I have a problem in my project and is : I have a microcantilever beam that is in plat.i have two force that act to this beam, 1. magnetic force from bottom and 2. flow drag force that act to cantilever when it bend in effect of magnetic force. i can model the magnetic force and is non-linear , for this matter i must model drag effect and after that i solve that in same time. but i can't model the drag force on microcantilever beam. in your opinion how can i model drag force.?

thanks

You can compute the drag force with a flat plate approximation.But since your problem is a microcantilevel, you might need to include a partial slip correction at the boundary for the computed drag.Have a look at any book on microflows to calculate slip correction.The drag on a flat plate can be found in any fluid mechanics book.

Thanks for your answer. I want to discribe more about my problem. with attention to this point that my microcantilever is horizontal and the flow also is, and with out of magnetic force i don't have drag force on it becouse the cantilever is prallel with flow, but after bending with magnetic force from bottom, now we have drag force, similar that i take quarter cylinder on opposite of flow in boundary layer(becouse is Micro). i want that you help me more, if possible and i can't find any reference , if you have any reference , i wait you.

sincerly

when you have flow over the cantilever, you have the skin friction drag even without the magnetic force.So I assume that the drag might be a sum of skin friction drag and drag due to the bending caused by magnetic forces.You can obtain the drag for microflows by replacing u with u+alpha*du/dn,where du/dn is to account for the partial slip which happens in microflows.More about it can be found in Microflows book by Karniadakis and Beskok.Regarding the magnectic part,look into the book of lifshitz,"Fluid mechanics".He might have given some analytical solution for magnetic drag.