Table 5: Comparison of our analytical expression of concentration profiles with numerical results and Villa et al. [1] results corresponding to Case 3, for , and , when and .

Dimensionless spatial coordinate
0.00.250.50.751.00

1.990.4y(z) Numerical0.0000000.0537700.0920210.1149230.122500
Analytical (25)0.0000000.0531680.0901540.1101790.119763
(error %)(0.0000)(1.1195)(2.0288)(4.0102)(2.2342)
Villa et al. [1] ( )0.0000000.0136570.0234100.0292600.031210
(error %)(0.0000)(74.6010)(74.5601)(74.5394)(74.5224)
1.00.2y(z) Numerical0.0000000.0499700.0850700.1059000.112800
Analytical (25)0.0000000.0496300.0844420.1050650.108007
(error %)(0.0000)(0.6804)(0.7640)(0.7884)(4.2491)
Villa et al. [1]0.0000000.0133580.0228620.0285490.030442
(error %)(0.0000)(73.2679)(73.1256)(73.0415)(73.0124)
0.50.1y(z) Numerical0.0000000.0483000.0820100.1019000.108500
Analytical (25)0.0000000.0480780.0816320.1014520.108007
(error %)(0.0000)(0.4596)(0.4609)(0.4396)(0.4543)
Villa et al. [1]0.0000000.0132160.0226010.0282100.030076
(error %)(0.0000)(72.6376)(72.7766)(72.3159)(72.2801)
0.250.05y(z) Numerical0.0000000.0475100.0805800.1001000.106500
Analytical (25)0.0000000.0468590.0794200.0986040.104941
(error %)(0.0000)(1.3702)(1.4395)(1.4945)(1.4638)
Villa et al. [1]0.0000000.0131460.0224730.0280440.029897
(error %)(0.0000)(72.3300)(72.1109)(71.9840)(71.9276)
0.10.02y(z) Numerical0.0000000.0470600.0797500.0990100.105400
Analytical (25)0.0000000.0468590.0794200.0986040.104941
(error %)(0.0000)(0.4271)(0.4137)(0.4100)(0.4354)
Villa et al. [1]0.0000000.0131040.0223970.0279460.029791
(error %)(0.0000)(72.1546)(71.9159)(71.7745)(72.3531)
0.010.002y(z) Numerical0.0000000.0467900.0792600.0983800.104700
Analytical (25)0.0000000.0465880.0789290.0979710.104259
(error %)(0.0000)(0.4317)(0.41756)(0.4157)(0.4212)
Villa et al. [1]0.0000000.0130800.0223520.0278870.029727
(0.0000)(72.0453)(71.7991)(71.6537)(71.6074)
0.0010.0002y(z) Numerical0.0000000.0467600.0792100.0983200.104600
Analytical (25)0.0000000.0465610.0788800.0979070.104191
(error %)(0.0000)(0.4255)(0.4166)(0.4200)(0.3910)
Villa et al. [1]0.0000000.0130770.0223470.0278810.029721
(error %)(0.0000)(72.0337)(71.7876)(71.6425)(71.5860)