Figure 1.
![Contributions to energy conservation in a finite volume [16].](https://sciendo-parsed.s3.eu-central-1.amazonaws.com/647392104e662f30ba54262a/j_tar-2023-0004_fig_001.jpg?X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Content-Sha256=UNSIGNED-PAYLOAD&X-Amz-Credential=ASIA6AP2G7AKISKFYITU%2F20260221%2Feu-central-1%2Fs3%2Faws4_request&X-Amz-Date=20260221T171132Z&X-Amz-Expires=3600&X-Amz-Security-Token=IQoJb3JpZ2luX2VjEOj%2F%2F%2F%2F%2F%2F%2F%2F%2F%2FwEaDGV1LWNlbnRyYWwtMSJHMEUCIQCySd1L9yAJPQ7UvaNmL8lA74x2ED%2BXD3DQdGLIAwLtHAIgW0XytHRIqeW28YvAqtCtf2fi59fTRe4n0S55vf3uyUoqxgUIsf%2F%2F%2F%2F%2F%2F%2F%2F%2F%2FARACGgw5NjMxMzQyODk5NDAiDJB%2BMCeKD2ss%2F6FzmyqaBc7yAoqzxOuJJpcwUp004K2Ob2iuAT%2FO5VQc6SOH%2B5t1WJHrX2ZrlO%2B6EYPRh8UF8VYEMnYEXiuZdzwy1ru6xlRVAyuZxxvf21Q1u10Dk6ubJr1ZBAv9JKEDobQxzAsTTqE4adj%2BDbA5hL7kJ3U%2F8KISjGvhwU6kwkIIaj8jYfwZ2wTOjWRR56USk5j4AZcSM7Job5olz7cM9HxLh2OskEo%2BZndjFgMLz%2BFD0Bi2iKKS3Aqo%2BUZ4do0NzoXetz64tULqvCNpAsk%2Fs%2Fu79YioE17thbN0fI2sAV3yZ0%2BVOfqpY0BAagIgP74M2iP26Tf9sL6boKy%2FwUwozrmxYM5ol%2BEvI%2FF7D%2B%2F%2BFjN%2BffbZl8dPbin0GORG2D%2B3hL1awmqrVmljtJ4XcluHJcl%2BLZZXJTZm6eXZz%2BWyFf6ga9gLVh7FvX3PxaCcLEOX%2BqlEekOoaTorNHZH5hDg5uog8MGO9erKXVeVPlbJzkMVQ7O8ONNShpM2zcGmAcHGWEMK9ffMir1yw0ro9fSqYF%2Fx547lYnEGdaefS9gcyP8b0a3sxKuAsJEj3ltkDnl84hz5jmOQY0uNswnOvjWbCinFf02aO1f%2FMiaB3JZSimc3cQXeS14vp6FSUZ%2FH%2FtuH3eYalfqLOKQriJcqd6NJuvnFCbLqyV1%2F2R3ETxH43ol14jbLlMuHq21ReE68BD%2Bsur5iy%2BZM3OcquG5TqhKNQscU8Q5Mpr8%2BiBdt8%2FhH2bN4Q9pNNxOcyEBAshGH8KA5JlG3fy6bXF2Nu3NQjiZNhAT0F7Hbii5NlntzrxSj4uLSetjLHHcMDx6X2ZvEo%2BsvO0cntDmiDKYVheeSPM11R49hVW4a4cXy4E5VeeARev5epJrszE0R5n314NGc%2F4SvaDCto%2BfMBjqxATRfbRzKZQraQG5us2TwRmhyXMllVtWUAqlvJw%2BTERUUG1dnSZ7ij%2BEJv%2BNLu1UzfC0JFDRFKk3RlmQdp4%2FzGr1g15LSx%2FYveUSfJHhEWkZa%2FsJHJtL3TTW6Fn%2FDU0yMgtP1RSL0AYHgkLNzcNqK2eu7EqFXEqXnTtNuHrt4jSHC7TfVSWIY0PkV98eajOv%2BzCTOJBNaIydMMkSxPZmkXx43XFbY5XNgwqySiCXY2nGxQQ%3D%3D&X-Amz-Signature=0e0900be5e0175cd311c73afb139c0120f6998bf21fab087ab90ac1b32a9bb6a&X-Amz-SignedHeaders=host&x-amz-checksum-mode=ENABLED&x-id=GetObject)
Figure 2.

Figure 3.
![Schematic view of the heater layers [11].](https://sciendo-parsed.s3.eu-central-1.amazonaws.com/647392104e662f30ba54262a/j_tar-2023-0004_fig_003.jpg?X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Content-Sha256=UNSIGNED-PAYLOAD&X-Amz-Credential=ASIA6AP2G7AKISKFYITU%2F20260221%2Feu-central-1%2Fs3%2Faws4_request&X-Amz-Date=20260221T171132Z&X-Amz-Expires=3600&X-Amz-Security-Token=IQoJb3JpZ2luX2VjEOj%2F%2F%2F%2F%2F%2F%2F%2F%2F%2FwEaDGV1LWNlbnRyYWwtMSJHMEUCIQCySd1L9yAJPQ7UvaNmL8lA74x2ED%2BXD3DQdGLIAwLtHAIgW0XytHRIqeW28YvAqtCtf2fi59fTRe4n0S55vf3uyUoqxgUIsf%2F%2F%2F%2F%2F%2F%2F%2F%2F%2FARACGgw5NjMxMzQyODk5NDAiDJB%2BMCeKD2ss%2F6FzmyqaBc7yAoqzxOuJJpcwUp004K2Ob2iuAT%2FO5VQc6SOH%2B5t1WJHrX2ZrlO%2B6EYPRh8UF8VYEMnYEXiuZdzwy1ru6xlRVAyuZxxvf21Q1u10Dk6ubJr1ZBAv9JKEDobQxzAsTTqE4adj%2BDbA5hL7kJ3U%2F8KISjGvhwU6kwkIIaj8jYfwZ2wTOjWRR56USk5j4AZcSM7Job5olz7cM9HxLh2OskEo%2BZndjFgMLz%2BFD0Bi2iKKS3Aqo%2BUZ4do0NzoXetz64tULqvCNpAsk%2Fs%2Fu79YioE17thbN0fI2sAV3yZ0%2BVOfqpY0BAagIgP74M2iP26Tf9sL6boKy%2FwUwozrmxYM5ol%2BEvI%2FF7D%2B%2F%2BFjN%2BffbZl8dPbin0GORG2D%2B3hL1awmqrVmljtJ4XcluHJcl%2BLZZXJTZm6eXZz%2BWyFf6ga9gLVh7FvX3PxaCcLEOX%2BqlEekOoaTorNHZH5hDg5uog8MGO9erKXVeVPlbJzkMVQ7O8ONNShpM2zcGmAcHGWEMK9ffMir1yw0ro9fSqYF%2Fx547lYnEGdaefS9gcyP8b0a3sxKuAsJEj3ltkDnl84hz5jmOQY0uNswnOvjWbCinFf02aO1f%2FMiaB3JZSimc3cQXeS14vp6FSUZ%2FH%2FtuH3eYalfqLOKQriJcqd6NJuvnFCbLqyV1%2F2R3ETxH43ol14jbLlMuHq21ReE68BD%2Bsur5iy%2BZM3OcquG5TqhKNQscU8Q5Mpr8%2BiBdt8%2FhH2bN4Q9pNNxOcyEBAshGH8KA5JlG3fy6bXF2Nu3NQjiZNhAT0F7Hbii5NlntzrxSj4uLSetjLHHcMDx6X2ZvEo%2BsvO0cntDmiDKYVheeSPM11R49hVW4a4cXy4E5VeeARev5epJrszE0R5n314NGc%2F4SvaDCto%2BfMBjqxATRfbRzKZQraQG5us2TwRmhyXMllVtWUAqlvJw%2BTERUUG1dnSZ7ij%2BEJv%2BNLu1UzfC0JFDRFKk3RlmQdp4%2FzGr1g15LSx%2FYveUSfJHhEWkZa%2FsJHJtL3TTW6Fn%2FDU0yMgtP1RSL0AYHgkLNzcNqK2eu7EqFXEqXnTtNuHrt4jSHC7TfVSWIY0PkV98eajOv%2BzCTOJBNaIydMMkSxPZmkXx43XFbY5XNgwqySiCXY2nGxQQ%3D%3D&X-Amz-Signature=befbe9a587a370ff22c4adaf6dc73773b59e8ba7bdff1566118d9f68ef159024&X-Amz-SignedHeaders=host&x-amz-checksum-mode=ENABLED&x-id=GetObject)
Figure 4.

Figure 5.

Penalty for each constraint_
| Constraint | Description | Penalty ice | Penalty temp. |
|---|---|---|---|
| No ice | - | ||
| T ε [Tmin, Tmax] | Temp. | - | |
| No ice & temp. | |||
| B ≤ Bmax | Ice & temp. |
IWT parameters used for the design of the IPS_
| IWT parameters | |
|---|---|
| α [°] | 1.70 |
| 67.48 | |
| T∞[K] | 259.95 |
| 1.2886 | |
| P∞[Pa] | 101,325 |
| MVD [μm] | 28.0 |
| 0.583 | |
| Δt[s] | 594 |
Power consumption comparison_
| IPS (constraint) | Thermopneumatic | ETIPS (no ice) | ETIPS (temp) | ETIPS (no ice/temp) | ETIPS (ice/temp) |
|---|---|---|---|---|---|
| Lip surf. (m2) | 0.14 | 0.19 | 0.19 | 0.19 | 0.19 |
| 10 | 13.02 | 6.53 | 13.60 | 5.97 | |
| 1.4 | 2.47 | 1.24 | 2.58 | 1.13 |
Heating element layers with material properties [4]_
| Material | |||
|---|---|---|---|
| Heating element (Alloy 90) | 41.02 | 8,906.26 | 385.19 |
| Erosion shield (SS 301 HH) | 16.27 | 8,025.25 | 502.42 |
| Elastomer (Cox 4300) | 0.256 | 1,384 | 1,256.04 ± 125.6 |
| Fibreglass/epoxy composite | 0.294 | 1,794.07 | 1,570.05 |
| Silicone foam insulation | 0.121 | 648.25 | 1,130.44 ± 125 |
Best design for each constraint_
| Constraint | Tmax [K] | Tmin [K] | GA | |||
|---|---|---|---|---|---|---|
| No ice | 3305.65 | 0 | 320.77 | 326.11 | 266.75 | CM-GA |
| Temp. | 1657.74 | 328.29 | 306.50 | 287.57 | 280.18 | C-GA |
| No ice & temp. | 3452.95 | 0 | 316.59 | 325.05 | 275.74 | M-GA |
| Ice & temp. | 1517.02 | 323.72 | 319.57 | 294.14 | 273.21 | CM-GA |