当天无时的英语表达是 be on duty for the day或 that very day。这些短语都指在同一天内发生的事情。例如：

1. 请在当天晚上前来领取您的奖品。[Please come to pick up your prize on the same day in the evening.]

2. 他在当天被逮捕了。[He was arrested on that day.]