Influence of variable thermal conductivity on axisymmetric slip flow in a pipe with a varying radius

This study examines wave propagation in elastic orthotropic tubes filled with a uniformly tapered fluid, focusing on the effects of slip velocity variations at the tube wall. A Newtonian fluid flows through tubes with different radii, and microscale gas flows may be influenced by temperature gradients, affecting viscosity and temperature-dependent thermal conductivity. An asymptotic series solution for low Reynolds number flow is employed to determine streamlines, velocity profiles, and variations in amplitude and wavelength of constrictions. A closed-form formula is derived to calculate the pressure drop, improving upon the Hagen-Poiseuille model by accounting for wavelength effects. Axisymmetric solutions to the governing differential equations are obtained under the assumption of no traction on the outer wall surface. Numerical analysis reveals that the slip parameter significantly influences axial and radial velocities as well as temperature profiles, providing insights into fluid behavior in elastic tubes.