A computational model has been developed to simulate the axial dispersion phenomena in laminar pipe flows. Peclet number (Pe = au(0)/D-m) and dimensionless time (tau = D(m)t/a(2)) have been covered over a wide range of 1-10(5) and 10(-8) to 10(2), respectively. An extensive comparison of predicted mean concentration profiles with the experimental data has been presented. The proposed computational model for concentration profiles was found to give an excellent agreement with the experimental measurements. Further, the results compare well with other analytical and experimental studies. The solution has been shown to be valid at both the short and long times and for all values of the Peeler number. (C) 2004 Elsevier Ltd. All rights reserved.