2-Naphthol reacted with 3-dicyanomethylidine-1-ethyl-2-oxoindoline in absolute ethanol to afford 2-Amino-3-cyano-1'-ethylspiro{benzo[f]chromen-4,3'-indolin}-2'-one, which used as key intermediate to synthesis fused spiropolyheterocyclic derivatives of pyrimido- benzochromen and/or pyridobenzochromen nucleus incorporated indoline moiety.

2-Naphthol reacted with 3-dicyanomethylidine-1-ethyl-2-oxoindoline in absolute ethanol to afford 2-Amino-3-cyano-1'-ethylspiro{benzo[f]chromen-4,3'-indolin}-2'-one, which used as key intermediate to synthesis fused spiropolyheterocyclic derivatives of pyrimido- benzochromen and/or pyridobenzochromen nucleus incorporated indoline moiety.

We study a steady laminar 2-D MHD viscous incompressible flow over a permeable wedge with convective boundary condition and radiation effects. The viscosity of fluid and it’s thermal conductivity is assumed to vary linearly with temperature. Similarity representation of the partial differential equations governing the problem is obtained via group method. Effects of convective heat transfer parameter b, radiation parameter R, thermal conductivity parameter S, on the velocity, temperature, concentration, wall temperature, rate of heat transfer and rate of mass transfer are investigated

The present paper investigates heat and mass transfer over a moving porous plate with hydrodynamic slip and thermal convective boundary conditions and concentration dependent diffusivity. The similarity representation of the system of partial differential equations of the problem is obtained through Lie group analysis. The resulting equations are solved numerically by Maple with Runge-Kutta-Fehlberg fourth-fifth order method. A representative set of results for the physical problem is displayed to illustrate the influence of parameters (velocity slip parameter, convective heat transfer parameter, concentration diffusivity parameter, Prandtl number and Schmidt number) on the dimensionless axial velocity, temperature and concentration field as well as the wall shear stress, the rate of heat transfer and the rate of mass transfer. The analytical solutions for velocity and temperature are obtained. Very good agreements are found between the analytical and numerical results of the present paper with published results.

The purpose of the present work is to construct new geometrical models for motion of plane curve by Dar-boux transformations. We get nonlinear partial differential equations (PDE). We have obtained the exact so-lutions of the resulting equations using symmetry groups method. Also, the Gaussian and mean curvatures of Monge form of the soliton surfaces have been calculated and discussed.