Whatsapp by default doesn't allow us to send messages without saving a mobile number in your contacts. However, often we need to send whatspp messages to persons whose mobile number we don't intend to save in our phone's contacts.
So, here is a nifty trick. Open the browser in your phone (preferably Chrome) which has Whatsapp installed in it. In the address bar just type : wa.me/ followed by the country code without + sign, followed by the mobile number to which you intend to send the message.
For instance, to send a whatsapp message to a mobile no. in India, say, 98048XXXXX (with India's country code being +91), one needs to type wa.me/9198048XXXXX in the address bar of the browser and tap on the result as shown in the screenshot below :
You will then be redirected to a screen which will look like the screenshot as under.
Click on 'Message' button and you are all set for the Whatsapp chat with the unsaved contact number.