  In the present work, we analyzed the Kantowski-Sachs cosmological model along
with teleparallel gravity, where a bulk viscous fluid containing
one-dimensional cosmic strings serves as the source for the energy$-$momentum
tensor. To obtain the deterministic solution of the field equations, we
employed the proportionality condition linking the shear scalar $(\sigma)$ and
the expansion scalar $(\theta)$, establishing a relationship between metric
potentials. Another approach employed is the utilization of the Hybrid
Expansion Law (HEL). The discussion focuses on the behaviour of the
accelerating universe concerning the specific choice of a nonlinear (or power
law model) of teleparallel gravity $f(T)=\alpha T + \beta T^m$, where
  $T$ is the torsion scalar, $\alpha$ , and $\beta$ are model parameters and
$m$ is restricted to greater than or equal to 2. The effective equation of the
state parameter $(\omega_{eff})$ of models I, II and III will support the
acceleration behavior of the universe. We observed that the null energy
condition and weak energy condition are obeyed but violate the strong energy
condition as per the present accelerating expansion. Under specific model
parameter constraints, the universe shows a transition from a decelerating to
an accelerated phase.
