A scientific report on the flow of Maxwell fluid with heat transfer in vertical oscillating cylinder

Abstract

The nonlinear nature of viscoelastic non-Newtonian fluids, introduce a unique challenge to physicists and mathematicians. By developing and utilizing viscoelastic models can play a special role in saving and treatments of every living species and to describe its particular characteristics. In the past three decades, viscoelastic fluid models are focused to improve its accuracy and reliability. Some rate type viscoelastic fluids include Maxwell fluid which effects in relaxation time. Such effect of relaxation time cannot be predicted by differential-type fluids. The polymers of low molecular weight are usefully described by Maxwell model. However, a keen interest of the researchers is seen in studying rate type fluids due to the fact that they incorporate both the elastic nature and memory behaviour together. In this article, viscoelastic Maxwell fluid is considered in cylindrical tube together with heat transfer due to convection caused by the buoyancy force. This problem is modelled using the classical approach and then solved for exact solution using joint the Laplace and Hankel transforms. Effects of pertinent parameters on Maxwell fluid velocity have been shown graphically. Behaviour of temperature is studied for various values of Prandtl number.