A gas turbine engine comprising: a high-pressure turbine ; a low-pressure turbine (LPT) downstream of the high-pressure turbine and having a LPT outer case and a LPT plenum extending circumferentially around a central axis , the LPT plenum distributing cooling air around the low-pressure turbine ; a mid-turbine frame assembly connecting the low-pressure turbine and the high-pressure turbine , the mid-turbine frame assembly having: a mid-turbine frame outer case defining an inlet for connection to a source of the cooling air, an intermediary plenum fluidly connected to the source of cooling air via the inlet , the intermediary plenum having a first air outlet and a second air outlet , and a mid-turbine frame plenum disposed radially inwardly of the mid-turbine frame outer case and fluidly connected to the source of the cooling air via the first air outlet of the intermediary plenum ; a cooling air conduit fluidly connecting the second air outlet of the intermediary plenum to the LPT plenum while bypassing the mid-turbine frame plenum ; and two protrusions being axially spaced apart from one another relative to the central axis and extending from the mid-turbine frame outer case in a direction having a radial component relative to the central axis , the two protrusions extending circumferentially around the central axis , the intermediary plenum being disposed between the two protrusions , characterised in that the first air outlet is a first aperture defined through a first protrusion of the two protrusions, and the second air outlet is a second aperture defined through a second protrusion of the two protrusions. a high-pressure turbine ; a low-pressure turbine (LPT) downstream of the high-pressure turbine and having a LPT outer case and a LPT plenum extending circumferentially around a central axis , the LPT plenum distributing cooling air around the low-pressure turbine ; a mid-turbine frame assembly connecting the low-pressure turbine and the high-pressure turbine , the mid-turbine frame assembly having: a mid-turbine frame outer case defining an inlet for connection to a source of the cooling air, an intermediary plenum fluidly connected to the source of cooling air via the inlet , the intermediary plenum having a first air outlet and a second air outlet , and a mid-turbine frame plenum disposed radially inwardly of the mid-turbine frame outer case and fluidly connected to the source of the cooling air via the first air outlet of the intermediary plenum ; a mid-turbine frame outer case defining an inlet for connection to a source of the cooling air, an intermediary plenum fluidly connected to the source of cooling air via the inlet , the intermediary plenum having a first air outlet and a second air outlet , and a mid-turbine frame plenum disposed radially inwardly of the mid-turbine frame outer case and fluidly connected to the source of the cooling air via the first air outlet of the intermediary plenum ; a cooling air conduit fluidly connecting the second air outlet of the intermediary plenum to the LPT plenum while bypassing the mid-turbine frame plenum ; and two protrusions being axially spaced apart from one another relative to the central axis and extending from the mid-turbine frame outer case in a direction having a radial component relative to the central axis , the two protrusions extending circumferentially around the central axis , the intermediary plenum being disposed between the two protrusions , characterised in that the first air outlet is a first aperture defined through a first protrusion of the two protrusions, and the second air outlet is a second aperture defined through a second protrusion of the two protrusions. <EOS>