How important is a hot fluid temperature in a heat exchange?

Question

Please consider an air to air heat exchanger.

On one side, we have 200°C hot air entering the heat exchanger, and leaving it at 150°C. And on the other side, we have 15°C fresh air to the inlet. Temperature is increased up to 130°C to the outlet.

So, hot air temperature difference is 50°C and cold air temperature difference is 115°C.

Considering this formula: $$\dot{Q} = \dot{m}_{hot}\cdot C_{hot}\cdot (T_{hot1}- T_{hot2}) = \dot{m}_{cold}\cdot C_{cold}\cdot (T_{cold2} - T_{cold1}) $$

$\dot{Q}$ = heat exchange rate in W
$\dot{m}$ = mass flowrate in m/s
C = specific heat
T1 = temperature in
T2 = temperature out

I wonder what would be the resulting temperature of cold air on exit if hot air temperature would be 250°C in and 200°C out. This formula would give me 130°C or so in any case since only the difference between temperature in and temperature out matters.

I think that C depends of the temperature but it seems to not vary that much to make a real difference in the resulting temperature.

Answer 1

The specific heat of gases does change with temperature. The higher the temperature, the higher the specific heat. But from 200°C to 250°C, there won't be a significant change in its specific heat value. So we can just stick with the formula using nominal specific heat values to find the exit temperature of cold air. Also, for gases, there are two specific heat values; specific heat at constant pressure, $C_p$, and specific heat at constant volume, $C_v$. Usually, in heat exchangers, we use $ C_p $ to calculate heat transfer.

You can refer to this link to get an idea of how specific heat changes with temperature: Specific Heat Capacities of Air

Hope this helped.

Answer 2

There is indeed a temperature dependence for heat capacity with air. The temperature dependence is even more significant if there is humidity in the air.

However, in this example, there is no mention of the actual flow rates that can have an effect on the in and out temperatures of a heat exchanger.

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heat exchanger and mass rates.

However, for a heat exchanger calculations, the boundary that heat is exchanged is the exchange surface area A. The heat that is lost through one fluid ($\dot{q}_{hot} $) and its transmitted through the area A ($\dot{q}_{A} $)is gained by the fluid on the other side $\dot{q}_{cold} $. I.e.

$$\dot{q}_{hot} = \dot{q}_{A} =\dot{q}_{cold} $$

So the heat exchange is rate (i.e. the power) is limited by the material and the design of the heat exchanger. Pumping more hot or cold fluid can affect the exit conditions.

In real life applications:

• mass flow rates for hot and cold
• input and output temperatures for hot
• input and output temperatures for cold

can all be design variables that can be used for the design and the operation of the heat exchanger.

E.g.: for an heating application, that the input temperature of the hot is known and the input and output temperature of the cold is known, changing the mass flows will affect the output temperature of the hot.

However, there is no restriction that the masses must be the same. More specifically, in a unit of time the masses involved can be vastly different.