The term private cloud is rather confusing with all the definitions in different websites. Different people have different opinions on what is a private cloud.
1) As an aside, it should be noted that an increasing number of IT companies are also starting to use the term "private cloud" to refer to the building of a cloud computing infrastrucuture -- or "internal cloud" -- within a company's own data centre. Such a development is not really cloud computing at all, and may be regarded as a last-ditch attempt to maintain the status quo. Under any sensible definition, a "private cloud" has to be a cloud computing arrangement where the hardware concerned is owned and housed in a vendor's shared data centre" source:www.explainingcomputers.com/cloud.html
2) "Cloud" is simply a trendy term for "on someone else's computer". (That, by the way, is also a great handy way of deciding whether or not it's a good idea to move something to the cloud or not.) If you run processes on computers owned by someone else who has a data center specifically for providing this service, that's the cloud. Virtualization is not strictly necessary, but usually done because it's a better deal for the cloud provider.
A private cloud is the same except that your company also owns the data center (or maybe owns the company that owns the data center). Theoretically, if you're a customer of Amazon's cloud services, and one day you get really, really rich and buy Amazon wholesale, you've moved from cloud usage to private cloud usage without anything else changing.https://softwareengineering.stackexchange.com/questions/257952/who-provides-hardware-resources-in-private-cloud
Some of my lecture notes says that cloud computing does not exist without virtualization. But none of the above answers states that a private cloud has to use virtualization.There are also many different versions of answers for the same question. It is not easy to grab an understanding of such a term when different people interpret it in different ways.