by using primitive variable formulation, solution for a duct flow problem is computed. in order to depict the secondary flow that arises due to the difference in temperature, it is of interest to compute the streamlines in the x-y plane (z-streamwise direction). the problem is how should the streamfunction be defined for such situation since

du/dx + dv/dy + dw/dz = 0

which implies

du/dx + dv/dy <>0 ?

any advice is greatly appreciated. thanks.

(1). Stream function is good for 2-D problem only. (2). For 3-D streamline, you can trace the fluid particle path. This is commonly done, and by changling the viewing angle, you can check the 3-D behavior of the flow field. (3). The secondary flow term is not very scientific, you will have to define it clearly first. (4). The existence of the secondary flow comes from the behavior of the primary flow direction. So, you need to define the primary flow direction first. (which can be another problem for 3-D flow) (5). Make sure that you know what you are looking for.(and also the definition of the secondary flow. It has been a problem for many engineers.)

thanks. can you suggest any reference on tracing the fluid particle path? thanks, again for you willingness to spend time on this. regards, yfyap

(1). pick a starting point, with u,v,w known. (2). determine the next point position based on the given delta(s), the distance traveled along the fluid particle path. (3). with the new position known, calculate the new velocity u,v,w based on neighboring points velocity field. (4). repeat the step-2 to determine the third point location, and so forth. (5). Most graphic post-processing tool should have this capability included.