Temperature-dependent thermal diffusivity of cupuassu pulp: Mathematical modeling and experimental validation

Cupuassu ( Theobroma grandiflorum ) is a fruit native to the Amazon, whose pulp is the most economically valuable product due to its unique sensory and nutritional properties. Knowledge of its thermophysical properties, particularly thermal diffusivity, is essential for designing effective heat treatments. The objective of this study was to determine the thermal diffusivity of cupuassu pulp from experimental data using an inverse method. Experiments were conducted by heating the pulp in an aluminum capsule from 10 °C to 80 °C in a thermostatic water bath, with a thermocouple positioned at the center of the sample. The Biot number of heating process exceeded 50, indicating dominant internal conductive resistance and justifying the adoption of a first-kind (Dirichlet) boundary condition in the two-dimensional transient heat conduction model. Thermal diffusivity ( α ) was estimated by solving the model using the finite difference method and fitting the predicted temperatures to the experimental data through Root Mean Square Error ( RMSE ) minimization via an exhaustive parameter search. To avoid solving a nonlinear partial differential equation, α was treated as locally constant within each time step and iteratively updated based on the temperature field from the previous time step. Four models were evaluated to describe the temperature dependence of the diffusivity: constant, square-root, linear, and power-law. Temperature-dependent models provided superior predictive performance, with the power-law model: α ( T ) = A + BT 3/2 , yielding the best fit ( RMSE ≈ 0.1 °C) and randomly distributed residuals. In addition, the α model was validated using two independent datasets, confirming its robustness for predicting heat transfer during thermal processing of cupuassu pulp.