@Rouben Rostamian  

Greetings for the day.

Many thanks for your reply. 

I tried to calculate the gradient for different values of time "t" by taking y=0 but unfortunately, I didn't get the result. One of the reasons may be I am using a different version of maple.  The screenshot of the error is attached herewith. 

Once again many thanks.

@tomleslie 

First of all thanks a lot for the answer and effort.

The second boundary condition is valid for t>0. I didn't mention this condition in my problem because I think it is not necessary for getting a numerical solution. This PDE along with iCBCs represent Stokes's second problem. A well known problem in fluid mechanics,