A new model for three-dimensional random roughness effect on friction factor and heat transfer in microtubes

In this paper we propose a novel bottom-up approach to generate a three-dimensional microtube surface with random roughness. This approach starts from four corner points with two defined coordinates and roughness height created by a Gaussian number generator, and then uses a bi-cubic Coons patch to form the curved surface. A computational fluid dynamics solver is used to isolate the roughness effect and solve the three-dimensional N–S equations for the water flow through the generated rough microtubes with diameter D = 50 μm and length L = 100 μm. No-slip, constant heat flux and periodic boundary conditions are applied to achieve the characteristics of fully developed flow. It is found that the wall roughness strongly affects the velocity near the wall and it almost has no effect on the flow at the center. When the mean diameter of a rough microtubes is used as the hydraulic diameter, the friction factor can still be predicted by the conventional flow theory. The temperature has large values at the peaks and small values at the valleys of the microtube surface. However, the roughness has almost no effect on the averaged Nusselt number Nu¯ because the effects of peaks and valleys counteract each other for the whole microtube. The local Nusselt numbers along the microtube randomly scatter from the theoretical value with a deviation less than 2%. The model has a potential to be used for direct simulations of three-dimensional surface roughness effect on the slip flow.