Study of Various Fluid Flow and Heat Transfer Problems in the Slip Regime

Abstract

Microdevices such as microelectromechanical system(MEMS) have been used in many science and technology applications. These devices and systems often involve fluid flow and heat transfer processes in microchannles. Hence, the study of fluid flow in microchannels and the associated heat transfer process is important for the design and application of microdevices and systems. This project will focus on the study of various microflow and heat transfer problems in the slip regime, including heat transfer in fluids flowing through microchannels, velocity and temperature fields in mixed electroosmotic and pressure-driven flow of fluids, and unsteady flow of fluids in rectangular microchannels in the slip regime. A mathematical model has been constructed to study the transient temperature field in fluids flowing through microchannels driven by pressure gradient in the slip regime. Based on the finite difference method, a computation scheme is then developed to obtain the solution of the temperature field. A subsequent numerical analysis, based on the established computation scheme, is then conducted to investigate the influence of boundary slip and heat convection due to fluid flow on the temperature field. Heat transfer in a mixed electroosmotic and pressure-driven flow is examined in the slip system. Exact solutions have been obtained analytically for the fluid flow and heat transfer problems. The influence of the axial dependence of both the dimensionless bulk temperature θb and the dimensionless wall temperature θw for various Pe ́clet number Pe and wall flux functions under slip condition are examined. The slip flow of an incompressible fluid flow through a rectangular microchannel has also been studied. A mathematical model, including the governing differential equation and boundary conditions, has been constructed for the problem. A new exact solution has been deduced analytically by using Fourier series expansion in the time domain and the separation of variable method in the spatial domain. Numerical analysis has also been carried out for some special cases to examine the influence of slip parameters on the velocity field.