A Transverse Flow Effect

We now examine how flow is affected when the director is fixed by a very strong magnetic field. Consider the situation pictured in Fig. 5.2 where a strong magnetic 

Notice, by equation (4.141), that p i = p i because gravity has been neglected and the magnetic potential does not depend explicitly on x. Our main concern is then reduced to solving equations (5.34) subject to the no-slip boundary conditions on u and v. It therefore only remains to solve 

The non-zero contributions to the rate of strain tensor A and the vorticity tensor W are 

The non-zero components of the dynamic viscous stress in equation (4.121) can be calculated using equations (5.32)i, (5.37), (5.38) and (5.39) to reveal 

Equation (5.46) shows that the pressure p is restricted to be a function of x and y. However, we know from equations (5.40) and (5.41) that the left-hand sides of (5.44) and (5.45) must be functions of z only, indicating that p x = o, and p y = b for some constants a and b. Hence we can take 

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