Which nursery? What species of walnut?

Sunset Western Garden book only lists one for Zone 13, the native Arizona walnut. Anything else is going to have a hard time, because even the AZ native walnuts barely make it here. They are better in higher altitudes ... like Walnut Canyon.

As a former walnut farmer in California I want you to take it back to the nursery and get your money back. Walnuts will not grow in the valley here and give you a crop. The sun will actually sunburn the fruit. These guys make me mad. I have of course seem almonds and pecans, and oddly enough even pistachio trees growing here. Pecans take the heat the best. Sorry this guy did this to you.

I tried a variety called Pedro here in Coachella valley. It struggled it's first year, died back to the root stock the second. The root stock keeps barely making it now for 2 more years but next time I want to plant something there, I'll be digging out what's left.
If you want a good nut tree, try Mahan Pecan. Western Schley is a good second for pollination but Mahan is self fertile so another tree is not required. They require a little work to get them started, but they do well in our deserts. There was a grove of them here for 50 years till the developers cut it down and I have one tree that's doing fine.
To get them started watch your water very carefully. If they get dry even one time, they shut down at that point and won't grow any more that year. Of course you can't over water either or you will get root rot, so extra care to get the water just right.
Also the same day, the same hour you plant it, paint the bark with white paint. This is a MUST with our intense sun.
Good luck.

Keep in mind that both ash trees and pecans are extremely high water users. If you are willing to keep up with their ever increasing thirst why not try a tree that will give something back - like pecan or deciduous fruit (peach, apricot, apple).

Here's a list of trees that have been proven to produce well here in the low desert.

Here is a link that might be useful: Deciduous fruits and nuts for the low desert