Numerical and series solutions for Von-Kármán flow of viscoelastic fluid inspired by viscous dissipation and Joule heating effects

Abstract

Present article aims at developing similarity solutions for heat transportation in swirling flow of viscoelastic fluid (obeying Jeffrey model) generated by an infinite porous rotating surface. The resulting thermal energy equation comprising frictional heating and Ohmic dissipation terms is mainly focused. Relevant equations simplified under boundary layer approximations have been solved analytically by a powerful homotopy based analytical scheme, while numerical solutions are constructed by a reliable MATLAB solver bvp4c. For homotopy based series solutions, total squared residual of the system is evaluated, and it is found to decline for increasing order of approximations. Both applied methods are shown to be in compliance with each other for wide range of viscoelastic fluid parameters. Computed solutions are utilized to understand the combined influence of viscoelasticity and viscous dissipation on heat transport phenomena associated with the Von-Kármán configuration. Subtle fluid dynamics entities such as resisting torque and Nusselt number are computed and elaborated. Results predict that the torque required by the disk drastically reduces when viscoelastic fluid assumption is applied. However, cooling rate of the disk in Newtonian fluid is better than that in viscoelastic fluid. Present results are found in agreement with that of the previous studies in a limiting situation.