Defining the Heat Transfer Coefficients
It is possible to divide the convective heat flux into four main categories depending on the type of convection condition (natural or forced) and on the type of geometry (internal or external flow). In addition, these cases can all experience either laminar or turbulent flow conditions, resulting in eight types of convection, as in Figure 4-16.
Figure 4-16: The eight categories of convective heat flux.
The difference between natural and forced convection is that in the forced convection an external force such as a fan creates the flow. In natural convection, buoyancy forces induced by temperature differences together with the thermal expansion of the fluid drive the flow.
Heat transfer books generally contain a large set of empirical and theoretical correlations for h coefficients. This module includes a subset of them. The expressions are based on the following set of dimensionless numbers:
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The Nusselt number, NuL = hL ⁄ k
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The Reynolds number, ReL = ρU L ⁄ μ
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The Prandtl number, Pr = μCp ⁄ k
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The Rayleigh number, RaL = GrLPr = ρ2 gαpCp ΔT L3 ⁄ (μk)
where
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h is the heat transfer coefficient (SI unit: W/(m2·K))
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L is the characteristic length (SI unit: m)
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ΔT is the temperature difference between the surface and the external fluid bulk (SI unit: K)
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g is the acceleration of gravity (SI unit: m/s2)
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k is the thermal conductivity of the fluid (SI unit: W/(m·K))
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ρ is the fluid density (SI unit: kg/m3)
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U is the bulk velocity (SI unit: m/s)
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μ is the dynamic viscosity (SI unit: Pa·s)
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Cp is the heat capacity at constant pressure of the fluid (SI unit: J/(kg·K))
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αp is the coefficient of thermal expansion (SI unit: 1/K)
Further, GrL refers to the Grashof number, which is the squared ratio of the viscous time scale to the buoyancy time scale multiplied by the Reynolds number.