Convective heat transfer occurs between a moving fluid and a solid surface.The rate of convective heat transfer between a surface at a temperature Ts, and a fluid at a temperature Tµ, is given by the Newton’s Law of Cooling written as:
In
the above equation, 
is
the convective heat flux (W/m2) and h is the local
convective heat transfer coefficient, also referred to as the local
convection coefficient.In general,
the local coefficient can vary from point to point along the surface of
the model where heat transfer is taking place.It
is therefore customary to define an average convection coefficient,
, where:
Although analytical expressions
of the heat transfer can be obtained for flow over bodies with very simple
geometries, one most often relies on empirical correlations to obtain
. It is customary to express the convection coefficient (average or
local), in a non-dimensional form called the Nusselt Number, the
expression for which is given below:
In the above equation kf is the thermal conductivity of the fluid and L is a characteristic dimension of the model under consideration, e.g the length of a flat plate or the diameter of a cylinder.There are two main classifications of convective heat transfer, forced convection and free convection. Forced convection occurs when the fluid flow is being driven over the surface by external means, such as a pump or a fan or atmospheric wind. Free convection occurs in buoyancy driven flows, i.e. temperature gradients in the fluid lead to density gradients causing a ‘free’ convective current to be established.Correlations for both types of convective heat transfer are given below.
In
the above expression, Re is the Reynolds Number given as 
and
Pr is the Prandtl Number given by 
. The other properties are as follows:
r - density of the fluid; m - dynamic viscosity of the fluid; a - thermal diffusivity of the fluid, n - kinematic viscosity of the fluid and n = m/r; L - a characteristic dimension of the model.For air, Pr @ 0.7, under standard conditions.The values of C, m and n are function of the geometry and the Reynolds number range.
For Laminar flow :
(valid
for Pr ³
0.6 and Re<
5 x 105)
For Turbulent flow :
(valid
for 0.6 £
Pr £
60 and 5 x 105£Re £
107)
In some cases, the plate is large enough for both laminar and turbulent flow to occur on the surface.For these cases, the correlation for combined flow is given below.
For Combined Laminar & Turbulent flow :
(valid
for 0.6 £
Pr £
60 and 5 x 105£Re £
107)
Note that, especially for cylinders, a number of correlations are given, where each is valid over a specific range of Reynolds number.
Also note that in general and specifically for the correlations given here the fluid properties such as thermal conductivity, viscosity, etc. are determined at the film temperature, where the film temperature is the average of the surface temperature and the fluid freestream temperature.
where b is the volumetric thermal expansion coefficient of the fluid, a thermodynamic property.The volumetric thermal expansion coefficient brings in the effects of buoyancy in free convection flows; for an ideal gas, b = 1/T, where T is the absolute temperature of the gas.The Grashoff number plays the same role in free convection that the Reynolds number plays in forced convection in that it is the ratio of buoyancy forces to viscous forces on the fluid.Another parameter which commonly occurs in empirical free convection correlations is the Rayleigh number, Ra, where
Ra = Gr Pr
Vertical
Flat Plate Correlations
For Laminar flow:
(
0 < RaL <109)
For Combined Laminar & Turbulent flow :
(
10-5 < RaD <1012)
For
Spheres
