A shroud assembly (210, 310) for a gas turbine engine, the shroud assembly (210, 310) configured to receive a cooling fluid flow, the shroud assembly (210, 310) comprising: a shroud support that extends arcuately about an axis; and a plurality of shroud segments that are attached to the shroud support and that are arranged annularly about the axis at different circumferential positions with respect to the axis, the plurality of shroud segments respectively including: an internal cooling passage that extends through the at least one of the plurality of shroud segments; at least one inlet for receiving and directing the cooling fluid flow into the internal cooling passage; and at least one outlet for outputting the cooling fluid flow from the internal cooling passage to an outlet chamber of the shroud assembly (210, 310); the internal cooling passage being hermetically sealed from the at least one inlet to the at least one outlet; the plurality of shroud segments (212, 312) including a first shroud segment and a second shroud segment, an intersegment joint defined circumferentially between the first and second shroud segments; further comprising a cooling flow path cooperatively defined by the shroud support and the first shroud segment, the cooling flow path including the internal cooling passage defined within the first shroud segment, the cooling flow path including the outlet chamber, which is configured to receive flow from the internal cooling passage, the outlet chamber defined between the first shroud segment and the shroud support and fluidly connected to the inter-segment joint; and further comprising a seal arrangement that extends across the inter-segment joint, wherein the seal arrangement, the first shroud segment, and the second shroud segment cooperatively define a seal chamber that is enclosed. a shroud support that extends arcuately about an axis; and a plurality of shroud segments that are attached to the shroud support and that are arranged annularly about the axis at different circumferential positions with respect to the axis, the plurality of shroud segments respectively including: an internal cooling passage that extends through the at least one of the plurality of shroud segments; at least one inlet for receiving and directing the cooling fluid flow into the internal cooling passage; and at least one outlet for outputting the cooling fluid flow from the internal cooling passage to an outlet chamber of the shroud assembly (210, 310); the internal cooling passage being hermetically sealed from the at least one inlet to the at least one outlet; the plurality of shroud segments (212, 312) including a first shroud segment and a second shroud segment, an intersegment joint defined circumferentially between the first and second shroud segments; further comprising a cooling flow path cooperatively defined by the shroud support and the first shroud segment, the cooling flow path including the internal cooling passage defined within the first shroud segment, the cooling flow path including the outlet chamber, which is configured to receive flow from the internal cooling passage, the outlet chamber defined between the first shroud segment and the shroud support and fluidly connected to the inter-segment joint; and an internal cooling passage that extends through the at least one of the plurality of shroud segments; at least one inlet for receiving and directing the cooling fluid flow into the internal cooling passage; and at least one outlet for outputting the cooling fluid flow from the internal cooling passage to an outlet chamber of the shroud assembly (210, 310); the internal cooling passage being hermetically sealed from the at least one inlet to the at least one outlet; the plurality of shroud segments (212, 312) including a first shroud segment and a second shroud segment, an intersegment joint defined circumferentially between the first and second shroud segments; further comprising a cooling flow path cooperatively defined by the shroud support and the first shroud segment, the cooling flow path including the internal cooling passage defined within the first shroud segment, the cooling flow path including the outlet chamber, which is configured to receive flow from the internal cooling passage, the outlet chamber defined between the first shroud segment and the shroud support and fluidly connected to the inter-segment joint; and further comprising a seal arrangement that extends across the inter-segment joint, wherein the seal arrangement, the first shroud segment, and the second shroud segment cooperatively define a seal chamber that is enclosed.