## 1 Introduction  
Thermoplastic polyurethane (TPU) is a polymer with an elasticity close to that of rubber but with better durability and toughness, and it is thus widely used in coatings, adhesives, thermoplastic elastomers, and sport equipment [1, 2]. Unfortunately, like most polymers, TPU presents low thermal conductivity, constraining its effectiveness for thermal management applications [3]. This problem is commonly faced in the development of plastic heat exchangers, for which the cheapness, low density, and elevated corrosion resistance of TPU are negatively counterbalanced by its intrinsically poor thermal conductivity [4]. On the other hand, nanostructured carbon fillers have attracted much interest due to their high thermal conductivity, which, for carbon nanotubes, is higher than 3000 W/K m at room temperature [5]. Carbon nanotubes are known as one of the stiffest manmade materials; moreover, their outstanding electrical and thermal conductivity have generated a lot of interest in the production of MWCNT-based nanocomposites with enhanced multifunctionality [6]. According to the literature, electrical and mechanical properties can be substantially improved by the incorporation of MWCNTs into the TPU matrix [7; 8; 9]. For instance, researchers have been actively exploring electrically conductive polymer nanocomposites for advanced strain-sensing applications. [PERSON] et al. reported the development of flexible and conductive nanocomposite strain sensors based on TPU [10]. By incorporating MWCNTs using a solution-mixing process and high-speed homogenization, they achieved an electrical percolation threshold as low as 0.1 wt%, thus obtaining a sensing material with an instantaneous gauge factor of 1389 at 50% strain. Furthermore, cyclic stress/release experiments underscored the robust recoverability and reproducibility of the strain-sensing effect. [PERSON] et al. tackled the challenge of maintaining the electrical conductivity of TPU nanocomposites during stretching, a crucial requirement for next-generation flexible electronics [11]. They developed highly stretchable and conductive MWCNT/TPU composite foams using a novel approach that involved melt-compounding, supercritical fluid treatment, and physical foaming. The introduction of a microcellular structure effectively suppressed the increase in electrical resistance during stretching. This approach not only preserved electrical conductivity but also enhanced the material elongation capability, opening the way for the development of stretchable and conductive polymeric materials for advanced electronics. [PERSON] et al. focused their attention on the fabrication of MWCNT/TPU electrospun films for strain sensing [12]. By varying the MWCNT content (from 10 up to 15 wt%) in electrospun nanofiber films, they observed improved electrical conductivity and enhanced strain-sensing capabilities. The MWCNT/TPU nanofiber film with a MWCNT content of 10% showed a gauge factor (GF) of 10.14 at 20% strain. With 12.5% MWCNTs, the strain-monitoring range was extended from 1% to 40%, with a GF of about 2.06. The sensor with this composition could measure pressures ranging from 0 to 220 kPa, with a linear sensitivity of approximately 0.432 kPa\({}^{-1}\) in the 0-5 kPa range. Moreover, nanocomposite films with a MWCNT loading of 12.5 wt% exhibited rapid responsiveness and excellent dimensional stability. These findings suggest the potential of these materials for use in human motion and pressure detection, highlighting the prospects of intelligent wearability. [PERSON] et al. presented a study detailing the development of robust, stretchable, and highly sensitive TPU nanocomposites filled with MWCNTs to be applied as piezoresistive strain-sensing materials [13]. The uniform dispersion of MWCNTs within the TPU matrix led to a notably low percolation threshold (0.1 wt%) and exceptional electrical conductivity. The strain-sensing capability of these materials was strongly correlated with the MWCNT concentration.