Inverse Heat Transfer Techniques and Thermal Analysis

Inverse heat transfer techniques address the retrieval of unknown thermal boundary conditions and material properties by interrogating observable responses such as surface temperature or radiative flux. This class of problems is intrinsically ill-posed: small measurement errors can engender large deviations in the reconstructed solution. To overcome this, regularisation strategies are routinely integrated into optimisation frameworks, constraining the solution space and stabilising the inversion. Forward models of heat conduction or coupled radiation–conduction phenomena are solved numerically—commonly via finite difference, finite element or boundary element methods—to generate temperature or flux predictions, which are then compared against experimental data. Sensitivity analysis informs the design of measurement schemes, while advanced control-inspired algorithms such as model predictive control have been adapted to furnish time-varying boundary estimates. Recent advances have emphasised hybrid approaches that combine stochastic or nature-inspired optimisers with physics-based solvers, facilitating the simultaneous recovery of multiple temperature-dependent properties in complex media. The global significance of these methods spans aerospace engine component testing, additive manufacturing thermal monitoring and biomedical hyperthermia treatment planning, underscoring their wide-ranging practical and industrial impact.

Research from Nature Portfolio

A foundational study demonstrated the joint estimation of temperature-dependent thermal conductivity and optical absorption in a semi-transparent slab by coupling radiative and conductive forward models. The authors applied a stochastic particle swarm optimisation to an inverse framework, exploiting distinct sensitivities of temperature response to conductivity and of radiative intensity to optical properties. By integrating both thermal and radiative measurements at the slab boundary, the technique achieved accurate recovery of both property profiles, establishing a benchmark for multi-signal inverse reconstruction in participating media.

Inverse Heat Transfer Techniques and Thermal Analysis publication trend

The graph below shows the total number of articles in inverse heat transfer techniques and thermal analysis across all publications each year (not limited to Nature Index journals).

Technical terms

Inverse Heat Conduction Problem (IHCP): The challenge of inferring unknown boundary conditions or internal thermal properties from measured temperature or flux data.

Regularisation: A stabilisation technique that imposes smoothness or boundedness constraints on the inversion to mitigate the effects of measurement noise and ill-posedness.

Sensitivity coefficient: A derivative quantifying how a change in a model parameter (for example, thermal conductivity) affects the predicted temperature or flux, used to optimise sensor placement and inversion stability.

Model Predictive Control (MPC): A dynamic optimisation approach that uses a forward heat conduction model to predict future system behaviour and adjust boundary estimates iteratively to minimise discrepancies with measured data.

Boundary Element Method (BEM): A numerical technique for forward heat conduction problems that formulates the solution in terms of boundary integrals, reducing the dimensionality of the discretisation.

References

1. Simultaneous retrieval of temperature-dependent absorption coefficient and conductivity of participating media. Scientific Reports (2016).
2. Solving of Two‐Dimensional Unsteady‐State Heat‐Transfer Inverse Problem Using Finite Difference Method and Model Prediction Control Method. Complexity (2019).
3. Inverse determination of sliding surface temperature based on measurements by thermocouples with account of their thermal inertia. Tribology International (2021).