Examining heat transfer in an annular region bounded by an inner stretching and outer stationary cylinder considering variable properties

This research offers a comparative analysis of how varying physical properties affect heat transfer in a fluid-filled annulus between coaxial cylinders. The fluid movement is driven by the linear expansion of the inner cylinder, with the outer cylinder remaining stationary. Additionally, the study considers two distinct variations of the variable viscosity function: (a) an inverse-linear temperature dependency and (b) an exponential temperature dependency, sometimes referred to as Reynolds law. To streamline the numerical integration process, the governing equations are transformed into ordinary differential equations that include a parameter <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mrow> <mml:mi>γ</mml:mi> </mml:mrow> </mml:math> , which is inversely proportional to the cylinder’s radius. The present findings are compared with an existing study under limiting conditions, and the comparison shows excellent agreement. Flow visualization via streamlines and isotherms shows that velocity and temperature profiles are higher for narrower gaps between cylinders compared to the wider gaps. The data of the skin friction coefficient and surface cooling rate are presented in both graphical and tabular forms. The research highlights how different gap sizes between stretching cylinders impact the required stretching force for the inner cylinder and influence the rate of surface cooling. Additionally, wider gaps result in a noticeable increase in the pressure distribution profile and influence the skin friction coefficient and Nusselt number differently.