The components of velocity in \(u\) and v in the direction
of \(s-\) and \(r-\) respectively. The \(R\), \(\rho\), \(\nu\),\(\alpha\), \(\tau\), \(c_{p}\), \(h_{w}\), and \(p\) are the radius,
density of the fluid, kinematic viscosity, thermal diffusivity of fluid,
ratio between heat capacity and base fluid, specific heat, heat transfer
coefficient, and pressure respectively. Further, \(\gamma\) takes the
form,\(\gamma=\left(\mu+\frac{k^{*}}{2}\right)j=\mu\left(1+\frac{K_{1}}{2}\right)j,\ \ \ j=\frac{\nu}{a}\).
Here \(K_{1}=\frac{k^{*}}{\mu}\) is the micropolar parameter. The
above equations \(\left(1\right)-(7)\) are translated into ordinary
differential equations by using the following non dimensional and no
similar variables [32].