A gas turbine transition duct comprising: an inner tubular body (10; 110), defining a transition channel and having a first upstream end and a first downstream end for coupling to a can combustor and to a turbine section of a gas turbine assembly, respectively; an outer tubular body (11; 111), arranged around the inner tubular body (10; 110) and having a second upstream end at the first upstream end of the inner tubular body (10; 110) and a second downstream end at the first downstream end of the inner tubular body (10; 110); wherein a convective cooling channel is defined between the inner tubular body (10; 110) and the outer tubular body (11; 111), the convective cooling channel having an inlet between the first downstream end and the second downstream end and being configured to convey a cooling flow along an outer surface of the inner tubular body (10; 110) from the first downstream end and second downstream end towards the first upstream end and second upstream end; wherein the outer tubular body (11; 111) is defined by a continuous wall that extends between the second upstream end and the second downstream end, passage of air across the continuous wall being prevented; characterized in that the inner tubular body (10; 110) has a first frame (15; 115) at the first downstream end and the outer tubular body (11; 111) has a second frame (22; 122) at the second downstream end, the second frame (22; 122) being arranged parallel to and at a distance from the first frame (15; 115); wherein the inlet of the convective cooling channel is defined between the first frame (15; 115) and the second frame (22; 122); and further characterized by a splitter in the inlet of the convective cooling channel, the splitter having an edge bent to guide the cooling flow along the outer surface of the inner tubular body. an inner tubular body (10; 110), defining a transition channel and having a first upstream end and a first downstream end for coupling to a can combustor and to a turbine section of a gas turbine assembly, respectively; an outer tubular body (11; 111), arranged around the inner tubular body (10; 110) and having a second upstream end at the first upstream end of the inner tubular body (10; 110) and a second downstream end at the first downstream end of the inner tubular body (10; 110); wherein a convective cooling channel is defined between the inner tubular body (10; 110) and the outer tubular body (11; 111), the convective cooling channel having an inlet between the first downstream end and the second downstream end and being configured to convey a cooling flow along an outer surface of the inner tubular body (10; 110) from the first downstream end and second downstream end towards the first upstream end and second upstream end; wherein the outer tubular body (11; 111) is defined by a continuous wall that extends between the second upstream end and the second downstream end, passage of air across the continuous wall being prevented; characterized in that the inner tubular body (10; 110) has a first frame (15; 115) at the first downstream end and the outer tubular body (11; 111) has a second frame (22; 122) at the second downstream end, the second frame (22; 122) being arranged parallel to and at a distance from the first frame (15; 115); wherein the inlet of the convective cooling channel is defined between the first frame (15; 115) and the second frame (22; 122); and further characterized by a splitter in the inlet of the convective cooling channel, the splitter having an edge bent to guide the cooling flow along the outer surface of the inner tubular body.