Analytical modelling of transient conduction heat transfer in tubes for industrial applications

In this work, analytical solutions for six different contour conditions are given to calculate the heat transfer by unsteady conduction in pipes with convection. The analytical models are valid for a diameter ratio \({R}_{\text{I}}/{R}_{\text{E}}\) from 0.1 to 0.9, dimensionless Biot (Bi) and Fourier (Fo) numbers, from 0.001 to 50 and 0.01 to 50, respectively. In determining the analytical solutions, the cylindrical functions of Bessel and Neumann were implemented. Using 864 combination values\({R}_{\text{I}}/{R}_{\text{E}} ;Bi ;Fo\), the dimensionless temperature distributions were calculated using the corresponding analytical solution and Heisler’s approximate method (HAM). In the comparison made between the analytical solutions and HAM, was verified in 5184 tests carried out that the HAM correlates with the analytical solutions on average, finding an average deviation of ± 10% and ± 20% for 73.2% and 92.1% of the points evaluated. The best fit was found for Case 5, with a mean deviation of ± 10% and ± 20% for 80.2% and 95.5% of the data used, respectively, while the weaker fit was detected for the Case 2 with a mean deviation of ± 10% and ± 20% for 69.7% and 89.8% of the data used.