A few ideas,
Could be a fabricated sheet metal "flume", attached and sealed/caulked on the upstream side. Could use slotted connections on the downstream end to accomodate expansion/contraction. If you are worried about the seal on the downstream side a bearing plate sealed to the concrete deck beneath the end of the flume might enable a tight enough fit with the flume section that seepage would be minimal, yet still provide for sliding from expans/contract.