Introduction:
The critical radius of insulation refers to the point at which the addition of insulation to a system results in an increase in heat loss. This concept is important in the field of thermal insulation, as it helps determine the optimal thickness of insulation for minimizing heat transfer.

Explanation:
When discussing the critical radius of insulation, it is essential to understand the mechanisms of heat transfer involved, namely conduction and convection.

Conduction heat loss:
Conduction is the transfer of heat through a solid material by molecular collisions. In the context of insulation, conduction heat loss occurs when heat is conducted through the insulation material itself. As the thickness of insulation increases, the conduction heat loss decreases due to the increased resistance to heat flow. This is because thicker insulation provides a longer path for heat to travel, reducing the rate of heat transfer.

Convection heat loss:
Convection is the transfer of heat through a fluid medium, such as air or water, by the movement of the fluid itself. In the case of insulation, convection heat loss occurs when heat is transferred from the warmer side of the insulation to the cooler side through the movement of air or other fluid.

Explanation of options:
a) Convection heat loss will be less than conduction heat loss:
This statement is incorrect. Convection heat loss is typically higher than conduction heat loss in insulation systems. This is because the movement of air or fluid can result in higher heat transfer rates compared to conduction through a solid material.

b) Heat flux will decrease:
Heat flux refers to the rate of heat transfer per unit area. As the critical radius of insulation is approached, the heat flux tends to decrease. This is because the addition of insulation reduces the temperature gradient across the insulation, resulting in a lower heat transfer rate.

c) Added insulation will increase heat loss:
This statement is correct. Once the critical radius of insulation is reached, the addition of more insulation will actually increase heat loss. This is because the increased thickness of insulation leads to a higher surface area for convection heat transfer. The movement of air or fluid around the insulation becomes more pronounced, resulting in increased heat loss.

d) Added insulation will decrease heat loss:
This statement is incorrect. As explained above, the addition of insulation beyond the critical radius will actually increase heat loss through convection.

Conclusion:
In conclusion, the correct statement is that the addition of insulation will increase heat loss once the critical radius is reached. Beyond this point, the increased thickness of insulation leads to higher convection heat transfer, resulting in increased heat loss.