A new method of inducing thermomechanical hydrodynamic flow in homeotropic nematic liquid crystals (NLC) is proposed based on using different anchoring conditions on the cell boundaries. Effect of different pairs of boundary conditions including hard, weak and conical on the director orientation, director gradient and NLC flow are studied, theoretically. Absorption of a linearly polarized laser light is considered to induce the need temperature gradient for the thermomechanical effect (TM) in the NLC cell. Coupling of fluidity to the director orientation distorts the director. Consequent optical nonlinearity is calculated and compared with the optical nonlinearity due to other kinds of the TM effect.