So you have a rigid container (no change in volume) filled only with air which is exposed to a constant heat source and a constant heat flux leaving the tank, right? And you say that the temperature increases up to a certain value, after which keeps a constant profile, correct?

Do you have the properties of air set as functions of temperature? If so, are they set to extrapolate the extreme values to higher temperatures or are they set to a constant (or to an initial value) after a certain temperature? Are you using convection correlations, where the heat transfer coefficient is calculated iteratively with temperature? All of the above can contribute to the described behavior. But of course, it can depend a lot on the complexity of your system.

Initially, all of the added heat goes into increasing the internal energy and hence the temperature of the gas. But as the temperature of the gas rises further above ambient, heat loss from the gas to the ambient surrounding increases. Eventually a temperature is reached at which the gas loses heat to the surroundings as fast as heat is supplied to it --- this is the maximum attainable temperature of the gas. Insulation slows down heat loss from the gas to the surroundings and hence results in a higher maximum attainable temperature of the gas. But no insulation is perfect; hence the maximum attainable temperature of the gas remains finite even with the best insulation.

Dear Sir,

I am doing numerical simulation with FLUENT no convection or no heat loss was considered.

Even without heat losses to the surroundings, the temperature of the gas cannot rise above that of the heat source. When the temperature of the gas equals that of the heat source, equilibrium is established: a quantum of energy is equally likely to move from the heat source to the gas as vice versa.

Dear LeniN V R

Could you tell us more in detail about your calculation model, please? It's better if you show the geometric domain and its boundary condition.