or Often the value for is referred to as the difference of two radii where the inner and outer radii are used to define the thickness of a pipe carrying a fluid, however, this figure may also be considered as a wall thickness in a flat plate transfer mechanism or other common flat surfaces such as a wall in a building when the area difference between each edge of the transmission surface approaches zero. In the walls of buildings the above formula can be used to derive the formula commonly used to calculate the heat through building components. Architects and engineers call the resulting values either the U-Value or the R-Value of a construction assembly like a wall. Each type of value (R or U) are related as the inverse of each other such that R-Value = 1/U-Value and both are more fully understood through the concept of an overall heat transfer coefficient described in lower section of this document. Convective heat transfer correlations Although convective heat transfer can be derived analytically through dimensional analysis, exact analysis of the boundary layer, approximate integral analysis of the boundary layer and analogies between energy and momentum transfer, these analytic approaches may not offer practical solutions to all problems when there are no mathematical models applicable. Therefore, many correlations were developed by various authors to estimate the convective heat transfer coefficient in various cases including natural convection, forced convection for internal flow and forced convection for external flow. These empirical correlations are presented for their particular geometry and flow conditions. As the fluid properties are temperature dependent, they are evaluated at the film temperature , which is the average of the surface and the surrounding bulk temperature, . External flow, vertical plane Recommendations by Churchill and Chu provide the following correlation for natural convection adjacent to a vertical plane, both for laminar and turbulent flow. k is the thermal conductivity of the fluid, L is the characteristic length with respect to the direction of gravity, RaL is the Rayleigh number with respect to this length and Pr is the Prandtl number. (Note: The Rayleigh number can be written as the product of the Grashof number and the Prandtl number) For laminar flows, the following correlation is slightly more accurate. It is observed that a transition from a laminar to a turbulent boundary occurs when RaL exceeds around 109. External flow, vertical cylinders For