Q:

12 v watt heater with nichrome coil

i am new here. First of all I am sorry for my bad english. 
I want a help from those who know about nichrome heater coil. I want to make a 12v dc incubator using nichrome wire as heating element, all I need is to produce almost 40 degree celsius in my styrofoam box. For this, how much length nichrome required? Which gauge ? How much watt does it consume? ( To know the the approximate backup time from a 12v 9ah battery) . How to calculate these things? Please help me.

i think if i connect a small length (small resistance) nichrome to 12v battery, most of the volt dropped in internal resistance of the battery, that will drain battery fast. If i connect a long nichrome to the 12v battery, most of the volatge dropped in the nichrome , but it will reduce the current ( look like a 12v bulb lighting with a 6v source). So at a specific length of nichrome that will produce 40'c heat efficiently. Hiw to find that length? That is my question.

A:

You don't have to deal with nichrome wire if you stay within the temperature limits of standard resistors, and 40°C stays within these easily. Buy a power resistor. The needed power depends on the heat loss. Calculate that first.
$$\dot{Q} = \lambda\cdot \frac{A}{d}(\vartheta_{1}-\vartheta_{2})$$
$$\lambda: \mathrm{thermal\ conduction\ coefficient\ of\ styrofoam}$$
$$A: \mathrm{surface\ area\ (on\ the\ outside\ for\ being\ on\ the\ safe \ side)}$$
$$d: \mathrm{distance\ (thickness\ of\ styrofoam\ wall)}$$
$$\vartheta: \mathrm{temperature\ (highest\ inside\ -\ lowest\ outside)}$$

