Maximum Possible Heat Transfer (Qmax)

\dot{Q}_{max} = \dot{m}_{min} c_{min} (T_{h,in} - T_{c,in})

Qmax =

ṁ =

cₚ =

Th,in =

Tc,in =

Enter your known values, leave one input blank, and solves for the missing one. Try different units for next level excitement!

Learning zone

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)

\dot{Q}_{max} = \dot{m}_{min} c_{min} (T_{h,in} - T_{c,in})

Where

$\dot{Q}_{max}$ = Maximum possible duty
$\dot{m}_{min}$ = Minimum stream mass flow
$c_{min}$ = Minimum stream specific heat
$T_{h,in}$ = Hot stream inlet
$T_{c,in}$ = Cold stream inlet

Missing one of these? Work it out first, then come back

Maximum possible duty — Heat Exchanger Effectiveness (ε = Q/Qmax), Heat Exchanger Duty (Q = U·A·F·LMTD)
Minimum stream mass flow — Number of Transfer Units (NTU), Capacity Rate Ratio (Cr)
Minimum stream specific heat — Number of Transfer Units (NTU), Capacity Rate Ratio (Cr)
Hot stream inlet — Lumped Capacitance Cooling Curve, Net Radiation Exchange Between Surfaces
Cold stream inlet — Lumped Capacitance Cooling Curve, Net Radiation Exchange Between Surfaces

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.