Table 1 A summarizing list of the pertinent parameters with their significance.

Magnetic parameter

\(M_{1}\)

\(\frac{{\sigma_{f} B_{0}^{2} }}{\rho C}\)

Prandtl number

\(\Pr\)

\(\frac{{xu_{w} }}{\alpha }{\text{Re}}_{n}^{{\frac{ - 2}{{j + 1}}}}\)

Sisk-fluid parameter

\(\Lambda\)

\(\Lambda = \frac{{{\text{Re}}_{n}^{{\frac{2}{j + 1}}} }}{{{\text{Re}}_{m} }}\)

Thermophoresis parameter

\(N_{Th} (or\,Nt)\)

\(\frac{{\tau D_{Th} \left( {T_{w} - T_{\infty } } \right)}}{{\upsilon_{{}} T_{\infty } }}\)

Brownian motion parameter

\(N_{Br} \,(or\,Nb)\)

\(\frac{{ \tau D_{Br} C_{\infty } }}{\upsilon }\)

Lewis number

Le

\(\frac{\alpha }{{D_{Br} }}\)

Forchheimer number

Fr

\(\frac{{C_{b} }}{\sqrt K }\)

Porosity parameter

\(\lambda\)

\(\frac{\upsilon }{\varepsilon K}\)

Radiation parameter

\(Rd\)

\(\frac{{16\sigma *T_{\infty }^{3} }}{3kk*}\)

Local Reynolds number

\({\text{Re}}_{m}\)

\(\frac{{\rho xu_{w} }}{m}\)