Transient heat conduction in tubes: dimensionless temperature profile under convective boundary conditions

In this work three analytical solutions were developed for calculating transient conduction energy transfer in tubes, considering convection boundary conditions. For each configuration, 412 temperature distributions were calculated using both the approximate Heisler method (AHM) and the exact analytical models, employing different combinations of the , Bi, and Fo parameters. The models were calibrated for a range of inner-to-outer radius ratios between 0.2 and 0.8, and for Fourier (Fo) and Biot (Bi) numbers ranging from 0.05 to 50 and 0.005 to 50, respectively.. Comparative evaluation, based on 1972 computational simulations, revealed that the AHM method agrees with the analytical solutions in a interval range of ±10% and ±20% of deviation in the 71.3% and 91.2% of the combinations computed, respectively. Among the cases evaluated, Case 2 showed the best degree of agreement, with mean deviations of ±10% and ±20% in 87.4% and 97.5% of the data, respectively. Conversely, Case 3 presented the weaker fit, reaching those same deviation ranges for 68.3% and 91.2% of the data used. At the individual parameter level, the provided the optimal fit in Case 1, with 89.4% and 98.1% of the data within the margins of ±10% and ±20%, respectively. While, the weaker fit was found for in Case 1, with 41.3% and 75.8%, of the data within the margins of ±10% and ±20%, respectively.