A gas turbine engine, comprising: a compressor section, a combustor section, a turbine section, and at least one rotatable shaft; a seal assembly including a seal plate mounted for rotation with the rotatable shaft and a face seal in contact with the seal plate at a contact area, the seal plate including a cooling passageway (78, 78', 78") having a circumferentially-extending section radially aligned with the contact area, wherein the cooling passageway (78, 78', 78") includes: an inlet section between an inlet and the circumferentially-extending section; and an outlet section between the circumferentially-extending section and an outlet; and a source of cooling fluid, wherein: the seal plate is arranged such that the cooling fluid flows through the cooling passageway (78, 78', 78") from the inlet to the outlet; the cooling passageway (78, 78', 78") is arranged such that the cooling fluid turns ninety degrees as the cooling fluid exits the inlet section and enters the circumferentially-extending section; the cooling passageway (78, 78', 78") is arranged such that the cooling fluid turns ninety degrees as the cooling fluid exits the circumferentially-extending section and enters the outlet section; and the circumferentially-extending section is rectangular in cross-section including a width in an axial direction and a height in the radial direction greater than the width, characterised in that: the outlet section is radially-extending such that cooling fluid flowing within the outlet section flows in a radial direction. a compressor section, a combustor section, a turbine section, and at least one rotatable shaft; a seal assembly including a seal plate mounted for rotation with the rotatable shaft and a face seal in contact with the seal plate at a contact area, the seal plate including a cooling passageway (78, 78', 78") having a circumferentially-extending section radially aligned with the contact area, wherein the cooling passageway (78, 78', 78") includes: an inlet section between an inlet and the circumferentially-extending section; and an outlet section between the circumferentially-extending section and an outlet; and an inlet section between an inlet and the circumferentially-extending section; and an outlet section between the circumferentially-extending section and an outlet; and a source of cooling fluid, wherein: the seal plate is arranged such that the cooling fluid flows through the cooling passageway (78, 78', 78") from the inlet to the outlet; the cooling passageway (78, 78', 78") is arranged such that the cooling fluid turns ninety degrees as the cooling fluid exits the inlet section and enters the circumferentially-extending section; the cooling passageway (78, 78', 78") is arranged such that the cooling fluid turns ninety degrees as the cooling fluid exits the circumferentially-extending section and enters the outlet section; and the circumferentially-extending section is rectangular in cross-section including a width in an axial direction and a height in the radial direction greater than the width, the seal plate is arranged such that the cooling fluid flows through the cooling passageway (78, 78', 78") from the inlet to the outlet; the cooling passageway (78, 78', 78") is arranged such that the cooling fluid turns ninety degrees as the cooling fluid exits the inlet section and enters the circumferentially-extending section; the cooling passageway (78, 78', 78") is arranged such that the cooling fluid turns ninety degrees as the cooling fluid exits the circumferentially-extending section and enters the outlet section; and the circumferentially-extending section is rectangular in cross-section including a width in an axial direction and a height in the radial direction greater than the width,