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Heat transfer calculators

13 calculations for energy balances, heat exchangers, insulation and heating or cooling times, each with its formula and practice problems.

Energy balances

Sensible heat

FormulaQ = ṁ × cp × (T₂ − T₁)
kg/h
°C
°C
Temperature rise (ΔT)—K
Heat duty (Q)—kW
Heat duty (Q)—MJ/h

No phase change. cp varies with temperature: use the value at the mean temperature. A negative result means heat removed.

Latent heat (steam, ice)

FormulaQ = ṁ × L  ·  ṁ = P ÷ L
kg/h
kW
Heat released by ṁ—kW
Flow needed for P—kg/h

Latent heat only (saturated steam condensing to saturated condensate). Sub-cooling the condensate adds some sensible heat. Values from steam tables, rounded.

Mixing temperature of two streams

FormulaTm = (ṁ₁ T₁ + ṁ₂ T₂) ÷ (ṁ₁ + ṁ₂)
kg/h
°C
kg/h
°C
Mixed temperature (Tm)—°C
Total flow—kg/h

Same fluid on both sides (same cp), no phase change, no losses. Also works with masses (kg) for a batch blend in a tank.

Energy to heat a tank

FormulaE = V × ρ × cp × (T₂ − T₁)  ·  P = E ÷ (t × η)
m³
kg/m³
°C
°C
h
%
Energy required (E)—kWh
Energy required (E)—MJ
Heating power (P)—kW

Ignores tank heat losses and the vessel metal: add 10 to 30 % depending on insulation. Electric immersion heater η ≈ 100 %; gas burner 80 to 90 %.

Heat exchangers

Exchanger heat balance: outlet temperature

FormulaQ = ṁh cph (Th,in − Th,out)  ·  Tc,out = Tc,in + Q ÷ (ṁc cpc)
kg/h
°C
°C
kg/h
°C
Heat duty (Q)—kW
Cold outlet (Tc,out)—°C

Assumes no losses to the surroundings. If the calculated cold outlet is above the hot inlet, the flows or temperatures are not consistent.

LMTD and required area

FormulaLMTD = (ΔT₁ − ΔT₂) ÷ ln(ΔT₁ ÷ ΔT₂)  ·  A = Q ÷ (U × LMTD)
°C
°C
°C
°C
kW
W/m²·K
LMTD—K
Required area (A)—m²

Valid for pure counter-current or co-current flow. For a multipass shell-and-tube unit, multiply the LMTD by the correction factor F (often 0.8 to 0.95).

Effectiveness-NTU (counter-flow exchanger)

FormulaNTU = UA ÷ Cmin  ·  ε = [1 − e−NTU(1−Cr)] ÷ [1 − Cr e−NTU(1−Cr)]  ·  Q = ε Cmin (Th,in − Tc,in)
kg/h
kg/h
W/m²·K
m²
°C
°C
Number of transfer units (NTU)—
Effectiveness (ε)—%
Heat duty (Q)—kW
Hot outlet (Th,out)—°C
Cold outlet (Tc,out)—°C

To rate an existing exchanger when U and A are known but the outlets are not. C = ṁ × cp; when both C are equal, ε = NTU ÷ (1 + NTU).

Overall U (films and fouling)

Formula1 ÷ U = 1 ÷ hi + e ÷ k + 1 ÷ ho + Rf
W/m²·K
W/m²·K
mm
W/m·K
m²·K/W
Clean U—W/m²·K
Fouled (design) U—W/m²·K

Thin wall: inside and outside areas taken as equal. k: carbon steel ≈ 45, stainless ≈ 16, copper ≈ 385 W/m·K. Cooling-tower water Rf: 0.0002 to 0.0004 m²·K/W.

Conduction, insulation and radiation

Conduction through a flat wall (2 layers)

FormulaU = 1 ÷ (1 ÷ hi + L₁ ÷ k₁ + L₂ ÷ k₂ + 1 ÷ ho)  ·  q = U (Ti − Ta)
°C
°C
m²
mm
W/m·K
mm
W/m·K
W/m²·K
W/m²·K
Overall coefficient (U)—W/m²·K
Heat flux (q)—W/m²
Total heat loss—kW
Outer surface temperature—°C

Set L₂ = 0 for a single layer. hₒ in still air including radiation: 8 to 12 W/m²·K; in wind: 20 to 40. k firebrick ≈ 1, mineral wool ≈ 0.04 to 0.06 W/m·K.

Heat loss from an insulated pipe

Formulaq' = 2π (Ti − Ta) ÷ [ln(r₂ ÷ r₁) ÷ k + 1 ÷ (r₂ ho)]
mm
mm
W/m·K
°C
°C
W/m²·K
m
Loss per metre (q')—W/m
Loss over length L—kW
Insulation surface temperature—°C
Bare pipe loss (same hₒ)—W/m

Radial conduction (Incropera); steel wall and inside film neglected (safe side). hₒ must include radiation. Surface above 60 °C: burn risk.

Radiation between surfaces

Formulaq = σ εeff (T₁⁴ − T₂⁴)  ·  εeff = ε₁  |  1 ÷ (1 ÷ ε₁ + 1 ÷ ε₂ − 1)
°C
°C
m²
Net radiant flux (q)—W/m²
Net radiant power—kW
Equivalent radiation coefficient (hr)—W/m²·K

Grey bodies, σ = 5.67 × 10⁻⁸ W/m²·K⁴, temperatures converted to kelvin. ε₂ is used only for parallel plates. ε: oxidised steel ≈ 0.8, paint ≈ 0.9, polished aluminium ≈ 0.05.

Heating and cooling times

Tank cooling (Newton's law)

Formulaτ = m cp ÷ UA  ·  T(t) = Ta + (T₀ − Ta) e−t/τ  ·  t = τ ln((T₀ − Ta) ÷ (Tc − Ta))
kg
W/K
°C
°C
h
°C
Time constant (τ)—h
Temperature after t—°C
Time to reach Tc—h

Well-mixed liquid (lumped model), constant UA, no draw-off or feed. To find UA, log a temperature drop over a few hours and invert the formula.

Batch heating time (steam coil)

Formulat = (m cp ÷ UA) × ln((Ts − T₀) ÷ (Ts − Tf))
kg
W/m²·K
m²
°C
°C
°C
Time—min
Initial duty—kW
Average duty—kW

Stirred vessel, saturated steam at constant temperature, losses neglected. Saturated steam: 1 barg ≈ 120 °C, 3 barg ≈ 144 °C, 7 barg ≈ 170 °C.

Learning and checking tools. The ranges shown are general guidance: always follow your plant's procedures, permits and set points. Nothing is sent anywhere: the calculations run in your browser.

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