## Mathematical Formulation of Laminar Boundary Layer

**Introduction:** Consider a steady, axisymmetric boundary layer flow of a viscous and incompressible fluid along a continuously stretching cylinder as shown in Fig. It is assumed that the stretching velocity U (x) and the surface temperature Tw(x) are of the form U x= U0 (x/1) and

Where U0, T0 and l are the ambient temperature and characteristic length, respectively. Under these assumptions along with the boundary layer approximations, the equations which model the problem under consideration are

Subject to the boundary conditions

Where u and v are the velocities in the x − and r − directions, respectively, T is the fluid temperature and α is the thermal diffusivity. The continuity equation can be satisfied by I stream function ψ, such that ∂ and . The momentum and energy equations can be transformed into the corresponding ordinary differential equations by the following transformation (Mahmood & Merkin, 1988; Ishak, 2009):

The transformed ordinary differential equations are:

Subject to the boundary conditions

Here, prime denotes differentiation with respect to η, and γ is the curvature parameter defined as:

The physical quantities of interest are the skin friction coefficient Cf and the local Nusselt number Nux, which are defined as:

Where the surface shear stress wτ and the surface heat flux qw are given by

With μ and k being the dynamic viscosity and the thermal conductivity, respectively. Using the similarity variables (5), we obtain

Where Re /x = Ux ν is the local Reynolds number.