Analytical solution for unsteady Walters-B fluid flow by a deforming surface with acceleration using OHAM based package BVPh2.0

Abstract

Current study aims at simulating fluid flow due to a deformable heated surface in an otherwise static viscoelastic fluid obeying Walters-B model. Velocity of the surface is supposed to grow as time from its initiation of motion progress. Simulations in this work are based on the assumption of quadratic surface temperature distribution. Temperature rise attributed to the frictional heating effect is accounted for in the analysis. By choosing appropriate base functions, homotopy solutions are developed for reasonably large values of material fluid parameter. Reliability of the analytical results is established by computing averaged squared residual of the system. The contributions of the surface acceleration and elasticity on the boundary layer formation are enlightened through the plots of velocity components and temperature. Skin friction measuring the stress experienced by the surface is evaluated and examined under different controlling parameters. The paper also presents a numerical solution using NDSolve of MATHEMATICA in a special case of steady flow, and such solution agrees very well with the corresponding homotopy solution.