International Scholarly Research Notices / 2013 / Article / Tab 5 / Research Article
Analytical Solution of Non-Isothermal Diffusion-Reaction Processes and Effectiveness Factors 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
0.0 0.25 0.5 0.75 1.00 1.99 0.4 y(z) Numerical 0.000000 0.053770 0.092021 0.114923 0.122500 Analytical (25 ) 0.000000 0.053168 0.090154 0.110179 0.119763 (error %) (0.0000) (1.1195) (2.0288) (4.0102) (2.2342) Villa et al. [1 ] (
) 0.000000 0.013657 0.023410 0.029260 0.031210 (error %) (0.0000) (74.6010) (74.5601) (74.5394) (74.5224) 1.0 0.2 y(z) Numerical 0.000000 0.049970 0.085070 0.105900 0.112800 Analytical (25 ) 0.000000 0.049630 0.084442 0.105065 0.108007 (error %) (0.0000) (0.6804) (0.7640) (0.7884) (4.2491) Villa et al. [1 ] 0.000000 0.013358 0.022862 0.028549 0.030442 (error %) (0.0000) (73.2679) (73.1256) (73.0415) (73.0124) 0.5 0.1 y(z) Numerical 0.000000 0.048300 0.082010 0.101900 0.108500 Analytical (25 ) 0.000000 0.048078 0.081632 0.101452 0.108007 (error %) (0.0000) (0.4596) (0.4609) (0.4396) (0.4543) Villa et al. [1 ] 0.000000 0.013216 0.022601 0.028210 0.030076 (error %) (0.0000) (72.6376) (72.7766) (72.3159) (72.2801) 0.25 0.05 y(z) Numerical 0.000000 0.047510 0.080580 0.100100 0.106500 Analytical (25 ) 0.000000 0.046859 0.079420 0.098604 0.104941 (error %) (0.0000) (1.3702) (1.4395) (1.4945) (1.4638) Villa et al. [1 ] 0.000000 0.013146 0.022473 0.028044 0.029897 (error %) (0.0000) (72.3300) (72.1109) (71.9840) (71.9276) 0.1 0.02 y(z) Numerical 0.000000 0.047060 0.079750 0.099010 0.105400 Analytical (25 ) 0.000000 0.046859 0.079420 0.098604 0.104941 (error %) (0.0000) (0.4271) (0.4137) (0.4100) (0.4354) Villa et al. [1 ] 0.000000 0.013104 0.022397 0.027946 0.029791 (error %) (0.0000) (72.1546) (71.9159) (71.7745) (72.3531) 0.01 0.002 y(z) Numerical 0.000000 0.046790 0.079260 0.098380 0.104700 Analytical (25 ) 0.000000 0.046588 0.078929 0.097971 0.104259 (error %) (0.0000) (0.4317) (0.41756) (0.4157) (0.4212) Villa et al. [1 ] 0.000000 0.013080 0.022352 0.027887 0.029727 (0.0000) (72.0453) (71.7991) (71.6537) (71.6074) 0.001 0.0002 y(z) Numerical 0.000000 0.046760 0.079210 0.098320 0.104600 Analytical (25 ) 0.000000 0.046561 0.078880 0.097907 0.104191 (error %) (0.0000) (0.4255) (0.4166) (0.4200) (0.3910) Villa et al. [1 ] 0.000000 0.013077 0.022347 0.027881 0.029721 (error %) (0.0000) (72.0337) (71.7876) (71.6425) (71.5860)
