Dear Vivek,

This is not always true. Taking for example a pipe, the uniform magnetic field is B= Bxex + Brer of constant magnitude B = (Bx^2 + Br^2)^0.5, where ex and er are unit vectors in cylindrical coordinates. The orientation of the magnetic field can form an angle Phi with the horizontal axis (the flow direction) such that Phi = Br/Bx.

We often choose Phi = 90 ° to simplify the calculation (sin Phi = 1). The direction of the magnetic field is perpendicular to the flow direction. But, we can also choose Phi = 0 ° or 45 ° for example. Here is a link that shows a study on the subject for different Phi angles.

http://www.j-mst.org/On_line/admin/files/10-J2010-35_333-339-340%EB%B0%B1_.pdf

With my best regards

Prof. Bachir ACHOUR

please look at this link may be it will be useful

http://www.trifield.com/content/about-electromagnetism/

regards

The influence of a magnetic field on the skin friction factor of steady fully-developed laminar flow through a pipe was studied experimentally. A mathematical model was introduced and a finite difference scheme used to solve the governing equations in terms of vorticity-stream function. The model predictions agree favourably with experimental results. It is observed that the pressure drop varies in proportion to the square of the product of the magnetic field and the sine of the magnetic field angle. Also, the pressure drop is proportional to the flow rate. This situation is similar to what applies in the absence of a magnetic field. It is found that a transverse magnetic field changes the axial velocity profile from the parabolic to a relatively flat shape. At first, the radial velocity rises more rapidly and then gradually decreases along the pipe until falling to zero. A numerical correlation can be written for the considerable distance required for the new axial velocity profile to establish. Owing to the changes taking place in the axial velocity profile, it exhibits a higher skin friction factor. The new axial velocity profile asymptotically approaches its limit as the Hartmann number becomes large.

Ref: Magnetic field effect on fluid flow characteristics in a pipe for laminar flow†

www.j-mst.org/On_line/admin/files/10-J2010-35_333-339-340백_.pdf