Articles written in Sadhana
Volume 45 All articles Published: January 2020 Article ID 0007 Original Article (Mechanical Sciences)
The present work aims to study the time-dependent thin porous film flow of an Oldroyd-B model on a heated infinite long flat plate. The fluid and the substrate are both at rest initially. Suddenly, the plate is jolted into motion in its own plane with an oscillatory velocity. Further, an insoluble surfactant is located at the freesurface but not in the bulk of the fluid. Inversion of Laplace transform is applied to obtain numerical solutions to the problem. Due to the difficult analytical inversions back to the real-time domain, the need to use numerical inverse Laplace transforms arises, and a numerical approach for this purpose is mentioned and applied. The analytical solution of the special case of the isothermal liquid film when the Reynolds number is vanishing small is obtained and discussed. The flow rate and skin friction are investigated and plotted. Depending on the selectedparameters, it is revealed that relaxation time constant lowers the velocity, while the effect of retardation time is opposed to that of relaxation time. It is noted that the Péclet number and capillary number enhance the heat transfer rate, whereas the converse is true for elasticity number. It is also observed that the motion of the free surface grows gradually with the increase of Darcy number. The Reynolds number is found to enhance the flow rate and lower skin friction. In the special case when the Reynolds number is vanishing small, it has been shown that the capillary number has an effect, unlike the elasticity number.