Narrow Results

The prime aim and essence of this study are to present a closed-form solution of the unidirectional velocity field for thin film flow generated by a third-grade liquid moving over a fixed or movable inclined plane in the presence of partial slip boundary condition. Consideration of partial slip makes this problem different from other published research works. Here lies the novelty of this study. The nondimensional, unidirectional velocity profiles rely on the material parameter of third-grade fluid, slip parameter and initial velocity of the movable plane. Study discloses that the fluid’s velocity decelerates with raising the material property of grade-3 fluid and it accelerates with the slip parameter and initial velocity of the inclined plane. The outcomes of this study are deliberated physically at length.

In the present article, we have discussed the closed-form analytical and numerical solutions of the peristaltic flow of a Jeffrey fluid in an inclined tube with different viscosities and with different wave shapes. The closed-form analytical solutions have been computed by Adomian decomposition method and the numerical solutions have been calculated using finite difference technique. A comparison of numerical and analytical solutions have been presented and found a very good agreement between the two solutions. The expressions for pressure rise and friction forces are computed using numerical integration with the help of mathematics software. At the end various physical parameters appearing in the problem are shown pictorially and the results have been discussed in detail. The phenomena for different wave shape are also discussed.

This paper looks at the dissipative heat transfer on the peristaltic flow of a Sisko fluid in an asymmetric channel. Flow exhibits slip at the channel walls maintained at nonuniform temperatures. Long wavelength approximation is utilized and perturbation solutions are obtained about Sisko fluid parameter. Closed form solutions for the stream function, axial pressure gradient, axial velocity, temperature and the heat transfer coefficient are presented. Influences of various interesting parameters are presented in graphical and tabular forms. Pumping and trapping phenomena are discussed for increasing velocity slip parameter. A comparative study on temperature and heat transfer coefficient for viscous, shear thinning and shear thickening fluids has been presented. Comparisons for viscous fluid are found in good agreement.

A two-dimensional wear contact problem with a stick zone is considered for a Hertzian cylindrical contact configuration and Archard’s equation of wear. A one-free-parameter simple model for the wear volume accumulation during the reciprocating wear process, which occurs in two symmetric variable slip zones, is developed and validated against numerical solutions available in the literature. The developed model takes into account the observed effect of non-monotonic evolution of the friction dissipated energy. The presented analytical modeling framework does not make use of any fitting parameters to be evaluated from experiments. The only free dimensionless parameter is suggested to be fixed based on numerical simulations for the maximum of the frictional damage that is proportional to the cumulative wear rate.