Heat-Transfer Coefficient for a Long Fin Cooled by Convection and Radiation

Nomenclature Aeff = effective surface area, π DLeff, m2 D = diameter, mm g = acceleration of gravity, m/s2 h = combined heat-transfer coefficient, hc + hr , W/m2-K hc = natural convection heat-transfer coefficient, W/m2-K hr = radiation heat-transfer coefficient, W/m2-K h = average combined heat-transfer coefficient, W/m2-K k = thermal conductivity of fin, W/m-K k f = thermal conductivity of fluid, W/m-K L = length, m Leff = effective length, m m = dimensionless fin parameter m = average dimensionless fin parameter NuD = Nusselt number, hc D/k f P = perimeter, m Pr = Prandtl number, ν/α Q = rate of heat transfer, W RaD = Rayleigh number, gβ(T − T∞)D/να T = temperature along the fin, ◦C T f = mean film temperature, (T + T∞)/2, ◦C U = uncertainty x = axial coordinate, m α = thermal diffusivity, m2/s = emissivity θ = excess temperature, T − T∞, ◦C ν = kinematic viscosity, m2/s σ = Stefan–Boltzmann constant, W/m2-K4 χ = dimensionless axial coordinate, x/L