Dual-face unilateral Laplace-transform formulation for estimating thermal diffusivity and the Biot number in finite-pulse laser-flash analysis with front-face heat loss

In this work, we develop a dual-face unilateral Laplace-domain formulation for finite-pulse laser-flash analysis under front-face heat loss. The specimen is modelled as a homogeneous one-dimensional slab heated by an exponentially decaying surface pulse, with linear heat exchange at the irradiated face and an insulated rear face. In the transformed domain, the front- and rear-face responses share the same pulse factor, temperature scale, diffusion-time prefactor, and heat-loss denominator. Their ratio cancels these common terms and isolates the through-thickness diffusion variable, yielding explicit multipoint formulas for the thermal diffusivity α , front-face Biot number B i , and adiabatic-limit temperature T S , including a self-calibrating route when the absorbed energy is unknown. Matched-model Monte Carlo simulations show that α is the best-conditioned quantity. At 5% noise, its bias is about −0.14%, its root-mean-square error (RMSE) is 1.44%, and 99.7% of estimates lie within ± 5 % . A finite-window late-time integral benchmark gives larger diffusivity RMSEs, reaching 7.88% at 5% noise, although its B i estimate is more accurate at the highest noise level. A two-dimensional axisymmetric forward model assesses model discrepancy from rear and lateral heat losses and uniform finite-depth energy deposition. Rear and lateral losses bias α downward, whereas finite-depth deposition produces the opposite effect. For a representative combined perturbation in which the rear-loss Biot number, the lateral-loss Biot number, and the normalized deposition depth are each set to 0.01, the diffusivity bias is about −2.23% and the RMSE about 2.26% at 2% noise, while the recovered front-face Biot number is more sensitive to model mismatch. Overall, the formulation provides an interpretable route for dual-face laser-flash data reduction with quantified noise sensitivity and limits of validity.