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Computational fluid dynamics problem

A rectangular obstacle is placed in a rectangular domain of incompressible fluid flow. The rectangular obstacle is placed where its left boundary touches the left boundary of the rectangular domain (obstacle moved to the left side). The top or bottom boundaries of the obstacle do not touch the rectangular domain boundary. This can be clearly seen in the image attached.

To apply finite difference method, what are the boundary conditions for the obstacle for the velocity components (no-slip) and temperature in a staggered grid. A MATLAB code (in text file since i was not allowed to attach matlab file) is also attached. Since the code does not work properly, I need to know the boundary conditions to modify the code to make it work. You can run the code to help me find a solution.

Please be kind to help me out.

Thank you. (Smirk)