## 1 Introduction  
Every material demonstrates a thermal response to temperature changes in its surroundings; therefore, a material's behavior could vary under different conditions. Most materials exhibit positive thermal expansion at high temperatures, although some materials may demonstrate negative thermal expansion. Thermosensitive gels are one such material; they shrink when submerged in high-temperature liquids such as aqueous polymeric solutions and then swell when submerged in cooler fluids. The thermosensitive gels used in this study were generated in a laboratory for application specifically in the upper heating system (or the lower cooling system) of a rectangular enclosure. Such systems have an disadvantageous property that limits heat transfer between two opposite horizontal walls; however, they offer an advantage: When thermosensitive gels and a polymeric solution fill the gap between the two opposite heat sources, the gels show distinctive mechanical behaviors of repetitive shrinking and swelling over a period of time. The system used in this study comprises N-isopropyl acrylamide (NIPA) gels and sodium polyacrylate (PAANa) solution in an integrated system; these materials form the focus of this study's observations. Theoretically, an aqueous polymeric solution is considered as an aqueous fluid comprising water and polymeric substances at a certain concentration. Polymeric solutions are important because of their application in multiple pharmaceutical and biomedical contexts [1] such as drug delivery [2] and enzyme or protein modifications [3,4]. Currently, thermosensitive gels have attracted considerable attention because they can be created using physical or chemical cross-linkers and form a unique class of polymeric materials that can retain quantities of water while maintaining their own structures [5]. Thermosensitive gels may be in either a sol or a gel phase depending on their temperature. The sol phase is considered as a fluid state, whereas the gel phase is related to a rigid, non-fluid state in which the shape/physical structure is preserved. Typically, the sol-gel state can be achieved only via a thermal stimulus. For biomedical applications in particular, the condition is suitable for in situ hydrogel formation at close to human-body temperature without requiring additional chemical initiators [6]. Theoretically, depending on its thermal characteristics, a thermosensitive gel may have either a lower critical solution temperature (LCST) or an upper critical solution temperature [7,8]. NIPA gel swells in aqueous solutions and absorbs a certain amount of the solution at temperatures below its LCST. At temperatures above its LCST, the gel shrinks and discharges the absorbed solution. Moreover, significant changes in volume occur because of small temperature changes close to the gel's LCST [9, 10, 11]. Exposing NIPA gel to a monotonic load above its LCST reveals a tougher mechanical behavior than is evident below its LCST in terms of nominal stress, stretch, and Young's modulus. This makes the gel suitable for health applications such as the regeneration of damaged tissues [12]. Furthermore, when NIPA gels are submerged in an aqueous polymer solution in a rectangular cavity, they exhibit repetitive vertical motions for a certain length of time [13]. [PERSON] et al. used a polymeric solution (polyacrylamideamide [PAA]) as a fluid for surrounding the gels because its density is between those of the gels in their swollen and shrunken states. When the gels were heated in the upper layer, they began to shrink, their volume decreased, and their density increased above that of the surrounding fluid. Consequently, the gels slowly moved toward the bottom of the cavity. Similarly, when the gels were cooled in the cavity's lower layer, the gels started to swell, their volume increased, and their density became lower than that of the surrounding fluid; hence, the gels moved upward. These conditions enabled the gels to vertically move in cyclical motions.