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46<br />
Journal of Science and Technology in the Tropics<br />
where δ = ( E + H ) /( F + 2 G)<br />
and Now, equating the<br />
2<br />
3<br />
coefficients of ε from Eqs. (11) and (12), and the coefficients of ε from Eqs.<br />
(9) and (10), we obtain:<br />
(23)<br />
(24)<br />
and<br />
(25)<br />
(26)<br />
where<br />
(2) (2) (2)<br />
From the set of Eqs. (23) - (26) for N , U , Φ along with another set of<br />
(1) (1) (1)<br />
Eqs. (19) - (21) for N , U , Φ , we can easily derive the following nonlinear<br />
dynamical equation:<br />
(27)<br />
where<br />
and<br />
are respectively the nonlinear coefficient and dissipative coefficient of Eq. (27).<br />
(1)<br />
Equation (27) is the well-known modified Burger equation. The term ( ν / 2 τ ) Φ<br />
in Eq. (27) is due to the effect of non-planar geometry [41, 42].<br />
NUMERICAL SOLUTION OF THE MODIFIED BURGER’S EQUATION<br />
AND GRAPHICAL REPRESENTATION<br />
As mentioned earlier the one-dimensional planar case ( ν = 0) has already been<br />
studied by Paul et al. [38]. In this case, we introduced ζ = ξ − U0τ ′ and τ ′ = τ ,
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