This may be him:

William H. Black

Residence Rockbridge County VA;
Enlisted on 5/14/1862 at Churchville, VA as a Private.
On 5/14/1862 he mustered into "H" Co. VA 14th Cavalry
He died of disease on 3/9/1863 at Alton, IL
(Died of diarrhoea)
He was listed as:
* POW 11/26/1862 Greenbrier County, WV
* Confined 11/28/1862 Wheeling, WV (Estimated day)
* Confined 12/1/1862 Camp Chase, OH (Estimated day)
* Confined 1/15/1863 Alton, IL (Estimated day)
He was described at enlistment as:
6', florid complexion, grey eyes, light hair
Other Information:
born in 1842
Buried: Alton, IL
(Brother of David S. Black.)

Sources used by Historical Data Systems, Inc.:
- The Virginia Regimental Histories Series

…………………………

William H. Black, Private, Company H, 14th Regiment Virginia Cavalry, enlisted May 14, 1862 at Churchill for the war, captured November 26, 1862 in Greenbrier Co., Va., received at the Military Prison at Wheeling, Va., (Atheneum Prison), 20 year old Farmer, 6’, florid complexion, gray eyes, light hair, resident of Rockbridge, Va., transferred December 6 to, Camp Chase, Ohio, received Alton Military Prison, Illinois January 10, 1863,, died March 9, 1863, Chronic Diarrhea

Compiled Service Records of Confederate Soldiers Who Served in Organizations from the State of Virginia