This　study　focuses　on　how　the　porous　medium　affects　the　plume　generated　due　to　line　heat　source　when　an　aligned　magnetic　field　is　present.　For　this　study,　the　momentum　equation　of　the　flow　model　is　modified　for　porous　medium　by　including　the　porosity　term.　A　mathematical　model　is　developed　as　coupled　partial　differential　equations　in　order　to　study　the　flow　problem.　Later,　a　numerical　solution　is　found　for　the　system　of　coupled　partial　differential　equations　that　are　transmuted　in　to　ordinary　differential　equations.　For　this　purpose,　the　numerical　characteristics　of　the　problem　are　derived　employing　a　shooting　approach　in　combination　with　the　built-in　MATLAB　tool　bvp4c.　The　graphical　illustrations　of　missing　and　specified　boundary　conditions　demonstrate　the　impacts　of　porosity　parameter　Omega,　magnetic　force　parameter　S,　Prandtl　number　Pr　and　magnetic　Prandtl　number　gamma　accompanied　by　a　discussion　of　their　corresponding　physical　implications.　The　novelty　of　this　developed　problem　is　proclaimed　with　justification　by　its　emphasis　on　the　principal　characteristics　of　heat　and　fluid　flow　affected　predominantly　by　the　presence　of　a　porous　medium.　The　thorough　examination　of　the　porosity　parameter　Omega　for　missing　conditions　depicts　that　the　temperature　and　velocity　profiles　enhance　while　current　density　drops　for　the　increasing　values　of　the　porosity　parameter　Omega.　Whereas,　for　specified　conditions,　the　skin　friction　and　magnetic　flux　enhance　but　heat　transfer　rate　declines　with　increment　in　Omega.