The Model 13 is built on the K frame regardless of the N marking.
The model 65 is built on the K frame.
Find a copy of the Standard Catalog of Smith and Wesson, sn data is in it.
Check the butt and crane area of the frame.
Look on frame inside the cylinder area to find the model number of a Smith and Wesson 357 mag snub 2 in stainless barrel
You have a fixed sight K frame. You will have to call S&W to find out the exact model.
Standard catalog of Smith and Wesson by supica and nahas
It is a J frame.
Call Smith and Wesson with the serial number and the will tell you.
Go to Smith and Wesson's website and they will send you one for free.
Compare it to known examples.
62092
You will have to find a copy of The Standard Catalog of Smith and Wesson and check each model number.