Active boundary heating and cooling can make a small object look much larger to thermal sensors, a step toward compact thermal camouflage and new ways to steer heat in devices.
(Nanowerk Spotlight) Heat does not travel like light. It does not form coherent beams, and it resists the wave-based manipulations that allow for compact optical devices. Because heat spreads by diffusion, it tends to wash out specific temperature patterns, forcing engineers to rely on thick insulation or heavy heat spreaders to control thermal signatures. These bulky solutions, however, are increasingly incompatible with demands for compact, flexible thermal management. That limitation matters because thermal signatures sit at the center of problems ranging from electronics cooling to energy harvesting and infrared detection.
Engineers can already manipulate steady heat flow with carefully patterned materials, but these methods typically falter when designers want a small object to appear, thermally, like a much larger one. The mathematics behind this effect (known as superscattering) demands a shell with negative thermal conductivity, a property that would paradoxically push heat from cold regions to hot ones without external work. Since no passive material behaves that way, researchers have turned to an active solution: replacing the impossible material with a ring of controllable heating and cooling elements that effectively “fake” the thermal signature of a massive object.
To get past that impasse, researchers have developed a design field that treats heat flow as something that can be engineered with the same deliberate control used in other wave and field technologies. Thermotics is the study of how heat moves through materials and how design can shape that motion. Transformation thermotics applies a specific mathematical tool to that problem. It uses coordinate transformations, a method that remaps space in equations, to prescribe how a material or shell should guide heat diffusion. Instead of changing the object, the designer changes the surrounding pathway for heat. The aim is to make the temperature field outside the shell match the field of a different, virtual object with a different size or shape.
In the superscattering case, the math says a small scatterer wrapped in an engineered shell can disturb external heat flow as strongly as a far larger object. The same math, however, drives part of the shell into an unphysical regime. It requires negative thermal conductivity in part of the shell, which blocks a passive implementation.
A study published in Advanced Science (“Active Thermal Metasurfaces Enable Superscattering of Thermal Signatures Across Arbitrary Shapes and Thermal Conductivities”) reports a workaround that replaces that requirement with active control. The paper uses active thermal metasurfaces (ATMs), meaning arrays of controllable heating and cooling elements placed along a boundary. By programming these elements to inject or extract heat in the spatial pattern dictated by the design equations, the device reproduces the external temperature field that the negative-conductivity shell would have produced, without requiring impossible materials.
Schematic diagram of the thermal superscatterer. a) A small thermal object (indicated by a small green man) with thermal conductivity 𝜅1 in a uniform background thermally conducting medium with thermal conductivity 𝜅b functions as the original thermal scatterer. b) The original thermal scatterer is covered by NTCS (the red shell) in the same background thermally conducting medium, resulting in thermal superscattering. c) The original thermal scatterer is surrounded by ATMs in the same background thermally conducting medium, also resulting in thermal superscattering. d) An enlarged thermal scatterer (indicated by a large blue woman) with thermal conductivity 𝜅a in the same background thermally conducting medium can produce the same thermal scattering signature (i.e., the same temperature distribution and heat flux distribution) as the region outside the dashed lines in (b,c). The red arrows indicate the direction of the heat flux, and the gray dashed lines in (b, c) serve as an equivalent thermal scattering cross-section for comparison. (Image: Reproduced from DOI:10.1002/advs.202519386, CC BY)
The paper frames the goal as thermal superscattering. Here, “scattering” describes how an inclusion disturbs the surrounding temperature field and heat flux, the flow of heat per unit area. A superscatterer does more than exaggerate the signature of a small object. It makes a compact object plus shell match the external thermal field of a larger virtual object, even when that virtual object extends beyond the physical footprint of the device.
To reach that goal, the authors start from a reference problem. In the reference space, a large target scatterer with thermal conductivity κₐ sits inside a background medium with thermal conductivity κ_b. In the physical device, a smaller object of arbitrary shape and conductivity sits inside a designed shell. A coordinate transformation links the two descriptions and forces the temperature distribution and heat flux outside a chosen boundary to match the reference case. The mapping also ties together three boundaries through the relation ρ₁ρ₃ = ρ₂², where ρ₁(θ) describes the inner boundary, ρ₂(θ) the shell boundary, and ρ₃(θ) the virtual enlarged boundary.
When the authors work through the transformation, they find that the shell generally needs anisotropic thermal conductivity, meaning it must conduct heat differently along different directions. The shell properties can also vary with position. Most importantly, the shell region that delivers superscattering carries an effective negative thermal conductivity in the transformation solution. That mathematical sign produces the correct field outside the device, but passive materials cannot supply it.
The paper’s central move replaces that negative shell with a combination that a laboratory can build. The authors use a positive-conductivity shell and add a boundary heat source distribution to supply the missing behavior. In the paper’s formulation, the device imposes a boundary heat-flux intensity q_s that relates to the normal heat flux q_n through q_s = −2q_n, using a sign convention for inward flux. This active boundary does not violate thermodynamics because the boundary elements draw electrical power to move heat. They act as distributed heat sources and sinks, not as a passive material that mysteriously drives heat uphill.
The authors also describe design cases that simplify the required parameters. One case uses conformal shapes, where the small and virtual enlarged objects share the same outline up to scaling. Under that condition, the transformation keeps the inner object conductivity equal to the target conductivity, κ₁ = κₐ, and the shell design depends mainly on the background and the chosen boundaries. The paper discusses three illusion types in this framework. A super-insulating case uses κₐ = 0 to make a small thermally blocked region behave like a much larger insulator. A super-conducting case uses κₐ = 1000κ_b to make a compact highly conducting inclusion act like a larger heat-funneling region. An equivalent thermal transparency case sets κₐ = κ_b so the exterior field matches the background, even though the interior field can still change.
A second simplifying case fixes the shell boundary to a circle, ρ₂(θ) = const, which removes angular terms and reduces the shell requirement to κ₂ = −κ_b. That choice keeps the core obstacle, the negative sign, but it clarifies how an active boundary can replace it in a symmetric geometry. The paper uses this setup to show, through calculations and simulations, that the approach can also reshape apparent geometry, not just apparent size.
The experimental demonstration focuses on the super-insulating mode with circular symmetry. The device uses 10 semiconductor thermoelectric modules arranged on a ring. Thermoelectric modules can pump heat in either direction depending on current polarity, so they provide controllable heating and cooling at discrete locations. The ring sits at R₂ = 30 mm and surrounds a central insulated disk at R₁ = 10 mm. To implement the required boundary heat source, the authors discretize the ideal continuous boundary into M = 10 segments, corresponding to Δθ = 36° spacing, and assign one module to each segment.
The testbed uses a copper sheet as the background conducting medium. Water baths set the ends of the sheet at 320 K and 287 K, which establishes a steady thermal gradient across the measurement region. The paper reports boundary temperatures near the detection area around 307 K and 297 K, with the room environment at T_room = 300.65 K. The setup uses insulation to reduce convective effects, then measures the surface temperature with an infrared camera after the system reaches steady state, reported after a 30 s settling period.
The key question is simple. Does the small insulated region, when paired with the active ring, produce the same external thermal signature as a much larger insulator? The paper compares four cases. An intact copper sheet shows nearly uniform temperature gradients. A small insulated region at R₁ = 10 mm only slightly perturbs that gradient. A large insulated region at R₃ = 90 mm produces a much stronger distortion of the isotherms, the lines of equal temperature. When the authors drive the ring modules to enforce the boundary heat-flux pattern predicted by the model, the measured temperature field resembles the R₃ = 90 mm case, even though the physical insulated core remains R₁ = 10 mm and the active elements sit at R₂ = 30 mm.
The paper characterizes this as a ninefold increase in apparent radius, comparing R₃ = 90 mm to R₁ = 10 mm. For a circular region, that scale factor implies 81 times the area. The result illustrates the paper’s definition of superscattering. The thermal disturbance extends beyond the size of the object and beyond the footprint of the active shell.
Finite-element simulations support both the design and the interpretation. The authors use simulations to compute the target boundary heat-flux distribution, evaluate discretization into a limited number of modules, and compare predicted temperature fields to measured ones. Additional simulations apply the same framework to noncircular geometries to show that the equations handle arbitrary shapes in principle when the transformation and boundary control follow the required prescriptions.
The work’s significance comes from what it replaces. Transformation thermotics can specify field-matching shells, but superscattering designs run into negative-conductivity requirements that block passive fabrication. This paper shows that an active thermal metasurface can supply the missing behavior by injecting and extracting heat along a boundary to enforce the field outside.
The paper also makes the trade-offs explicit. Stronger apparent amplification demands greater boundary heat flux, which raises power consumption and heat dissipation demands at the active elements. Within those engineering limits, the approach widens the design space for controlling how objects appear to steady heat flow, independent of their true size.
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