Analysis of Stokes system with solution-dependent subdifferential boundary conditions

We study the Stokes problem for the incompressible fluid with mixed nonlinear boundary conditions of subdifferential type. The latter involve a unilateral boundary condition, the Navier slip condition, a nonmonotone version of the nonlinear Navier–Fujita slip condition, and the threshold slip and leak condition of frictional type. The weak form of the problem leads to a new class of variational–hemivariational inequalities on convex sets for the velocity field. Solution existence and the weak compactness of the solution set to the inequality problem are established based on the Schauder fixed point theorem.

The Study of Navier Slip Condition on the Flow and Heat Transfer in a Coolant Surrounded an Exponentially Stretching Sheet

The paper presents the study of velocity profiles in a hydrodynamic flow and heat transfer in a Newtonian fluid over an exponentially stretching sheet. Navier slip condition is used at the boundary. The stretching of the sheet is assumed to be nonlinearly proportional to the distance from slit. Non-linear partial differential equations characterize the flow phenomenon with boundary conditions in a semi infinite domain. The equations are transformed to nonlinear ordinary differential equations by applying suitable local similarity transformation. The series solution of the transformed equations are obtained by using differential transform method and Pade approximation with assistance from the shooting method in obtaining the unknown initial values. The solution is obtained in a power series with assured convergence. The effects of various parameters on velocity and temperature profiles are presented graphically.