As illustrated in Figure 1(a), low-magnification microscopy (5×) reveals that the forewing of the butterfly exhibits a triangular outline bordered by evenly distributed black cilia. The distance between the wing root and its distal margin is about 3 cm, longitudinal veins run outwards and divide the surface into irregular polygonal areas. The wing scales are mostly green with some black lines stretching across and the ones near the margins show bright green iridescence when exposed to light. Figure 1(b) demonstrates that the wing surface consists of two different layers of scales: a basal layer of scales that is black and an overlaying layer of scales, where neighboring scales overlap to some extent, resulting in bright coloration under exposure to light. On greater magnification, the scales are long and narrow with a length of up to 150 μm and a maximum width of 50 μm. The upper edges of many of these scales are serrated, but the bright-coloured scales have smooth edges, and look like narrow willow-leaves (Figure 1(c)). Each scale has one colour, and in any case, matte yellow or iridescent green. The orderly, tile-like arrangement across the wing generates the characteristic vibrant pattern [11].

(a) (b) (c)

Figure 1.Papiliomaackii front wing [11]. (a) 5:1, (b) 15:1, (c) 150:1.

As shown in Figure 2(a), Ultra-Depth Three-Dimensional Microscopy reveals that the forewing of Papilioxuthus exhibits a triangular profile, measuring approximately 4.6 cm in maximum length and 2.75 cm in maximum width. It has a wing design that consists of black and white stripes in rotation along the wing root, to the margins. These stripes run along the wing veins in the central area with a series of curved and crescent-shaped spots forming outer edges where they have no iridescence or pigment reflections. As it is observed in the marginal scales, in more detail (Figure 2(b)), the black and the white scales are regularly arranged, with white scales forming triangular patches surrounded by black scales, developing a more specific alternating scheme. An increase in magnification of the black-white boundary (Figure 2(c)) reveals a sharply defined distribution, with both black and white scales exhibiting similar morphology, approximately 150 μm in longitudinal length and 60 μm in lateral width [11].

Figure 2.Papilioxuthus wing [11]. (a) 5:1, (b) 15:1, (c) 50:1.

As shown in Figure 3(a), the forewing of Kaniskacanace measures approximately 2.6 cm in length and 0.7 cm in width, displaying an irregular, triangular outline with pronounced undulations. The wing exhibits a black background that darkens progressively from the root toward the margin, with the apex marked by prominent white bands resembling tree-bark patterns. Magnified observation of the black–white boundary region (Figure 3(c)) reveals interspersed scales of both colors. Under 150× magnification (Figure 3(b) and Figure 3(d)), both white and black scales measure approximately 150 μm in length and 50 μm in maximum width, each bearing three serrations along the upper posterior edge. The morphology of the scales is therefore nearly identical, differing only in pigmentation [11].

(a) (b)

(c) (d)

Figure 3.Kaniskacanace wing [11]. (a) 5:1, (b) 150:1, (c) 150:1, (d) 150:1.

Scanning electron microscope (SEM) image of Figure 4(b), butterfly wing scale surface at magnification 500x. The microstructure has a set of parallel ridges arranged in a highly ordered way, as shown in Figure 4(b), the structure resembles willow leaves. Further magnification at 5000x reveals branching along both sides of the ridge, as illustrated in Figure 4(a). Figure 4(c) provides additional morphological details, showing that the surface in between the ridges is occupied by a network-like mesh structure, consisting of hexagonal or irregular polygonal cavities. These vein-like micro structures are light-trapping pits and microcavities and boost scattering, reflection, and absorption of incident light. Morphology indicates a lamellar structure, the ridges are used to achieve the structural stability and create optical pathways, and the porous mesh enables the amplified photothermal conversion and structural coloration. Geometrically, the inter-ridge (vein) distance has a value of about 3 µm and the average pit sizes have dimensions of about 0.6 µm in length and 0.3 µm in width [11].

Figure 4. Scanning image of the Papiliomaackii wing [11]. (a) 5000:1, (b) 500:1, (c) 10,000:1.

Scanning electron microscope (SEM) image of the butterfly wing scale surface at 500x magnification is shown in Figure 5(a). Each scale exhibits a similar shape, as can be observed in Figure 5(a). Further morphological details are presented in Figure 5(b), where the surface reveals are a series of parallel ridges oriented horizontally, forming the primary structural framework of the scale. Between these ridges lies a network of irregularly structural microcavities, most of which are circular or elliptical pits. Notably, the image shows both nearly circular pits and elongated elliptical pits, illustrating the diversity of cavity morphology within the mesh-like structure. The circular pits exhibit isotropic geometry, whereas the elliptical pits display pronounced anisotropy with distinct long and short axes. Quantitative analysis indicates that the average distance between adjacent ridges is approximately 2.6 μm, while the pits have an average length of 0.8 μm and width of 0.3 μm [11].

Figure 5. Scanning images of the Papilioxuthus wing [11]. (a) 500:1, (b) 10,000:1.

Figure 6(a)shows a scanning electron miscroscope (SEM) image of a butterfly wing scale at 500x magnification, highlighting the orderly arrangement of the scales. Each scale exhibits approximately 7 to 8 serrations at the top. In Figure 6(b), the surface is characterized by parallel ridges running diagonally, forming the primary structural framework. Periodically placed elliptical pores or cavities are located between these ridges. Although the pore sizes vary slightly, they are uniformly distributed within the ridge structure. Morphometric analysis indicates that the mean distance between adjacent ridges is approximately 1.2 μm, and the elliptical pits have average dimensions of 0.8 μm in length and 0.3 μm in width [11].

In conclusion, based on the size and parameter values of the SEM images of the three butterfly wings the shape and morphology of the units as well as the structural distribution were compiled and listed in Table 1.

Following the morphological analysis, the extracted microstructural parameters of the butterfly wings summarize in Table 1 were used as the basis for constructing a 3D CAD model of a bioinspired thermal insulation panel. These characteristic dimensions were scaled up to functional sizes suitable for wall panel integration, while preserving the geometric integrity of the original biological features.

Figure 6. Scanning images of theKaniskacanace wing [11]. (a) 500:1, (b) 10,000:1.

Table 1. Analyze the table of characteristic parameters of butterfly microstructure.

We will scale up the sizes of the butterfly’s wing microstructures to 10, in order to convert every unit to millimeters without losing important dimensionless parameters of aspect ratio, periodicity and surface-to-volume ratio. Scaling laws of heat transfer and wave propagation [12] show that scaling geometry at constant material refractive index and ratio of thermal conductivity ratios holds the dimensionless, Nusselt, Biot, and optical interference numbers fixed, and leaves the functional behavior of the system the same. This means that the 10 mm scale model scales down microscale light scattering, multi reflection and confinement of localized heat, which effectively scales the photothermal regulation mechanisms shown by the butterfly to a scaleable macro scale such that can be analyzed in the context of architectural insulation [12][13].

The scaling was performed using the magnification equation [14] (I):

where:

M is the magnification factor, I is the target (scaled) dimension used in the wall panel, A is the actual size of the biological microstructure. After scaling up every value in Table 1, we will use those values to construct the 3D model of each model using AutoCAD, which can be observed in Figure 7.

3.4.1. Parameters and Material Selection

The exterior convective heat transfer coefficient for sun-exposed vertical façades was taken as 12 - 15 W∙m⁻²∙K⁻¹. This range corresponds to the combined natural +

Traditional model Papiliomaackii model

Papilioxuthus model Kaniskacanace model

Figure 7. The model of the butterfly’s scale wing.

forced convection model commonly used in building simulation h = 5.7 + 3.8 Vz (McAdams’s form implemented in EnergyPlus), where Vz is the local wind speed. The chosen range (≈1.7 m∙s⁻¹ - 2.5 m∙s⁻¹) represents light–to–moderate effective wind conditions typical of sheltered or partially sheltered urban façades in Abidjan [15]-[17]. The indoor air movement used the internal value of 5 - 7 W/m²∙K in the simulation. For boundary conditions, the temperature inside the room is set 25˚C at a constant room temperature, and the outside, 28˚C representative of average climatic conditions in Abidjan Côte d’Ivoire [18].

To further analyses the thermal insulation performance, we simulated and analyzed in terms of total temperature and total surface heat flux, surface radiosity through the Fluent module in Consol multiphysics. First, the three models were given common material attributes. The model material used is polylactic acid (PLA). Although PLA is not currently used as a mainstream construction material in West Africa at the present, but its usage in the present work can be explained by its ability to be 3D printed and the possibility of being localized by using renewable biomass resources like maize and cassava [19]. An example is Cote d’Ivoire which in 2022 alone harvested an estimated 6.3 million tons of cassava, one of the leading producers of cassava in Africa and the world [20]. It is also a large-scale producer of maize and it produces about 1.1 to 1.3 million tons of maize annually which forms a large part of the cereal supply of West Africa [21]. Such rich sources of agriculture offer a long-term source of PLA which is produced locally using local starch crops like maize and cassava. Therefore, the local manufacturing plants of PLA might be established; this would allow reducing production costs dramatically and make PLA-based biomimetic insulation materials effective economically and suitable to the environment to be used in the local construction sectors. In addition, PLA also has low thermal conductivity with a range of 0.0643 to 0.0904 W/m∙K) which is significantly lower than concrete 1.0 - 1.8 W/m∙K and typical clay bricks 0.82 W/m∙K. Its average mass of about 1233 kg/m³ (1.233 g/cm³) is lightweight and efficient insulation [22]. Secondly, we set up all boundary in the software such: exterior convective heat transfer coefficient, ambient temperature, extermal radiation source generate accordingly to the coordinate (Latitude: 5.28˚N, Longitude: 4.03˚W [23]) and a normal mesh element configuration was employed in COMSOL Multiphysics to discretize the geometric domain. The mesh was generated automatically by the software, ensuring an optimal balance between computational efficiency and numerical accuracy. To be sure the mesh generated we will not affect the result we will do the mesh-independence test to confirm that numerical results are insensitive to discretisation.

3.4.2. Mesh Generation and Quality Assessment

We used COMSOL Multiphysics to set up a normal mesh and discretize the computational domains of all the four models. The automatic tetrahedral meshing algorithm was chosen because it offers a good balance between the numerical and computational efficiency. Table 2 summarizes the mesh statistics and size parameters for each configuration.

Table 2. Mesh statistics and element size parameters for all models.

The quality of all generated meshes fell within the range of 0.61 to 0.67 average element quality that is fine in terms of steady state thermal simulations. Even though minimum element quality values slightly varied due to complex geometrical curvatures, no invalid or inverted elements were detected during automatic validation in COMSOL Multiphysics. All configurations converged successfully by the solver, and this is a good indication of numerical soundness. All the meshes used the same refinement parameters, which were: curvature factor = 0.6, narrow region resolution = 0.5 and the maximum rate of element growth = 1.5 to provide smooth elements transitions at the fineness and coarse zones, without affecting the fidelity of the biomimetic microstructures. Overall, the developed meshing approach ensured a uniform geometric resolution between all the biomimetic and traditional models, allowing them to be directly compared to each other in terms of their thermal behaviour at the same level of computation.

3.4.3. Mesh-Independence Verification

A mesh-independence test was done to ensure that mesh density did not affect numerical results. Surface averaged values of temperature, normal heat flux and surface radiosity were measured on both the Normal and Fine mesh models with the same set of boundary conditions and material properties. The test result was summarized in Table 3.

Table 3. Mesh-independence results (surface-averaged quantities).

The relative percentage error for each variable was computed using:

Error(%)= (Resultoffinemesh−Resultofnormalmesh)/Resultoffinemesh [24]

The results of the mesh-independence verification in Table 3 confirm that the numerical outcomes are insensitive to spatial discretization. All the critical thermal quantities had relative deviations less than 2% and the major ones had less than 1% of deviation, which met the 3% independence criterion. The amount of temperature and radiosity was almost mesh independent, and smaller deviations in the heat flux were within reasonable numerical error. This therefore led to the conclusion that the Normal mesh setup was accurate enough to be used in further simulations and also to be computationally efficient without compromising the accuracy.

The thermal conditions of the two boundaries of the material in thermal simulation are different. The hot side (yellow color) refers to the surface directly exposed to the heat source whereas the temperatures reach its maximum while the cold side (red color) is the other side opposite to the heat source and its temperature is the lowest due to the dissipation of the energy. This can be observed inFigure 8. To further evaluate the thermal insulation performance. We will analyse Figure 9 which present the temperature distributions curves along the material thickness. Figure 9 allows to compare the traditional model to the biomimetic structure using the numerical values. As can be seen in Figure 8, the highest temperature calculated from the simulated radiation is in the yellow color and the low temperature is the red color. The yellow color which is the hot side and the red color which is cold side. The temperature line graphs indicate that the conventional design has the highest peak of the hot side temperature (65.17˚C at x = 0) and the lowest of the cold side temperature (46.71˚C at x = 0.08), which is accompanied by a huge temperature difference 18.46˚C. High heat transfer and consequently poor insulation are represented by this sharp drop. Conversely, the biomimetic designs (Kaniskacanace, Papiliomaackii, and Papilioxuthus) have lower peak temperatures (53˚C - 58˚C) on the hot side and higher (51˚C - 54˚C) on the cold-side, leading to significantly smaller changes in temperature 1.6 to 3.9˚C. This low gradient implies much greater thermal resistance. Papilioxuthus (1.63˚C drop) and Papiliomaackii (1.89˚C drop) are the most insulated followed by Kaniskacanace (3.89˚C drop) that exhibits mid-range performance. Therefore, the line chart substantiates the fact that butterfly-inspired microstructures provide much better thermal insulation than the conventional smooth surface.

Papiliomaackii model Papilioxuthus model

Kaniskacanace model Traditional model

Figure 8. Temperature nephogram.

Papiliomaackii model Papilioxuthus model

Kaniskacanace model Traditional model

Figure 9. Temperature line chart.

The thermal insulation performance of models can be observed in Figure 10. The traditional structure exhibited the highest surface temperature rise, reaching a maximum of approximately 37.9˚C at 1.5 h, which corresponds to rapid heat penetration and low thermal resistance. Comparatively, the biomimetic designs based on butterfly wing designs Papilioxuthus, Kaniskacanace and Papiliomaackii had much lower heating with temperatures not exceeding 34˚C - 35˚C. This indicates a slower rate of heat transfer through the material. Moreover, the curves of the biomimetic models are flatter, with smaller temperature gradients over time, confirming their superior ability to delay and suppress heat conduction. Two of them, Papilioxuthus and Papiliomaackii demonstrate the most stable profiles, which indicate the most efficient insulation. In sum, the time-temperature diagram directly supports that butterfly-inspired microstructures are better than traditional smooth surfaces to increase thermal insulation.

Figure 10. Temperature-time curve chart of bionic models.

In Figure 11, the light red shading corresponds to the hot with elevated temperature and the opposite the darker red tones are the cold side with lower temperature. To better analyses we get insight into the thermal insulation behavior in the Figure 12. Comparison of the rate and heat penetration extent can be made in these plots thus quantifying the effectiveness of every structure in thermal flow resistance. The conventional design has strong variance, with values ranging from −12.67 W/m² to a positive peak of 37.76 W/m². Such sharp bends suggest unsteady and focused heat transfer channels, which result in inefficient thermal resistance. Conversely, the butterfly-inspired systems are good at trapping and redistributing the heat. At x = 0.003 m, the surface flux of Kaniskacanace is very high 284.71 W/m², but it also rapidly decreases with depth, up to a value of almost zero and even negative values −10.81 W/m² at x = 0.06 m. The trend of this behavior indicates intense attenuation of heat transfer because the energy is scattered and dissipated. Papiliomaackii exhibits the same trend without the extreme initial peak. Beginning with 238.3 W/m² on the hot end, the flux swings in moderate −9.22 to +7.32 W/m² steps throughout the thickness, but with small overall magnitudes. This means that there are efficient redistribution of heat and a steady decline of thermal penetration among all designs. Papilioxuthus has the best stable and controlled performance of all designs. The flux in it is constantly low throughout the material, and it varies within a very narrow range of −12.82 W/m² to −6.40 W/m². The flat, suppressed curve reflects minimal and evenly distributed heat transfer, representing the most effective thermal insulation. Overall, the biomimetic microstructures reduce both the magnitude and variability of heat flux compared to the traditional surface, thereby enhancing thermal resistance.

Papiliomaackii model Papilioxuthus model

Kaniskacanace model Traditional model

Figure 11. Heat flux nephogram.

Papiliomaackii model Papilioxuthus model

Kaniskacanace model Traditional model

Figure 12. Heat flux line chart.

According to the curves, Papilioxuthus shows the best performance in insulation when compared to Papiliomaackii and Kaniskacanace with traditional design showing worst attitude at thermal control.

The heat flux response in Figure 13 indicates evident differences between the traditional and bio-mimetic models. The traditional model structure demonstrates the largest initial peak 757.77 W/m² and the strongest negative flux that changes with time −10.44 W/m² at 6 h, which is in line with the fast and unstable heat transfer. The bionic models on the other hand show reduced peaks and faster suppression of flux to near zero levels, which reflects greater thermal resistance. At 584.54 W/m², Kaniska starts to decrease but soon levels off to −1.78 W/m², Papiliomaackii and Papilioxuthus stabilize even at a faster rate and their flux values are very low −1.65 and −1.46 W/m², respectively. Of them, Papilioxuthus has one of the most stable and controlled behavior, which is an indicator of the best insulation. Overall, the butterfly-inspired microstructures significantly reduce both the magnitude and variability of heat flux compared to the traditional surface, hereby enhancing thermal insulation performance.

The yellow area is the hot side corresponds to the surface direct contact with the heat source and surface radiosity is the greatest. The opposite side is the cold side which is red color has the lower temperature. This can be observed on Figure 14. to better compare the traditional model to the bionic, we have will observe Figure 15 which allow to compare numerical the value of the surface radiosity of

Figure 13. Heat flux-time curve chart of bionic models.

Papiliomaackii model Papilioxuthus model

Kaniskacanace model Traditional model

Figure 14. Surace radiosity nephogram.

Papiliomaackii model Papilioxuthus model

Kaniskacanace model Traditional model

Figure 15. Surface radiosity line chart.

each model. The surface radiosity line charts clearly show the better insulation of the biomimetic models in comparison with the traditional structure. The traditional model has the greatest radiosity throughout the distance 714.82 W/m² to 587.90 W/m² at 0.08 m, with high radiative heat loss and low insulation ability. Conversely the bionic designs minimise the amount and the variation of surface radiosity. The lowest starting value is observed to be Papiliomaackii 624.64 W/m² to 631.20 W/m² at 0.08 m and the most stable profile is Papilioxuthus 641.23 W/m² to 646.26 W/m² at 0.08 m with considerably less fluctuations, which implies that radiation is effectively suppressed. Kaniskacanace 659.29 W/m² to 646.91 at 0.08 m demonstrates intermediate performance because the values are higher than those of the other two but overall lower than those of the traditional surface. The biomimetic models seen general, increase thermal resistance through a reduction in radiative heat loss, and Papilioxuthus and Papiliomaackii have the best insulation properties.

In Figure 16, At x = 0 m, the radiosity was in the range of 439 to 455 W/m² reflecting similar baseline thermal radiative performance. Nevertheless, upon increasing distance, different distinctions were observed between the bioinspired and traditional models. traditional model: The surface radiosity peaked quickly at x = 1.5 m to a value of 534.6 W/m², after which it began to decrease slowly. Radiosity steadily decreased beyond x = 3.5 m, to values near 468 W/m² at x = 6 m. This implies that there is a strong absorption at the beginning and difficulty to maintain constant thermal radiations at long distances. Kaniskacanace model: This model exhibited the maximum radiosity 518.9 W/m² at x = 1.5 m, however thereafter the decrease was smoother than in the traditional case. At x = 6 m the value decreased to approximately 474.6 W/m² and it appears that despite being very efficient initially, its ability to retain radiative stability over long range. Papilioxuthus model: This model made marginally lower peak radiosity 514.5 W/m² at x = 1.5 m than Kaniskacanace, however, had a smoother drop pattern. radiosity at x = 6 m was approximately 475.7 W/m² slightly greater than Kaniskacanace. This implies better thermal stability over distances, which is explained by

Figure 16. Surface radiosity-time curve chart of bionic model.

better light-trapping microstructures. Papiliomaackii model: This model provided the most consistent radiosity profile with the maximum of 515.8 W/m² and comparatively high performance throughout the whole distance range. Radiosity even at x = 6 m was 470.7 W/m², with a slower rate of decrease than in the conventional model. This indicates that Papiliomaackii’s surface morphology optimizes both absorption and redistribution of incident radiation.