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{{Short description|Quantity relating heat flux and temperature difference}}In thermodynamics, the heat transfer coefficient or film coefficient, or film effectiveness, is the proportionality constant between the heat flux and the thermodynamic driving force for the flow of heat (i.e., the temperature difference, {{math|ΔT}} ). It is used in calculating the heat transfer, typically by convection or phase transition between a fluid and a solid. The heat transfer coefficient has SI units in watts per square meter per kelvin (W/m2K).The overall heat transfer rate for combined modes is usually expressed in terms of an overall conductance or heat transfer coefficient, {{mvar|U}}. In that case, the heat transfer rate is: where (in SI units): The general definition of the heat transfer coefficient is: where: The heat transfer coefficient is the reciprocal of thermal insulance. This is used for building materials (R-value) and for clothing insulation.There are numerous methods for calculating the heat transfer coefficient in different heat transfer modes, different fluids, flow regimes, and under different thermohydraulic conditions. Often it can be estimated by dividing the thermal conductivity of the convection fluid by a length scale. The heat transfer coefficient is often calculated from the Nusselt number (a dimensionless number). There are also online calculators available specifically for Heat-transfer fluid applications. Experimental assessment of the heat transfer coefficient poses some challenges especially when small fluxes are to be measured (e.g. {{nowrap|< 0.2 W/cm{{sup|2}}}}).JOURNAL, Chiavazzo, Eliodoro, Ventola, Luigi, Calignano, Flaviana, Manfredi, Diego, Asinari, Pietro, A sensor for direct measurement of small convective heat fluxes: Validation and application to micro-structured surfaces, Experimental Thermal and Fluid Science, 2014, 55, 42–53, 10.1016/j.expthermflusci.2014.02.010,iris.polito.it/bitstream/11583/2528491/1/Sensor_ETFS-D-13-00440_v06.pdf, JOURNAL, Maddox, D.E., Mudawar, I., Single- and Two-Phase Convective Heat Transfer From Smooth and Enhanced Microelectronic Heat Sources in a Rectangular Channel, Journal of Heat Transfer, 1989, 111, 4, 1045–1052, 10.1115/1.3250766,heattransfer.asmedigitalcollection.asme.org/article.aspx?articleid=1440217,

Composition

A simple method for determining an overall heat transfer coefficient that is useful to find the heat transfer between simple elements such as walls in buildings or across heat exchangers is shown below. This method only accounts for conduction within materials, it does not take into account heat transfer through methods such as radiation. The method is as follows: Where: As the areas for each surface approach being equal the equation can be written as the transfer coefficient per unit area as shown below: or Often the value for dx_w 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 T_f, which is the average of the surface T_s and the surrounding bulk temperature, {{T}_{infty }}.

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.JOURNAL, Churchill, Stuart W., Chu, Humbert H.S., Correlating equations for laminar and turbulent free convection from a vertical plate, International Journal of Heat and Mass Transfer, November 1975, 18, 11, 1323–1329, 10.1016/0017-9310(75)90243-4, BOOK, Sukhatme, S. P., A Textbook on Heat Transfer, 2005, Universities Press, 978-8173715440, 257–258, Fourth, 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 (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 cylinders with their axes vertical, the expressions for plane surfaces can be used provided the curvature effect is not too significant. This represents the limit where boundary layer thickness is small relative to cylinder diameter D. The correlations for vertical plane walls can be used when

where mathrm{Gr}_L is the Grashof number.

External flow, horizontal plates

W. H. McAdams suggested the following correlations for horizontal plates.BOOK, McAdams, William H., Heat Transmission, 1954, McGraw-Hill, New York, 180, Third, The induced buoyancy will be different depending upon whether the hot surface is facing up or down.For a hot surface facing up, or a cold surface facing down, for laminar flow:

and for turbulent flow: For a hot surface facing down, or a cold surface facing up, for laminar flow: The characteristic length is the ratio of the plate surface area to perimeter. If the surface is inclined at an angle θ with the vertical then the equations for a vertical plate by Churchill and Chu may be used for θ up to 60°; if the boundary layer flow is laminar, the gravitational constant g is replaced with g cos Î¸ when calculating the Ra term.

External flow, horizontal cylinder

For cylinders of sufficient length and negligible end effects, Churchill and Chu has the following correlation for 10^{-5}