Police have deployed specialised teams, including underwater divers, to search the city after Tyron Charles disappeared on September 6.
While no body has been discovered, detectives believe Mr Charles has been seriously harmed after examining evidence.
Officers on Saturday arrested a man on suspicion of the murder of the 29-year-old from Denholme.
The 28-year-old local man remains in police custody.
West Yorkshire Police today confirmed that a second man, 60, was also arrested on Monday.
An investigation was launched following Mr Charles' disappearance earlier this month, and police deployed its Underwater Search Unit.
Divers have been searching a series of locations in the Denholme area including, Doe Park Water Activities Park.
Detective Chief Inspector Jim Griffiths, of the Homicide and Major Enquiry Team, said: “We have not discovered a body, however evidence recovered from the scenes suggest that Mr Charles has come to serious harm.
“A number of scenes remain in place today as our specialist teams are continuing their enquiries to determine what has happened to Tyron. I would appeal to anyone who may have seen or heard from him on or after Wednesday September 6 or who has any information, however small it may seem, to come forward.
“Officers are in regular contact with Mr Charles’ family and supporting them at this time.”
Anyone with any information is asked to contact police via 101 quoting 13170414379.
Information can also be passed anonymously and in confidence to Crimestoppers on 0800 555 111.