**4. Conclusions**

The HNEMD scheme is used for the investigation of thermal conductivity under the influence of varying polarization values for various screening lengths *κ* (= 1.4, 3) and Coulomb couplings Γ (= 10, 100) but constant force field strength**.** It has been shown that the current HNMED scheme with polarization and earlier HPMD and GKR-EMD techniques have comparable efficiency over the suitable range of plasma parameters, both generating reasonable data of polarized λ0. New simulation results provide more reliable and ample results for the polarized thermal conductivity for a whole range of (Γ, *κ*) than previous known simulation data. Thermal conductivity results estimated from this newly developed HNEMD scheme are in well matched with available numerical results generally underpredicting within 20% - 35%. The current HNEMD data with less statistical noise and best efficiency have been computed by taking different parameters (*N*, 1/ Γ, *κ* and Γd) for the current HNEMD scheme to measure the thermal conductivity of 2D DP systems, at constant *F*\* = 0.02. For future work, the HNEMD method introduced here may easily extend to other physical systems with varying force field with modifications.

## **Acknowledgements**

We are grateful to the National High Performance Computing Center of Xian Jiaotong University and National Advanced Computing Center, National Center of Physics (NCP), Pakistan for allocating computer time to test and run our MD code.
