Batch Cooling Heat Duty Calculator | Unsteady State Heat Transfer
Batch Cooling Calculator
Unsteady-State Heat Transfer Analysis (WellβMixed Batch + Constant UΒ·A)
1. Batch Properties
Preset fills Cp and density. Verify at operating temp.
kg
kJ/kgΒ·K
kg/mΒ³
kW
2. Cooling Target
Β°C
Β°C
Optional: Latent Load
kJ/kg
kg
3. Cooling System
Β°C
Β°C
kJ/kgΒ·K
kg/mΒ³
Optional: Heat Transfer Coeff (U)
W/mΒ²K
mΒ²
-
min
Cooling Performance
--
Cooling Time
--
Peak Duty
--
Avg Duty
Temperature Profile (Exponential Decay)
Detailed Analysis
| Total Heat Removed | -- |
| Sensible Heat | -- |
| Latent Heat | -- |
| Heat Generated | -- |
| Effective UA (FΒ·UΒ·A) | -- |
| Rep. Coolant Temp | -- |
| Steady State Tss | -- |
| Est. Coolant Flow | -- |
| Required UA (Design) | -- |
Note: Flow estimate based on Average Duty and Coolant
ΔT.
Technical Notes
Variable Definitions
- M: batch mass (kg).
- Cp: batch specific heat (kJ/kgΒ·K).
- MCp: thermal capacitance (kJ/K) = MΒ·Cp.
- T0, Tf: initial and target batch temperatures (Β°C).
- Tc: representative coolant temperature (Β°C). This tool uses (Tc_in + Tc_out)/2.
- qΜgen: internal heat generation (kW).
- U: overall heat transfer coefficient (W/mΒ²Β·K).
- A: heat transfer area (mΒ²).
- F: effectiveness/correction factor (β).
- UA: effective conductance (kW/K) = (U/1000)Β·AΒ·F.
- Tss: steady-state temperature where cooling equals heat generation.
Formulas / Logic
- Well-mixed batch model: MCpΒ·dT/dt = βUAΒ·(T β Tc) + qΜgen.
- Steady state: Tss = Tc + qΜgen/UA.
- Temperature profile: T(t)=Tss+(T0βTss)Β·exp(βUAΒ·t/MCp).
- Cooling time to target: t = (MCp/UA)Β·ln[(T0βTss)/(TfβTss)].
- Sensible heat removed: Qsens = MCpΒ·(T0βTf) (kJ).
- Latent heat (optional): Qlat = mlatΒ·hlat (kJ).
- Heat generated: Qgen=qΜgenΒ·t (kJ, with kWΒ·s β kJ).
- Average duty: QΜavgβ(Qsens+Qlat)/t + qΜgen.
- Coolant flow estimate: αΉc=QΜavg/(Cp_cΒ·ΞT_c) (kg/s).
Model corresponds to a lumped-capacitance batch (perfect mixing) with
constant UA and constant coolant temperature represented by Tc_mean.
Use as a screening/design tool.
Assumptions / Notes
- Batch is well mixed (uniform temperature). If stratified, actual time may differ.
- UA is constant. In reality, U can vary with viscosity, fouling, agitation, and coolant flow regime.
- Coolant temperature is represented by mean of inlet/outlet (valid for small ΞT or roughly constant overall conditions).
- Feasibility requires Tf > Tss. If heat generation is high, target may be unreachable without higher UA or lower coolant temperature.
- Latent heat is treated as a lumped load added to total heat removed; it does not change the exponential profile.
Standards / References
- Standard unsteady-state energy balance for well-mixed tanks (lumped parameter heat transfer).
- Heat transfer coefficient ranges are engineering screening values; confirm with process/mechanical design standards and vendor data.
- For detailed design, consider transient simulation or rigorous exchanger/jacket models if required by project standards.