ANS:C - goes through a minimum.

As the difference between the wall temperature and bulk temperature increases, the boiling heat transfer coefficient typically goes through a maximum before decreasing. When the temperature difference is small, the boiling heat transfer coefficient increases as the temperature difference increases. This is because a higher temperature difference promotes more vigorous boiling and convective motion within the fluid, leading to increased heat transfer. However, as the temperature difference continues to increase, it reaches a point where the boiling becomes more violent and can lead to the formation of a vapor film layer around the heated surface. This vapor film layer acts as an insulating barrier, reducing the heat transfer coefficient. Therefore, beyond a certain point, further increases in the temperature difference result in decreasing boiling heat transfer coefficients. So, the correct option is: goes through a maximum.