We have studied viscous energy damping of kink Magnetohydrodynamic (MHD) waves in weakly twisted magnetic flux tubes. The flux tube has been modelled as a homogeneous internal region with a straight magnetic field, surrounded by a radially non-uniform and magnetically twisted transitional layer embedded in a homogeneous ambient with a straight field. Using a modal expansion technique, we have solved an initial value problem for the incompressible viscous MHD equations and obtained spatio-temporal behaviour of the perturbations of the kink mode in linear regime. In the transitional layer, the perturbations are subject to phase mixing which enhances the viscous effects in the region. We show that magnetic twist can increase or decrease the efficiency of viscous damping of the phase-mixed perturbations in the non-uniform transitional layer. Using the temporal evolution of the total energy, we have obtained the viscous dissipation time as a power function of the Reynolds number. Our results show that magnetic twist could decrease or increase the viscous dissipation time.
