This　work　generalizes　Evans＇　homogenous　nonequilibrium　molecular　dynamics　(HNEMD)　algorithm　for　computing　the　thermal　conductivity　of　strongly-coupled　complex　(dusty)　plasma　liquids　(SCCDPLs)　described　by　the　Yukawa　potential.　The　effects　of　external　field　strength　along　with　different　screening　strengths　on　the　conductivity　of　Yukawa　liquids　have　investigated　using　HNEMD　simulations.　We　have　carried　out　some　more　linear　and　nonlinear　molecular　dynamics　calculations　of　the　thermal　conductivity,　and　the　obtained　simulation　results　of　SCCDPLs　are　presented　for　various　plasma　coupling　and　screening　parameters.　Our　calculations　show　that　Yukawa　liquid　exhibits　a　non-Newtonian　behavior　that　the　thermal　conductivity　increases　with　increasing　field　strength　which　explains　interaction　contributions　in　Yukawa　conductivity,　for　the　first　time.　The　simulation　results　obtained　with　different　external　filed　strengths　are　in　reasonable　agreement　with　earlier　simulation　results　and　with　reference　set　of　data　showed　deviations　within　less　than　+/-　10%　for　most　of　the　present　data　point.　It　is　shown　that　new　simulations　extended　the　range　of　field　strength　(0.001　＜=　F-*＜=　0.1)　used　in　the　earlier　studies　in　order　to　find　out　the　size　of　the　linear　regimes　and　to　explain　the　nature　of　nonlinearity　of　SCCDPLs.