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application of Differential Transform Approaches namely Two Dimensional Differential
Transform Method (TDDTM), Reduced Differential Transform Method (RDTM), Hybrid
Differential Transform Finite Difference Method (HDTFDM) and multistep HDTFDM to
solve real life problems. The real-life problems studied are the Dispersion phenomenon,
Groundwater Recharge phenomenon, Infiltration phenomenon, Imbibition phenomenon
namely countercurrent, co current, fingering, fingero-imbibition in both homogeneous and
heterogeneous porous media with inclination and magnetic field.Using these three
Differential transform approaches an approximate solution of the counter -current
imbibition phenomenon, co-current imbibition phenomenon, instability phenomenon and
fingero-imbibition phenomenon in homogeneous and heterogeneous porous media with
inclination and magnetic field effect which occur during the secondary oil recovery is
discussed in this thesis. The technique involves calculating the differential coefficients in
an iterative manner which reduces the computational work to a great extent but at the
same time produces approximate convergent solutions which are in close agreement
with existing solutions and are also in total agreement with the physical situation.All three
Differential Transform Approaches were applied to two real problems of dispersion and
fingero-imbibition phenomenon. The results obtained by all three methods were analysed
and compared

Key words: Counter-current imbibition, Co-current imbibition, Instability phenomenon,
Finger-Imbibition phenomenon, homogeneous and heterogeneous porous media,
Differential Transform Method, Two-Dimensional Differential Transform Method
(TDDTM), Reduced Differential Transform Method (RDTM), Hybrid Differential Transform
Finite Difference Method (HDTFDM) and multistep HDTFDM.

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