A turbine rotor blade (260, 602, 702, 802, 902, 1002, 1102, 1202, 1302, 1402, 1502, 1602), comprising: a platform with a first side and a second side; an airfoil extending from the first side of the platform, characterised in that it further comprises: an attachment portion (360, 660, 760, 860, 960, 1060, 1160, 1260, 1360, 1460, 1560, 1660) extending from the second side of the platform, wherein the attachment portion (360, 660, 760, 860, 960, 1060, 1160, 1260, 1360, 1460, 1560, 1660) includes first and second side surfaces and a base surface (370, 670, 770, 870, 970, 1070, 1170, 1270, 1370, 1470, 1570, 1670) on an underside of the attachment portion (360, 660, 760, 860, 960, 1060, 1160, 1260, 1360, 1460, 1560, 1660) between the first and second side surface, and wherein the base surface (370, 670, 770, 870, 970, 1070, 1170, 1270, 1370, 1470, 1570, 1670) includes at least one curved segment or angled segment, wherein the base surface (370, 670, 770, 870, 970, 1070, 1170, 1270, 1370, 1470, 1570, 1670) forms a slot cavity (450,650,750,850,950,1050,1150,1250,1350,1450,1550,1650) with a flat slot bottom (416,616,816,916,1016,1116,1216,1316,1416,1516,1616) and fluid passages with feed inlets (372-375, 472-475, 572-575, 672-675, 772-775, 872-875, 972-975, 1072-1075, 1172-1175, 1272-1275, 1372-1375, 1472-1475, 1572-1575, 1672-1675) defined in the base surface (370, 670, 770, 870, 970, 1070, 1170, 1270, 1370, 1470, 1570, 1670) in an axial row, wherein the base surface (370, 670, 770, 870, 970, 1070, 1170, 1270, 1370, 1470, 1570, 1670) is shaped such that the slot cavity (450, 650, 750, 850, 950, 1050, 1150, 1250, 1350, 1450, 1550, 1650) has a cross-sectional area that decreases along a generally axial direction from a forward end to an aft end, and wherein the feed inlets (372-375, 472-475,572-575, 572-575,672-675,772-775,872-875,972-975,1072-1075, 1172-1175, 1272-1275, 1372-1375,1472-1475,1572-1575,1672-1675) are positioned in the base surface (370,670,770,870,970,1070,1170,1270,1370,1470,1570,1670) such that a radial depth of each feed inlet (372-375, 472-475, 572-575, 672-675, 772-775, 872-875, 972-975, 1072-1075, 1172-1175, 1272-1275, 1372-1375,1472-1475, 1572-1575, 1672-1675) increases along the generally axial direction. a platform with a first side and a second side; an airfoil extending from the first side of the platform, characterised in that it further comprises: an attachment portion (360, 660, 760, 860, 960, 1060, 1160, 1260, 1360, 1460, 1560, 1660) extending from the second side of the platform, wherein the attachment portion (360, 660, 760, 860, 960, 1060, 1160, 1260, 1360, 1460, 1560, 1660) includes first and second side surfaces and a base surface (370, 670, 770, 870, 970, 1070, 1170, 1270, 1370, 1470, 1570, 1670) on an underside of the attachment portion (360, 660, 760, 860, 960, 1060, 1160, 1260, 1360, 1460, 1560, 1660) between the first and second side surface, and wherein the base surface (370, 670, 770, 870, 970, 1070, 1170, 1270, 1370, 1470, 1570, 1670) includes at least one curved segment or angled segment, wherein the base surface (370, 670, 770, 870, 970, 1070, 1170, 1270, 1370, 1470, 1570, 1670) forms a slot cavity (450,650,750,850,950,1050,1150,1250,1350,1450,1550,1650) with a flat slot bottom (416,616,816,916,1016,1116,1216,1316,1416,1516,1616) and fluid passages with feed inlets (372-375, 472-475, 572-575, 672-675, 772-775, 872-875, 972-975, 1072-1075, 1172-1175, 1272-1275, 1372-1375, 1472-1475, 1572-1575, 1672-1675) defined in the base surface (370, 670, 770, 870, 970, 1070, 1170, 1270, 1370, 1470, 1570, 1670) in an axial row, an attachment portion (360, 660, 760, 860, 960, 1060, 1160, 1260, 1360, 1460, 1560, 1660) extending from the second side of the platform, wherein the attachment portion (360, 660, 760, 860, 960, 1060, 1160, 1260, 1360, 1460, 1560, 1660) includes first and second side surfaces and a base surface (370, 670, 770, 870, 970, 1070, 1170, 1270, 1370, 1470, 1570, 1670) on an underside of the attachment portion (360, 660, 760, 860, 960, 1060, 1160, 1260, 1360, 1460, 1560, 1660) between the first and second side surface, and wherein the base surface (370, 670, 770, 870, 970, 1070, 1170, 1270, 1370, 1470, 1570, 1670) includes at least one curved segment or angled segment, wherein the base surface (370, 670, 770, 870, 970, 1070, 1170, 1270, 1370, 1470, 1570, 1670) forms a slot cavity (450,650,750,850,950,1050,1150,1250,1350,1450,1550,1650) with a flat slot bottom (416,616,816,916,1016,1116,1216,1316,1416,1516,1616) and fluid passages with feed inlets (372-375, 472-475, 572-575, 672-675, 772-775, 872-875, 972-975, 1072-1075, 1172-1175, 1272-1275, 1372-1375, 1472-1475, 1572-1575, 1672-1675) defined in the base surface (370, 670, 770, 870, 970, 1070, 1170, 1270, 1370, 1470, 1570, 1670) in an axial row, wherein the base surface (370, 670, 770, 870, 970, 1070, 1170, 1270, 1370, 1470, 1570, 1670) is shaped such that the slot cavity (450, 650, 750, 850, 950, 1050, 1150, 1250, 1350, 1450, 1550, 1650) has a cross-sectional area that decreases along a generally axial direction from a forward end to an aft end, and wherein the feed inlets (372-375, 472-475,572-575, 572-575,672-675,772-775,872-875,972-975,1072-1075, 1172-1175, 1272-1275, 1372-1375,1472-1475,1572-1575,1672-1675) are positioned in the base surface (370,670,770,870,970,1070,1170,1270,1370,1470,1570,1670) such that a radial depth of each feed inlet (372-375, 472-475, 572-575, 672-675, 772-775, 872-875, 972-975, 1072-1075, 1172-1175, 1272-1275, 1372-1375,1472-1475, 1572-1575, 1672-1675) increases along the generally axial direction.