Amina Al-Jeffery, 21, from Swansea, who has dual British and Saudi Arabian nationality, claims Mohammed Al-Jeffery locked her up after she "kissed a guy".
Her lawyers have taken legal action in London in a bid to protect her but her father has denied the claims.
The judge said a ruling on the case would be issued in public.
Barristers Henry Setright QC and Michael Gration, representing Miss Al-Jeffery, have asked Mr Justice Holman to look at ways of coming to her aid.
The judge has been analysing the case in the Family Division of the High Court in London and the hearing ended late on Thursday.
Lawyers are due to file final documentation on Monday and Mr Justice Holman is scheduled to deliver a ruling on Wednesday.
Mr Justice Holman has said there are reasons to be very concerned about Miss Al-Jeffery's welfare.
And he rejected an application from Mr Al-Jeffery for restrictions to be placed on what journalists can report.
The judge has been told Miss Al-Jeffery left Swansea and moved to Saudi Arabia at her father's insistence four years ago.
He has heard that Miss Al-Jeffery's mother and siblings are back in south Wales.
Neither Miss Al-Jeffery nor her father, an academic who is in his 60s, have been at the court hearing.
Barrister Marcus Scott-Manderson QC, representing Mr Al-Jeffery, told Mr Justice Holman at the end of proceedings on Thursday that Mr Al-Jeffery wanted "reporting restrictions".
But Mr Justice Holman said: "No. Afraid not."
He said there were good reasons for staging the hearing in public - even though it was in a family court - and allowing journalists to report freely.
Mr Justice Holman said the case involved the welfare of an adult who was a British citizen.
"I happen to think that the case raises issues that require to be ventilated in public," said the judge.
"I dare say the publicity is extremely disagreeable to the father."

The Hoyer Group's diesel carrier came to a halt on the northbound hard shoulder at junction 16 for Stoke-on-Trent at about midday but the rear later burst into flames.
The motorway has reopened with one northbound lane closure and there are delays, said North West Motorway Police.
The driver of the tanker was unharmed.
A Hoyer Group spokesman said: "A detailed investigation will be undertaken to establish the cause of the incident and any learnings."

The three Grade II-listed thatched houses at Silvergate caught fire late on Saturday afternoon.
Norfolk Fire and Rescue Service incident commander Simon Mason said crews may remain at the scene for a second night.
A National Trust spokeswoman thanked firefighters who "worked tirelessly".
Residents from two houses have gone to stay with family and friends, while the third family has been re-homed in a holiday cottage, the National Trust said.
"We do not know the cause or full extent of the fire yet but, most importantly, there have been no reports of any injuries and all of the tenants were able to get out of the cottages," said the trust's spokeswoman.
"We are enormously grateful to the crews who reached the cottages quickly, worked tirelessly to tackle the fire and have maintained a constant presence."
About 70 firefighters attended the blaze as it ripped through the roofs of the cottages.
"We expect to be on the scene for the remainder for the day and maybe over the night," said Mr Mason.
An investigation into the cause of the fire has been launched.
A father accused of imprisoning his daughter at their home in Saudi Arabia has failed in a bid to limit reporting of the case.
[NEXT_CONCEPT]
A fuel tanker broke down and then caught fire forcing the closure of a stretch of the M6 in Staffordshire.
[NEXT_CONCEPT]
Three families lost their homes when fire engulfed a row of National Trust cottages on the Blickling estate in Norfolk.