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Lesson 28 · Newton's law of cooling
The film is where the heat gets stuck
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The film is where the heat gets stuck

Conduction happens inside solids. Convection happens where a solid meets a moving fluid, and almost all of the resistance lives in a thin, sluggish layer of fluid clinging to the surface — the boundary-layer film. Newton's law of cooling prices that film in one number: Q˙=hA ΔT\dot{Q} = h A \, \Delta T. Read aloud: Q-dot equals h A delta-T.

Letter by letter, because a formula with undefined letters is a formula you do not own. Q˙\dot{Q} (say Q-dot — the dot means per second) is the heat rate in watts. hh is the convection coefficient, or film coefficient, in W/(m2⋅K)\mathrm{W/(m^2 \cdot K)}: the watts one square metre of surface moves for every kelvin of difference. AA is the wetted area in m2\mathrm{m^2} — the area the fluid actually touches. ΔT\Delta T (say delta-T) is the surface-to-fluid difference in kelvin: the surface minus the bulk fluid, and never a temperature on its own. Whichever of the four the question leaves blank is the one you solve for.

Learn the magnitudes and you will catch your own mistakes: still air gives hh around 55–2525, forced air 1010–200200, flowing water 500500–10,00010{,}000, and condensing steam higher still. A film coefficient of 3 belongs to nothing in a working plant.

The same film has a second face. Write R=1hAR = \dfrac{1}{hA} — R equals one over h A — and you have the film's thermal resistance RR in kelvin per watt, exactly the way a resistor is measured in volts per amp. One face for computing heat, one face for stacking layers in series. They are the same fact, and this chapter uses both.

AQΔTh

Q˙=hA ΔT\dot{Q} = h A \, \Delta T

  • Q˙\dot{Q}= Heat transfer rate (power)
  • hh= Convection coefficient (heat transfer coefficient)
  • AA= Surface area (area)
  • ΔT\Delta T= Surface-to-fluid ΔT (temperature difference)
Newton's Law of Cooling (Q = hAΔT) solver →
hAR

R=1hAR = \frac{1}{h A}

  • RR= Film resistance (thermal resistance)
  • hh= Convection coefficient (heat transfer coefficient)
  • AA= Wetted area (area)
Convection Film Resistance solver →