Flow over a Needle Moving in a Stream of Dissipative Fluid Having Variable Viscosity and Thermal Conductivity

Abstract

In this article, the boundary layer flow around a thin needle is examined. Non-constant thermal conductivity as well as viscosity is the art of present study. Governing equations are modeled in the presence of frictional heating and are simplified by utilizing boundary layer assumptions. To obtain a self-similar solution, boundary layer equations are further transformed into dimensionless forms by utilizing axisymmetric similarity variables. For further investigation of the problem, attained self-similar nonlinear equations with suitable boundary conditions are solved numerically using MATLAB bvp5c. A comparative study with existing findings is carried out. Impact of velocity ratio parameter, size of the needle, variable viscosity parameter, Prandtl number, fluid friction and variable thermal conductivity parameters on dimensionless velocity, skin friction coefficient, temperature and local Nusselt number are investigated through graphical analysis. It is observed that flow with variable viscosity and thermal conductivity is significantly different and realistic in comparison with constant properties-based flow. It is also noted that the temperature of the fluid and the thickness of the thermal boundary layer are related directly to reduction in needle size. Further, considerable enhancement is observed in heat transfer rate for the variable properties case.