You are perhaps thinking of Farnham’s Freehold.
Hugh Farnham is a practical, self-made man, and when he sees the clouds of nuclear war gathering, he builds a bomb shelter under his house, hoping for peace and preparing for war. But when the apocalypse comes, something happens that he did not expect. A thermonuclear blast tears apart the fabric of time and hurls his shelter into a world with no sign of other human beings.
Farnham and his family have barely settled down to the backbreaking business of low-tech survival when they find that they are not alone after all. The same nuclear war that catapulted Farnham 2,000 years into the future has destroyed all civilization in the northern hemisphere, leaving Africans as the dominant surviving people.
In the new world order, Farnham and his family, being members of the race that nearly destroyed the world, are fit only to be slaves (or dinner). After surviving a nuclear war, Farnham has no intention of being anyone’s slave, but the tyrannical power of the Chosen race reaches throughout the world. Even if he manages to escape, where can he run to?
https://www.amazon.com/Farnhams-Freehold-audiobook/dp/B0056A41SG/ref=sr_1_1
Ferdinand Feghoot always whetted my appetite.