I too recently bought a new Dell laptop. Whilst the fan is audible, it shouldn't make a noise like an airplane!
I take it you've checked that there's nothing obstructing or stuck in the air inlet and outlook vents? If so, there's nothing else you can do to it yourself. You need to contact Dell, if you bought it direct from them, or otherwise the seller you bought it from.
If from Dell, speak to their customer support. They're very good. I can't remember the exact guarantee terms, but for a new laptop I'd be surprised if they don't arrange an express courier service to send it back and fix it. You're possibly even entitled to reject it if it's brand new, but you may not want to do so if you've already installed stuff on it.
If it was another seller let's hope that they give proper after-sales service. If it was an eBay seller let us know if you have any problems. Don't let them mess you about. If you want, you're entitled to return it for a full refund if still within eBay's 30 day money back guarantee. The seller would have to send you a prepaid return label.
