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Maximum Possible Heat Transfer (Qmax)

Q˙max=m˙mincmin(Th,in−Tc,in)\dot{Q}_{max} = \dot{m}_{min} c_{min} (T_{h,in} - T_{c,in})

Worked example: 0.9 kg/s air, 200 C gas against 25 C air → Qmax 158.3 kW — press Try an example to run it live, then adjust anything.

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Maximum Possible Heat Transfer (Qmax) explained

ṁcminTh,inTc,inQmax

Before asking how well an exchanger performs, you have to know what perfection would look like. Q̇max is that reference: an infinitely long counterflow unit in which the limiting stream is brought all the way to the other stream's inlet temperature. Only the minimum capacity rate may be used — if you used the larger one, the smaller stream would have to overshoot past the other stream's inlet, which is the second law being violated in plain sight.

Worked example: 0.9 kg/s of air (cₚ ≈ 1005 J/(kg·K)) entering at 25 °C against exhaust gas at 200 °C. Q̇max = 0.9 × 1005 × 175 = 158.3 kW. Whatever the real recuperator recovers, it is a fraction of that number, and that fraction is the effectiveness. This is also the quickest audit tool on a plant walkdown: measure the two inlet temperatures and the limiting flow, compute Q̇max, compare it with the duty the process is actually getting, and you have a percentage that tells you whether a cleaning, a re-pass or a new exchanger is the honest recommendation. Trap: the inlet-to-inlet difference, never the inlet-to-outlet difference of one stream.

Maximum Possible Heat Transfer (Qmax) formula

Q˙max=m˙mincmin(Th,in−Tc,in)\dot{Q}_{max} = \dot{m}_{min} c_{min} (T_{h,in} - T_{c,in})
Where
  • Q˙max\dot{Q}_{max}= Maximum possible duty (kW)
  • m˙min\dot{m}_{min}= Minimum stream mass flow (kg/h)
  • cminc_{min}= Minimum stream specific heat (J/(kg·K))
  • Th,inT_{h,in}= Hot stream inlet (°C)
  • Tc,inT_{c,in}= Cold stream inlet (°C)

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Part of this formula set

The effectiveness-NTU method

5 formulasSizing or rating a heat exchanger without knowing the outlet temperatures — capacity rates, NTU, effectiveness and the maximum possible duty.