The　present　investigation　centers　on　the　impact　of　viscous　dissipation　and　ohmic　heating　on　the　plume　generated　by　a　line　heat　source　under　the　impact　of　an　aligned　magnetic　field.　In　this　study,　the　flow　model　is　adapted　to　incorporate　ohmic　heating　and　viscous　dissipation　by　including　the　respective　terms　in　the　energy　equation.　A　mathematical　model　is　formulated　as　a　system　of　coupled　partial　differential　equations　to　analyze　the　flow　problem.　Subsequently,　a　numerical　solution　is　derived　with　stream　function　formulation　for　the　system　of　coupled　partial　differential　equations,　which　transmutes　it　into　ordinary　differential　equations.　To　achieve　this,　the　numerical　properties　of　the　problem　are　established　through　the　utilization　of　the　Shooting　method　in　tandem　with　the　MATLAB　tool　bvp4c.　The　graphical　representations　of　both　missing　and　specified　boundary　conditions　depict　the　effects　of　the　magnetic　parameter,　viscous　dissipation　variable,　magnetic　force　parameter,　Prandtl　number,　and　magnetic　Prandtl　number.　These　are　accompanied　by　a　discussion　of　their　respective　physical　implications.　The　observed　results　claimed　that　the　velocity,　current　density,　and　temperature　distribution　decrease　for　enhancing　magnetic　parameters.　Meanwhile,　the　skin　friction　and　magnetic　flux　drop　while　the　heat　transfer　rate　increases　with　an　increment　in　magnetic　parameters.　These　fluid　flow　and　heat　transfer　characteristics　were　observed　to　decrease　for　increasing　viscous　dissipation.　The　current　work　is　novel　in　incorporating　ohmic　heating　viscous　dissipation　in　energy　equations　coupled　with　Max-well　and　magnetic　induction　equations.