Table 3: Comparison of our analytical expression of concentration profiles with numerical results and Villa et al. [1] results corresponding to Case 2, for , and , when and .

Dimensionless spatial coordinate
0.00.250.50.751.00

20.4 Numerical0.0000000.0595100.1026000.1286000.137400
Analytical (20)0.0000000.0583070.1002710.1255350.133966
Villa et al. [1]0.0000000.0596540.1028250.1289380.137675
1.010.2 Numerical0.0000000.0543800.0931600.1164000.124100
Analytical (20)0.0000000.0550770.0931820.1166170.123772
Villa et al. [1] ( )0.0000000.0543160.0930420.1162410.123967
0.50.1 Numerical0.0000000.0521600.0891000.1111000.118400
Analytical (20)0.0000000.0520360.888690.1108290.118125
Villa et al. [1]0.0000000.0520900.0889710.1109660.118275
0.250.05 Numerical0.0000000.0511600.0872600.1087000.115900
Analytical (20)0.0000000.0510520.0870750.1085100.115625
Villa et al. [1]0.0000000.0510650.0870990.1085420.115660
0.10.02 Numerical0.0000000.0505900.0862100.1074000.114400
Analytical (20)0.0000000.0504740.0860190.1071440.114151
Villa et al. [1]0.0000000.0504760.0860230.1071490.114157
0.010.002 Numerical0.0000000.0502500.0855900.1066000.113500
Analytical (20)0.0000000.0501300.0853930.1063330.113278
Villa et al. [1]0.0000000.0501300.0853930.1063330.113278
0.0010.0002 Numerical0.0000000.0502200.0855300.1065000.113500
Analytical (20)0.0000000.0500960.0853300.1062530.113191
Villa et al. [1]0.0000000.0500960.0853300.1062530.113191