The boundary conditions for the above mathematical model are given as
\[u=u_w\left(x\right)=cx,v(x)=0,T=T_w\ \ \ \ \ \ \ at\ \ \ \ \ y=0\ \ \ \]
\[u\to 0, \ T\to T_\infty\ \ as\ \ \ \ \ y\to\infty\]
Here, fluid density is \(\rho_\infty\), \(k\) is the thermal conductivity, \(B_0\) is the uniform magnetic field, \(\mu\)dynamic viscosity, \(g\) is the acceleration due to gravity, \(B^*, \ \sigma,\ \mu_0, \ c_p\) represents the thermal expansion coefficient, electrical conductivity of the fluid, magnetic permeability and specific heat at constant pressure, respectively. Also, \(M\) indicates magnetization, \(H\) symbolizes as magnetic field of strength. The term \(\mu_0M\frac{\delta H}{\delta x}\)in equation (2) denote the component of ferromagnetic body force per unit volume and rely on the existence of magnetic gradient. The second term of equation (3) in left hand side i.e. \(\mu_{0\ \ }T\ \left(\frac{\delta M}{\delta T}\right)\left(u\frac{\delta H}{\delta x}+v\frac{\delta H}{\delta y}\right)\)presents the adiabatic heat due to magnetization.