Abstract
In this study, the effect of thermal radiation on micro-polar fluid flow over a wavy surface is studied. The optically thick limit approximation for the radiation flux is assumed. Prandtl’s transposition theorem is used to stretch the ordinary coordinate system in certain directions. The wavy surface can be transferred into a calculable plane coordinate system. The governing equations of micro-polar fluid along a wavy surface are derived from the complete Navier-Stokes equations. A simple transformation is proposed to transform the governing equations into boundary layer equations so they can be solved numerically by the cubic spline collocation method. A modified form for the entropy generation equation is derived. Effects of thermal radiation on the temperature and the vortex viscosity parameter and the effects of the wavy surface on the velocity are all included in the modified entropy generation equation.
Highlights
In recent years, the heat convection of wavy surfaces has been studied extensively because of its wide practical applications
The results indicate that increasing NR leads to increased temperature distribution, and to enhanced entropy generation due to heat transfer of the flow field
Is over 0.5, which means that as the value of NR increases, the thermal radiation heat flux is absorbed into the fluid, which leads to enhanced entropy generation due to heat transfer of the flow field, heat transfer dominates entropy generation over the wavy surface
Summary
The heat convection of wavy surfaces has been studied extensively because of its wide practical applications. Yao [1,2] proposed a simple transformation to study the natural convection heat transfer of isothermal vertical wavy surfaces, e.g., sinusoidal surfaces. Results show that the local heat transfer rate varies periodically along the wavy surface, with a frequency equal to twice the frequency of the surface. Study of natural convection and study of mixed convection along a vertical wavy surface was provided by Moulic and Yao [3] They showed that the total mixed convection heat flux along a wavy surface is smaller than that of a flat surface. Yao [4] showed that the enhanced total heat-transfer rate seems to depend on the ratio of the amplitude and wavelength of a surface. Micro-polar fluids possess certain microscopic effects that come from local structure and micro-motion of the fluid [6,7,8,9], and can be used to study the behavior in fluid media such as polymeric fluids, liquid crystals and animal blood
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