An exact solution for the calendering analysis of a third-order fluid

This paper presents the exact solution for calendering a third-order fluid under lubrication approximation. The solution obtained is valid for all values of the third-order fluid parameter. This exact solution is compared to the perturbation solution. The results show that the perturbation solution is valid for very small values of the third-order fluid parameter. Therefore, no significant deviation from the corresponding results of the Newtonian fluid is observed with the perturbation solution. The interesting quantities for mechanically designing a calendering system such as the force separating the two rolls and total power input into both rolls are calculated and shown graphically for large third-order fluid parameter. The material’s rheological features modify the pressure, flow characteristics, and all other operating variables significantly. In fact, the nip region pressure increases with increasing third-order fluid parameter. The exiting sheet thickness, power input, and roll separating force also increase with increasing third-order fluid parameter.