Upto the critical radius of insulation, added insulation will increase heat loss.

Explanation:
In order to understand why added insulation increases heat loss up to the critical radius, let's first understand the concept of critical radius of insulation.

Critical radius of insulation:
The critical radius of insulation is the radius at which the total heat loss from a system is minimum. Beyond this critical radius, adding more insulation will actually increase the heat loss.

Now, let's analyze each option to determine the correct answer:

a) Convection heat loss will be less than conduction heat loss:
This statement is not necessarily true. Convection and conduction heat loss depend on various factors such as temperature difference, surface area, and thermal conductivity. The relationship between convection and conduction heat loss is not directly related to the critical radius of insulation.

b) Heat flux decrease:
Heat flux is the rate of heat transfer per unit area. As we add insulation, the heat flux decreases because the insulation material acts as a barrier to slow down heat transfer. This statement is true, but it does not directly relate to the critical radius of insulation.

c) Added insulation will increase heat loss:
This statement is correct. Up to the critical radius of insulation, adding more insulation will actually increase the heat loss. This is because the added insulation increases the surface area of the system, which results in more heat loss. Additionally, the insulation material itself may have some thermal conductivity, leading to heat transfer through conduction.

d) Added insulation will decrease heat loss:
This statement is incorrect. Adding insulation will only decrease heat loss beyond the critical radius.

Therefore, the correct answer is option 'C' - added insulation will increase heat loss.

To summarize, up to the critical radius of insulation, adding more insulation will increase heat loss. This is because the added insulation increases the surface area and may conduct heat. Beyond the critical radius, adding more insulation will not provide any significant benefit in reducing heat loss.