Analysis of transient heat conduction in tubes under convective boundary conditions

In this work, six analytical solutions are given to estimate the energy exchange by transient conduction in pipes with convection conditions. The developed models were adjusted for an interval RI/ RE from 0.2 to 0.8, dimensionless Fourier (Fo) and Biot (Bi) numbers, from 0.05 to 50 and 0.005 to 50, respectively. In each case, 616 tests of temperature distributions were computed using the Heisler approximate method (HAM) and the exact models proposed, for different combinations of R-I/R-E, Bi, and Fo. For the comparison made between the analytical solutions and the HAM, 3696 tests were used, detecting that the HAM correlates with the analytical method with an average deviation of +/- 10% and +/- 20% for 71.2%, and 90.4% of the different values of RI/RE, Fo, and Bi combinations evaluated. The best fit was found for Case 5, with a mean deviation of +/- 10% and +/- 20% for 81.1% and 92.3% of the data used, respectively, while the weaker fit was detected for Case 2, with a mean deviation of +/- 10% and +/- 20% for 67.9% and 88.2% of the available tests.