$\mathit{a}$	Constant
$\mathit{B}\mathit{e}$	Bejan Number $[-]$
$\mathit{B}\mathit{r}$	Brinkman number $[-]$
${\mathit{c}}_p$	Specific heat $\left[{\mathrm{JKg}}^{-1}{\mathrm{K}}^{-1}\right]$
$\mathit{E}\mathit{c}$	Eckert number $[-]$
$\mathit{f}$	Dimensionless stream function
$k$	Thermal conductivity $\left[{\mathrm{Wm}}^{-1}{\mathrm{K}}^{-1}\right]$
$\mathit{P}\mathit{r}$	Prandtl number $[-]$
$\mathit{R}\left(\mathit{x}\right)$	Shape and size of the needle [m]
$\mathit{R}{\mathit{e}}_{\mathit{x}}$	Local Reynold number $[-]$
$\mathit{T}$	Temperature field [K]
$\mathit{U}$	Composite velocity [${\mathrm{m}\mathrm{s}}^{-1}$]
${\mathit{u}}_{\mathit{w}},{\mathit{u}}_{\infty }$	Velocity of needle and free stream, respectively [${\mathrm{m}\mathrm{s}}^{-1}$]
$\mathit{u},\mathit{v}$	Velocity components in axial and radial directions, respectively [m]
$\mathit{x},\mathit{r}$	Spatial coordinates measured in axial and radial directions, respectively [m]
$\mathsf{\theta }$	Non-dimensional temperature $[-]$
$\mathsf{\rho }$	Density of fluid $\left[{\mathrm{kg}\mathrm{m}}^{-3}\right]$
$\mathsf{\mu }$	Dynamic viscosity $\left[{\mathrm{kg}\mathrm{m}}^{-1}{\mathrm{s}}^{-1}\right]$
$\mathit{\Psi }$	Dimensional stream function $\left[{\mathrm{m}}^2{\mathrm{s}}^{-1}\right]$
$\mathit{\epsilon }$	Velocity ratio parameter