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Newton's law of cooling and convection coefficient

Short answer

Newton's law: Q = hA(T_s - T_inf). The convective coefficient h is the heat flux per unit temperature difference, depending on flow type, fluid properties, geometry, and phase. Typical ranges: natural convection air 2-25, forced air 25-250, forced water 250-15000, boiling water 2500-100000 W/m^2K.

State Newton's law of cooling. Define the convective heat transfer coefficient and list the factors on which it depends. Give typical ranges of h for natural convection of air, forced convection of air, forced convection of water and boiling water.

Newton's law of cooling: the rate of convective heat transfer between a surface and a fluid is proportional to the surface area and to the temperature difference between the surface and the fluid:

Q=hA (Ts−T∞)Q = hA\,(T_s - T_\infty)

Convective heat transfer coefficient

hh (W/m2^2 K) is the heat flow per unit area per unit temperature difference between the surface and the bulk fluid. It is not a property of the fluid alone; it depends on the whole flow situation. It is found from h=−kf (∂T/∂y)wall/(Ts−T∞)h = -k_f\,(\partial T/\partial y)_{wall}/(T_s-T_\infty), which links it to the fluid conductivity and the temperature gradient at the wall.

Factors affecting hh

  • Type of flow: natural or forced, laminar or turbulent.
  • Fluid properties: density, viscosity, thermal conductivity, specific heat, expansion coefficient.
  • Fluid velocity and temperature difference.
  • Geometry: shape, size, orientation and roughness of the surface.
  • Phase change (boiling, condensation) raises hh very much.

Typical ranges

Situationhh (W/m2^2 K)
Natural convection, air2 to 25
Forced convection, air25 to 250
Forced convection, water250 to 15 000
Boiling water2500 to 100 000
Condensing steam5000 to 100 000

✓ Answer checked by Claude Sonnet 5.5

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