where Ec is the Eckert number, Pr is the Prandtl number, Sc is the Schmidt number, Sr is the Soret number, Du is the Dufour number, M is the Magnetic field parameter, Gr is the thermal Grashof number, Gc is the Solutal Grashof number, k is the porous parameter, [b.sub.1] is the joule-heating parameter, [lambda] is the variable thermal conductivity, and [gamma] is the variable suction parameter while u and v are dimensionless velocity components in x- and y-directions, respectively, and t is the dimensionless time.

Figures 11(a) and 11(b) graphically show the influence of Dufour number Du on the velocity and temperature profiles, respectively.

(1) Velocity profiles increased due to increase in thermal Grashof number, solutal Grashof number, porous parameter, Eckert number, Soret number, Dufour number, and dimensionless time while it decreased due to increase in magnetic parameter and suction parameter.

where M = [C.sub.f]([T.sub.[infinity]] - [T.sub.m])/(1 + [C.sub.s]([T.sub.m] - [T.sub.s])) is the melting parameter, Le = [alpha]/D is the Lewis number, Df = [D.sub.1][DELTA]C/[alpha][DELTA]T is the Dufour number, and Sr = [D.sub.2][DELTA]T/[alpha][DELTA]C is the Soret number.

The Dufour number and Soret number are chosen in such a way that their product is constant according to definition provided that the mean temperature [T.sub.m] is kept constant (Kafoussias and Williams [30]).

Du = ([D.sub.m][K.sub.t][DELTA][ca.sup.2]/[C.sub.s][C.sub.p][DELTA]T][lambda]) (

Dufour Number)

Du = ([D.sub.m][K.sub.t][DELTA]c[a.sup.2]/[C.sub.s][C.sub.p][DELTA]T[lambda]) (

Dufour Number)

Permeability parameter, Sr = [D.sub.m][k.sub.T] ([T.sub.0] - [T.sub.[infinity]]) / [T.sub.m][upsilon]([C.sub.0] - [C.sub.[infinity]]) is the Soret number, Df = [D.sub.m][k.sub.T]([C.sub.0] - [C.sub.[infinity]]) / [c.sub.s][c.sub.p] [upsilon]([T.sub.0] - [T.sub.[infinity]]) is the Dufour number, Gr = g[beta]([T.sub.0] - [T.sub.[infinity]]) [[sigma].sup.2.sub.0] / [upsilon][U.sub.0] is the local Grashof number and Gm = g[[beta].sup.*] ([C.sub.0] - [C.sub.[infinity]]) [[sigma].sup.2.sub.0] / [upsilon][U.sub.0] is the local modified Grashof number.

The values of Dufour number (Df) and Soret number (Sr) are chosen in such a way that their product is constant provided that the mean temperature [T.sub.m] is kept constant as well.

The effects of various physical parameters like the Prandtl number, the mass transfer parameter, the wall shrinking parameter, the permeability parameter, Dufour number, and Soret number on the temperature and concentration profiles are obtained.

where K =(v/k'a) is the permeability parameter, Pr is the Prandtl number of the fluid with Pr = v/[sigma], [D.sub,f] = ([D.sub.m][k.sub.T] ([C.sub.w] - [C.sub.[infinity]])/[c.sub.s][c.sub.p] v([T.sub.w] - [T.sub.[infinity]]) is the Dufour number, Sc = (v/[D.sub.m]) is the Schmidt number, Sr = ([D.sub.m][k.sub.T]([T.sub.w] - [T.sub.[infinity]]) /v[T.sub.m]([C.sub.w] - [C.sub.[infinity]]) is the Soret number, and is the mass transfer parameter showing the strength of the mass transfer at the sheet.

Aly, "Effects of chemical reaction and thermal stratification on MHD free convective heat and mass transfer over a vertical stretching surface embedded in a porous media considering Soret and

Dufour numbers," Chemical Engineering Journal, vol.