Engineering
Heat Exchanger Calculator — PHE Duty, LMTD & Area
Calculate plate heat exchanger (PHE) duty, Log Mean Temperature Difference (LMTD), and required heat transfer area. Free dairy engineering calculator.
Formula
(flowRate / 3600) * specificHeat * 1000 * (outletTemp - inletTemp)
flowRate
Fluid Flow Rate (kg/hr)
specificHeat
Specific Heat (Cp) (kJ/kg·K)
inletTemp
Process Fluid Inlet Temperature (°C)
outletTemp
Process Fluid Outlet Temperature (°C)
hotInlet
Hot Fluid Inlet Temperature (°C)
hotOutlet
Hot Fluid Outlet Temperature (°C)
uValue
Overall Heat Transfer Coefficient (U) (W/m²·K)
Worked Example
1
Given:
flowRate = 20000
hotInlet = 76
hotOutlet = 74
inletTemp = 4
outletTemp = 72
specificHeat = 3.9
uValue = 3000
2
Apply the formula:
(flowRate / 3600) * specificHeat * 1000 * (outletTemp - inletTemp)
3
Result:1518 kW1518 °C1518 m²
What is a Plate Heat Exchanger (PHE)?
A Plate Heat Exchanger (PHE) transfers heat between two fluids (typically milk and hot water) across thin corrugated metal plates. PHEs are the standard heat transfer equipment in dairy plants for pasteurization, preheating, cooling, and regeneration.
How to Use This Calculator
- Enter hot fluid inlet and outlet temperatures (°C) — typically hot water
- Enter cold fluid inlet and outlet temperatures (°C) — typically milk
- Enter the fluid flow rate (L/hr or kg/hr)
- Enter the specific heat of the fluid (default: 3.9 kJ/kg·K for milk)
- Enter the overall heat transfer coefficient U (W/m²·K)
- The calculator computes heat duty (Q), LMTD, and required area (A)
Key Formulas
Heat Duty (Q)
Q (kW) = ṁ × Cp × ΔT
Where:
- ṁ = mass flow rate (kg/s)
- Cp = specific heat (kJ/kg·K)
- ΔT = temperature difference of process fluid (T_out − T_in)
Log Mean Temperature Difference (LMTD)
For counter-current flow:
LMTD = (ΔT₁ − ΔT₂) / ln(ΔT₁/ΔT₂)
Where:
- ΔT₁ = Hot fluid inlet − Cold fluid outlet
- ΔT₂ = Hot fluid outlet − Cold fluid inlet
Required Heat Transfer Area (A)
A (m²) = Q / (U × LMTD)
Typical U Values for Dairy PHE
| Application | U (W/m²·K) |
|---|---|
| Milk–water (pasteurization) | 2,000–4,000 |
| Milk–milk (regeneration) | 1,500–3,000 |
| Milk–CIP water | 2,000–3,500 |
| Cream–water | 1,500–2,500 |
| Whey–water | 1,800–3,200 |
Specific Heat Values
| Fluid | Cp (kJ/kg·K) |
|---|---|
| Water | 4.18 |
| Whole milk | 3.85–3.93 |
| Skim milk | 3.95–4.00 |
| Cream (40% fat) | 3.20–3.50 |
| Whey | 3.90–4.00 |
Example Calculation
Pasteurize 20,000 L/hr of milk from 4°C to 72°C using hot water at 76°C returning at 74°C (counter-current):
- ṁ = 20,000 / 3600 × 1.032 kg/L = 5.73 kg/s
- Cp of milk = 3.9 kJ/kg·K
- ΔT (milk) = 72 − 4 = 68°C
Q = 5.73 × 3.9 × 68 = 1,518 kW
LMTD calculation:
- ΔT₁ = 76 − 72 = 4°C
- ΔT₂ = 74 − 4 = 70°C
- LMTD = (4 − 70) / ln(4/70) = 18.5°C
Required area (U = 3,000 W/m²·K): A = 1,518,000 / (3,000 × 18.5) = 27.3 m²
Design Considerations
- Fouling factor: Add 15–20% safety margin on area for milk fouling
- Pressure drop: Typically 0.5–2.0 bar across PHE; check pump capacity
- Regeneration efficiency: Modern PHEs achieve 92–96% heat recovery
- Gasketing: Use EPDM gaskets for dairy; NBR for CIP chemicals