of noise. We develop a completely data-driven, compressive-sensing based method to address this issue by utilizing complex weighted networks with continuous-time oscillatory or discrete-time evolutionary-game dynamics. For any node, compressive sensing enables accurate reconstruction of the dynamical equations and coupling functions, provided that time series from this node and all its neighbors are available. For a neighboring node of the hidden node, this condition cannot be met, resulting in abnormally large prediction errors that, counterintuitively, can be used to infer the existence of the hidden node. Based on the principle of differential signal, we demonstrate that, when strong noise is present, insofar as at least two neighboring nodes of the hidden node are subject to weak background noise only, unequivocal identification of the hidden node can be achieved.

This article reports convection heat transfer in a short and tall annular enclosure with two discrete isoflux heat sources of different lengths. The discrete heat sources are mounted at the inner wall and the outer wall is maintained at a lower temperature, whereas the top and bottom walls and the unheated portions of the inner wall are kept at adiabatic. An implicit finite-difference method is employed to solve the vorticity–stream function formulations of the governing equations. The significant influence of the discrete heaters on the flow and heat transfer is analyzed for a wide range of modified Rayleigh numbers, aspect ratio, and length ratio (ϵ) of heat sources. Our numerical results reveal that the average Nusselt number decreases with aspect ratio, whereas the magnitude of maximum temperature increases with the aspect ratio. For most of the parametric cases considered in the present study, the heat transfer rate is found to be higher at the bottom heater than at the top heater except for ϵ = 0.5. The effect of heater length ratio on the heat transfer rate is noticeable for unit aspect ratio, whereas its effect is insignificant as the aspect ratio increases. Furthermore, it was found that the maximum temperature is found generally at the top heater except for the case ϵ = 0.5, where the maximum temperature is found at the bottom heater.

This article reports a numerical study of natural convection in a vertical annulus filled with a fluid-saturated porous medium, and with internal heat generation subject to a discrete heating from the inner wall. The relative importance of discrete heating on natural convection in the porous annulus is examined via the Brinkman-extended Darcy equation. The inner wall of the annulus has a discrete heat source and the outer wall is isothermally cooled at a lower temperature. The top and bottom walls and the unheated portions of the inner wall are kept adiabatic. The governing equations are numerically solved using an implicit finite difference method. A wide range of numerical simulations is conducted to understand the effects of various parameters like heat source length, heat source location, Darcy number, radius ratio, and Rayleigh numbers due to external and internal heating on the flow and heat transfer. The numerical results reveal that the placement of the heater near the middle portion of the inner wall yields the maximum heat transfer and minimum hot spots rather than placing the heater near the top and bottom portions of the inner wall. The heat transfer increases with an increase in the external Rayleigh number and Darcy number, while it decreases with an increase in the internal Rayleigh number, porosity of the porous medium, and the size of the heater. Further, we found that the size and location of the heater has a profound influence on the heat transfer rate and maximum temperature in the annular cavity.

The current study aims to analyze the magnetohydrodynamic natural convective fluid flow and heat transmission features of the ternary-hybrid nanofluid filled the partially heated porous square cavity under the impacts of heat absorption/generation and thermal radiation. The governing equations are solved using the Marker and Cell method. In the present study, three different types of nanoparticles, such as molybdenum disulfide (MoS2), single-walled carbon nanotube (SWCNT), and silver (Ag), are suspended in an inorganic (water) or non-polar organic (kerosene) solvent. Nine different shapes of nanoparticles are utilized in this study. The outcomes show that for the fixed pertinent parameter values of the existence and nonexistence of heat generation/absorption, the MoS2+SWCNT+Ag/water ternary-hybrid nanofluids synthesized by lamina-shaped nanoparticles, the average thermal transmission rate is increased by 40.8523%, 36.329%, and 38.7025%, respectively, than sphere-shaped nanoparticles. In addition, utilizing the MoS2+SWCNT+Ag/kerosene ternary-hybrid nanofluids synthesized by lamina-shaped nanoparticles, the average heat transmission rate is augmented by 38.0322%, 33.0464%, and 35.5868%, respectively, than sphere-shaped nanoparticles. The current study reveals that the fluid flow and heat transfer efficiency are significantly increased by improving the nanoparticle volume fraction and shape factors depending upon the existence of heat absorption/generation. The high average heat transfer efficiency is observed when lamina-shaped nanoparticles are dispersed into the water compared to kerosene in the presence of a heat source. This study can enhance heat transmission efficiency in various industrial and engineering fields, such as heat exchangers, solar collectors, and fuel cells.