Thermal radiation heat transfer of non-Newtonian fluid along a needle

The purpose of this study was to investigate laminar natural convection heat transfer along a thin needle in non-Newtonian fluids. Particular interest was to examine the heat transfer rate and the skin friction as well as the similarity velocity and temperature profiles for different non-Newtonian fluid indices, n. Also this study examined the behavior of non-Newtonian power-law fluid due to the effects of thermal radiation heat transfer and different needle sizes as well as various Prandtle numbers. The study was initiated by determining a set of transformation variables which reduced the original boundary layer equations to the ordinary differential equations.

The technique of numerical analysis used to obtain these ordinary differential equations was the Runge-Kutta algorithm. This algorithm was used to generate solutions based on corrections to initial guesses for the initial values given to the slopes of the velocity profiles and temperature profiles at the wall. The corrections were obtained by satisfying the asymptotic boundary layer so that the mean square errors between the computed variables and the asymptotic values are minimized.

Solutions of these equations were based on incompressible, viscous flow where the properties such as viscosity and thermal conductivity were assumed to be constant. The radiation properties of the medium were assumed to be optically thick. For an optically thick medium, a diffusion approximation or Rosseland approximation can be applied. In the optically thick medium, the radiation heat flux can not travel a long distance because the medium is optically dense. Therefore, the radiation heat transfer may be considered as heat conduction. The radiation heat flux term was simplified by means of Rosseland approximation. Then this term was linearized by using the Taylor expansion. The momentum and temperature profiles were presented for various Prandtl numbers and conduction to radiation parameter as well as several non-Newtonian cases according to different values of n. The results show the effects of radiation, Prandtl numbers and needle shape on non-Newtonian fluid as well as the Newtonian fluid.