# Heat transfer problem

## Main Question or Discussion Point

Hi all,

I am currently considering a heat transfer problem. In this problem a rectangular vessel made of stainless steel is heated by a surrounding jacket with hot combustion flue gases flowing through it. This means that the heating of the rectangular vessel is achieved primarily through conductive heat transfer through the outer wall of the vessel. The vessel is filled with reactants with the hope of raising the temperature inside the vessel to a minimum temp required for reaction to proceed. What I am trying to calculate is whether the energy required for the reaction to proceed can be provided by the hot gases circulating the vessel, and what the temperature inside the vessel would be?

Now, the energy content of the hot flue gases is 12 MJ/kg, while the enthalpy for reaction of the reactants is 1 MJ/kg. The flowrate of the flue gases is 1.86 kg/hr, which corresponds to 0.006 MW. The flowrate of the reactants is 3 kg/hr, which means that the 0.0009 MW is required for the reaction to proceed. This suggested that there is sufficient energy for the reaction to proceed.

What I am unsure to do however is to estimate the heat loss by conduction through the vessel wall, as I do not know what the temperature inside the vessel is. How do I estimate/calculate the temperature inside the vessel in order to calculate the heat loss? I can assume that the temperature of the hot gases is 1473 K, the heat transfer area is 0.3 m^2, the length is 1.5 m, the thickness is 0.003 m, and the thermal conductivity is 25 W/mK.

Cheers,
Dave

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russ_watters
Mentor
What I am unsure to do however is to estimate the heat loss by conduction through the vessel wall, as I do not know what the temperature inside the vessel is. How do I estimate/calculate the temperature inside the vessel in order to calculate the heat loss? I can assume that the temperature of the hot gases is 1473 K, the heat transfer area is 0.3 m^2, the length is 1.5 m, the thickness is 0.003 m, and the thermal conductivity is 25 W/mK.
I'm not following: if the vessel is jacketed, it is gaining heat through the wall, not losing it, right?

I'm not following: if the vessel is jacketed, it is gaining heat through the wall, not losing it, right?
Hi Russ, yes you are right. My fault there.

Chestermiller
Mentor
If you are going to do this right, you need to take into account the kinetics of the reaction. Any info about that?

If you are going to do this right, you need to take into account the kinetics of the reaction. Any info about that?
The actual reaction that we are trying to achieve is pyrolysis. The biomass, which is situated inside the vessel, is heated to elevated temperatures where it undergoes thermal decomposition to give various solid, condensable, and non-condensable products. Given the complexity of the pyrolysis reaction, I would only be able to provide rough estimates from literature values.

CWatters
Homework Helper
Gold Member
+1 but perhaps start by assuming steady state....

You appear to be able to calculate the power leaving the vessel via the reaction products. To calculate the temperature gradient between gas and reactants you would also need to know the thermal conductivity between the two. Might be able to measure that at lower temperatures.

+1 but perhaps start by assuming steady state....

You appear to be able to calculate the power leaving the vessel via the reaction products. To calculate the temperature gradient between gas and reactants you would also need to know the thermal conductivity between the two. Might be able to measure that at lower temperatures.
Hi there, are you referring to the thermal conductivity of the wall? I have assumed a value of 25 W/mK for stainless steel. I can also assume an air boundary on either side of the wall. This allows me to calculate Q = k*A*(dT/x), where x is the thickness. What I am unsure of is how to interpret the value from this calculation to calculate the T inside the reactor. In order to use the previous equation I have to assume a temperature on the other side of the wall anyway.

CWatters
Homework Helper
Gold Member
Hi there, are you referring to the thermal conductivity of the wall? I have assumed a value of 25 W/mK for stainless steel. I can also assume an air boundary on either side of the wall. This allows me to calculate Q = k*A*(dT/x), where x is the thickness. What I am unsure of is how to interpret the value from this calculation to calculate the T inside the reactor. In order to use the previous equation I have to assume a temperature on the other side of the wall anyway.
Rearrange to get dT. The inside is that much cooler than the outside temperature.

Rearrange to get dT. The inside is that much cooler than the outside temperature.
In order to do this I would need to know Q, which in this case is the heat transfer by conduction. All I know in this problem is the dimensions and material of the wall separating the two regions, the power of the flow in the hot zone (W), and the power required for the reaction (W) from calculating the enthalpy of reaction and the flowrate.

I just want to clarify that this is not a homework problem. I am considering a real world problem and may be missing some necessary information to calculate the inside temperature.

CWatters
Homework Helper
Gold Member
In order to do this I would need to know Q, which in this case is the heat transfer by conduction.
I thought you might calculate that from info about the reactants..

Now, the energy content of the hot flue gases is 12 MJ/kg, while the enthalpy for reaction of the reactants is 1 MJ/kg. The flowrate of the flue gases is 1.86 kg/hr, which corresponds to 0.006 MW. The flowrate of the reactants is 3 kg/hr, which means that the 0.0009 MW is required for the reaction to proceed.
but I think you would also need to know the flow and return temperature of the reactants and their specific heat capacity.

Chestermiller
Mentor
Is this a batch process, or a continuous flow process? What is the composition of the flue gas? Can you please provide a diagram of the system?