Oesophagus is not deemed incorrect, however esophagus is recognised as a more common version of spelling the food pipe.
Esophagus is an important organ in vertebrates. It helps the food to pass from pharynx to stomach. It is a muscular tube and usually 25 to 30 cm long. It associates mouth to stomach. It can be divided into three parts that are cervical, thoracic and abdominal. The wall of esophagus are lined with muscles which have the ability to contract and relax. Esophagus passes food by relaxation and contraction of the muscles to the stomach, this process is known as peristalsis. The arteries and veins of the esophagus are called esophageal arteries and esophageal veins respectively.
It is spelled esophagus. You can find it in a any dictionary.