Johansen, Per2; Roemer, Daniel Beck1; Andersen, Torben Ole4; Pedersen, Henrik C.2
1 Department of Energy Technology, The Faculty of Engineering and Science, Aalborg University, VBN2 Fluid Power and Mechatronic Systems, The Faculty of Engineering and Science, Aalborg University, VBN3 The Faculty of Engineering and Science (ENG), Aalborg University, VBN4 Aalborg U Robotics, The Faculty of Humanities, Aalborg University, VBN
A conventional simplification of the thermal problem in fluid film lubrication analysis is performed by assuming that the main direction of heat flow is conduction through the film thickness, and thereby neglecting convection. However, in a significant amount of applications, convection is not negligible, whereby the majority of design engineers exclusively use numerical solvers. This paper presents a perturbation series expansion of the temperature field for small values of the Brinkman number. The derived perturbation solution and the more conventional analytical solution, where convection is neglected, are compared to a numerical test case. The comparison shows a significant improvement in the region where the convection term and conduction term are of the same order.