A closed cubical box made of perfectly insulating material has walls of thickness t...the only way for heat to enter or leave the box is through the solid cylindrical metallic plugs each of cross sectional area A and length t fixed in opp. walls of the box. A source of energy generating heat is enclosed inside the box .Left side of the box is at 100 degree celsius and right side at 4 degree celcius....I want to ask THE DIRECTION OF HEAT FLOW....(Will the heat flow out towards 100 degrees region also?)

Pls help...

In this case we can not say that where the heat will flow as temp inside the box is not known but the must condition is that

rate of heat generation = heat flow rate from box to 100 degreeC region + heat flow rate from box to 4 degreeC region

Initially you can solve the question by taking inner temp greater than 100 in this case.

If you assume that inner temp is less than 100 than the condition becomes

rate of heat generation + heat flow rate from box to 100 degreeC region = heat flow rate from box to 4 degreeC region

by these conditions you can find the temp inside the box and tell the correct direction of flow.

Basically you have to assume the direction yourself innitially, and put the condition according to that, the answer will come same in both the cases. When you have found the temp in the box from above conditions you can tell the direction of heat flow correctly only then.