We know in connection whth the intake of food another sensation,called appetite.

暂时延迟回答，让我们先来回忆一下，除了饥饿之外我们还知道与摄入食物有关的称作胃口的另一感觉。
（可把 in connection with the intake of food 这个介词短语看作是another sensation 定语）

这句没错。只不过语序变了，这样写写你看明白不。

...besides hunger we know another sensation in connection with the intake of food...

在这里another sensation 充当know的宾语, called appetite是补语，in connection with the intake of food是修饰宾语的，大部分时候是后置的，此处例外。

至于为何要这样写，我想是为了使句子连贯紧凑。这样写sensation 可以和appetite 连在一起，也起到了强调appetite的作用。不然，按照我们中国人写英语的模式：十有八九写成 ...we know another sensation called appetite, which is in connection with the intake of food...真是既冗长又失去重点。

in connection with the intake of food 是another sensation 的定语，called appetite也是sensation 的定语。可以这么写，besides huger we know another sensation that connection with the intake of food,called appetite.
sensation 在定语从句在作主语，按理应当加that，这句子有些错误。