Laminar natural convection of yield stress fluids in annular spaces between concentric cylinders

Abstract

Abstract This paper aims to investigate the laminar natural convection of Bingham fluids between horizontal concentric cylinders. The governing equations are solved numerically by using the Galerkin’s weighted residuals scheme of finite element method with a non-uniform unstructured triangular grid. The effects of various parameters such as the Rayleigh number ( 10 3 ≤ R a ≤ 10 6 ) , yield number ( 0 ≤ Y ≤ Y max ) , ratio of gap width to inner cylinder radius ( 0.5 ≤ L / R i ≤ 5 ) and fixed Prandtl number ( Pr = 100 since results are not sensitive to Pr in the tested range) on the flow and temperature profiles as well as on the heat transfer and morphology of yielded/unyielded regions are presented and discussed. The heat transfer rate shows a positive dependence on the Rayleigh number and L / R i , however, there is an optimum value for L / R i which maximizes the heat transfer rate. The results also show that the yield number has a significant impact on the flow and temperature fields and the heat transfer performance. In fact, the heat transfer rate decreases with the rise of the yield number and above a certain value of Y , the convection does not occur, and heat transfer is only due to conduction. It is found that while the enhancement of the Rayleigh number augments the heat transfer, it is not necessarily associated with a decrease in the size of the unyielded zones.