Checking energy balance within a conjugate heat transfer analysis

At times it can be important to check energy balance within a CHT simulation; for example, this should always be done as a final check before making design decisions on a system. According to Engineering toolbox (my favorite go-to engineering resource), energy transferred with a fluid can be expressed as Q = (mdot)(C_p)(DeltaT), with mdot representing mass flow rate and C_p being specific heat.

I ran a CHT simulation of the U-Type heat exchanger (one of our tutorials) to demonstrate how a hand calculations can be done to check energy balance. Result control area averages were added to all 4 inlets/outlets in the model. In order to calculate energy on each side of the heat exchanger, temperature delta needs to be calculated.

I started by calculating heat transfer on the water side of the heat exchanger. The inlet boundary condition specified a MFR of 0.01 kg/s at 10 deg C/283.15 K. Referencing the outlet side area average, the area temperature is 340.88 K. This represents a 57.73 K temperature delta. The specific heat is a material property and can be checked via the material definition; a specific heat of 4180 J/kgK was used.
(0.01 kg/s)
(4180 J/kg-K)*(57.73 K) = 2413.11 J/s = Watts.

The air side has a specified MFR of 0.2 kg/s, specific heat of 1004 J/kg-K, and a temperature delta of 12.44 K. Multiplying this together, this is 2497.95 J/s = Watts.

Comparing the two, they are about within 3-4% of each other. Although it always depends on the use case, in general I consider this good agreement and within an acceptable range. It’s also important to keep in mind several factors which will impact the accuracy of the energy balance:

  • Mesh: the result of the area average at the outlet can impact the final temperature used to calculate temperature delta across the fluid. SimScale’s area averages are not area weighed, instead it is a general average of the temperature across all cells on the outlet surface, regardless of cell size.

  • Specific heat properties: In the calculations above I assumed a constant specific heat value. In reality, specific heat varies as a function of temperature. This resource shows isobaric air specific heat as a function of temperature. Although for my analysis specific heat does not change significantly, depending on the application the changes in material properties need to be accounted for.