Theeffectsofbothfirst-andsecond-orderresistance,duetothesolidmatrixofnon-Darcyporousmedia,viscousdis-sipation,Ohmicheating,andtemperature-dependentviscosityonlaminarmixedconvectionboundarylayerflowandheattransferonacontinuouslymovingverticalsurface,havebeenstudied.Thefluidviscosityisassumedtovaryasaninverselinearfunctionoftemperatureundertheactionofatransversemagneticfield.Localsimilaritysolutionsareobtainedfortheboundarylayerequationsgoverningtheflowalongamovingverticalisothermalsurfacewithuniformelocity.Theeffectsofvariousparameters,suchasthefirst-andsecond-ordersolidmatrixresistance,magneticfield,Eckertnumber,buoyancyforce,andviscosity/temperatureparameter,onthevelocityandtemperatureprofilesaswellastheskinfrictioncoefficientandwallheattransferarepresentedgraphicallyandintabularform