First, a geographic correction: Knoxville is in Tennessee, not Iowa. There is a Knoxville, Iowa (Marion County, population ~7,000), but the Knoxville relevant to Tennessee travel is the state's third-largest city, ~180 miles east of Nashville.
Distance: ~180 miles (290 km)
Drive Time: 2.75–3.25 hours via I-40 West
Route: Direct interstate the entire way. Crosses the Cumberland Plateau (Monteagle Mountain—steep grades, truck lanes).
If you did mean the Iowa Knoxville:
Distance: ~650 miles (1,045 km)
Drive Time: 9.5–10.5 hours via I-80 East → I-74 East → I-57 South → I-24 West
Route: Crosses Mississippi River at Quad Cities, traverses Illinois, enters Tennessee at Memphis, then I-40 East to Nashville.
Context clue: The Tennessee Knoxville is a major city (UT Vols, 1982 World's Fair, Gateway to Smokies); the Iowa Knoxville is a charming county seat. Odds are 99:1 you meant Tennessee.