  This article examines the dynamics of gravitational collapse in
$f(\mathcal{R},\mathcal{T},\mathcal{Q})$ gravity, where
$\mathcal{Q}=\mathcal{R}_{\mathrm{ab}}\mathcal{T}^{\mathrm{ab}}$. We consider
self-gravitating anisotropic cylindrical geometry whose interior is filled with
dissipative matter configuration and match it with exterior cylindrically
symmetric spacetime at the hypersurface through junction conditions. We employ
the Misner-Sharp and M\"{u}ler-Israel Stewart formalisms to derive the
dynamical as well as transport equations corresponding to the model
$\mathcal{R}+\Phi\sqrt{\mathcal{T}}+\Psi\mathcal{Q}$, where $\Phi$ and $\Psi$
are arbitrary coupling constants. We then establish some relations between
these equations through which the impact of effective matter variables, heat
dissipation and the bulk viscosity on the collapse rate is studied. Further, we
express the Weyl scalar in terms of the effective matter sector. We also obtain
the conformal flatness by applying some restrictions on the considered model
and taking dust configuration into the account. Finally, we investigate various
cases to check whether the modified corrections increase or decrease the
collapse rate.
