The director of health and human services, in respect to institutions under the director’s control, and the director of the department of corrections, in respect to the institutions under the department’s control, may send any inmate, student, or patient of an institution, or any person committed or applying for admission to an institution, to the university of Iowa hospitals and clinics for treatment and care. The department of health and human services and the department of corrections shall respectively pay the traveling expenses of such patient, and when necessary the traveling expenses of an attendant for the patient, out of funds appropriated for the use of the institution from which the patient is sent.