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thermodynamics Thermodynamics is a branch of physics that deals with heat, work, and temperature, and their relation to energy, entropy, and the physical properties of matter and radiation. The behavior of these quantities is governed by the four laws of ther ...
, the heat transfer coefficient or film coefficient, or film effectiveness, is the
proportionality constant In mathematics, two sequences of numbers, often experimental data, are proportional or directly proportional if their corresponding elements have a constant ratio, which is called the coefficient of proportionality or proportionality constan ...
between the
heat flux Heat flux or thermal flux, sometimes also referred to as ''heat flux density'', heat-flow density or ''heat flow rate intensity'' is a flow of energy per unit area per unit time. In SI its units are watts per square metre (W/m2). It has both a ...
and the thermodynamic driving force for the flow of heat (i.e., the temperature difference, ). It is used in calculating the
heat transfer Heat transfer is a discipline of thermal engineering that concerns the generation, use, conversion, and exchange of thermal energy (heat) between physical systems. Heat transfer is classified into various mechanisms, such as thermal conduction, ...
, typically by
convection Convection is single or multiphase fluid flow that occurs spontaneously due to the combined effects of material property heterogeneity and body forces on a fluid, most commonly density and gravity (see buoyancy). When the cause of the convecti ...
or
phase transition In chemistry, thermodynamics, and other related fields, a phase transition (or phase change) is the physical process of transition between one state of a medium and another. Commonly the term is used to refer to changes among the basic states o ...
between a fluid and a solid. The heat transfer coefficient has
SI units The International System of Units, known by the international abbreviation SI in all languages and sometimes Pleonasm#Acronyms and initialisms, pleonastically as the SI system, is the modern form of the metric system and the world's most wid ...
in watts per square meter
kelvin The kelvin, symbol K, is the primary unit of temperature in the International System of Units (SI), used alongside its prefixed forms and the degree Celsius. It is named after the Belfast-born and University of Glasgow-based engineer and ph ...
(W/m2/K). The overall heat transfer rate for combined modes is usually expressed in terms of an overall conductance or heat transfer coefficient, . In that case, the heat transfer rate is: :\dot=hA(T_2-T_1) where (in SI units): *: surface area where the heat transfer takes place (m2) *: temperature of the surrounding fluid (K) *: temperature of the solid surface (K) The general definition of the heat transfer coefficient is: :h = \frac where: *:
heat flux Heat flux or thermal flux, sometimes also referred to as ''heat flux density'', heat-flow density or ''heat flow rate intensity'' is a flow of energy per unit area per unit time. In SI its units are watts per square metre (W/m2). It has both a ...
(W/m2); i.e., thermal power per unit
area Area is the quantity that expresses the extent of a region on the plane or on a curved surface. The area of a plane region or ''plane area'' refers to the area of a shape or planar lamina, while ''surface area'' refers to the area of an open s ...
, q = d\dot/dA *: difference in temperature between the solid surface and surrounding fluid area (K) The heat transfer coefficient is the reciprocal of
thermal insulance In the context of construction, the R-value is a measure of how well a two-dimensional barrier, such as a layer of insulation, a window or a complete wall or ceiling, resists the conductive flow of heat. R-value is the temperature difference per ...
. 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 The thermal conductivity of a material is a measure of its ability to conduct heat. It is commonly denoted by k, \lambda, or \kappa. Heat transfer occurs at a lower rate in materials of low thermal conductivity than in materials of high thermal ...
of the
convection Convection is single or multiphase fluid flow that occurs spontaneously due to the combined effects of material property heterogeneity and body forces on a fluid, most commonly density and gravity (see buoyancy). When the cause of the convecti ...
fluid by a length scale. The heat transfer coefficient is often calculated from the Nusselt number (a
dimensionless number A dimensionless quantity (also known as a bare quantity, pure quantity, or scalar quantity as well as quantity of dimension one) is a quantity to which no physical dimension is assigned, with a corresponding SI unit of measurement of one (or 1) ...
). There are also online calculators available specifically for
Heat-transfer fluid In fluid thermodynamics, a heat transfer fluid is a gas or liquid that takes part in heat transfer by serving as an intermediary in cooling on one side of a process, transporting and storing thermal energy, and heating on another side of a pr ...
applications. Experimental assessment of the heat transfer coefficient poses some challenges especially when small fluxes are to be measured (e.g. ).


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. Note that 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: : \frac = \frac + \frac + \frac Where: * U = the overall heat transfer coefficient (W/(m2·K)) * A = the contact area for each fluid side (m2) (with A_ and A_ expressing either surface) * k = the
thermal conductivity The thermal conductivity of a material is a measure of its ability to conduct heat. It is commonly denoted by k, \lambda, or \kappa. Heat transfer occurs at a lower rate in materials of low thermal conductivity than in materials of high thermal ...
of the material (W/(m·K)) * h = the individual convection heat transfer coefficient for each fluid (W/(m2·K)) * dx_w = the wall thickness (m). As the areas for each surface approach being equal the equation can be written as the transfer coefficient per unit area as shown below: : \frac = \frac + \frac + \frac or : U = \frac 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 In the context of construction, the R-value is a measure of how well a two-dimensional barrier, such as a layer of insulation, a window or a complete wall or ceiling, resists the conductive flow of heat. R-value is the temperature difference per ...
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 In fluid thermodynamics, the film temperature () is an approximation of the temperature of a fluid inside a convection boundary layer. It is calculated as the arithmetic mean of the temperature at the surface of the solid boundary wall () and the ...
T_f, which is the average of the surface T_s and the surrounding bulk temperature, . :=\frac


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 The thermal conductivity of a material is a measure of its ability to conduct heat. It is commonly denoted by k, \lambda, or \kappa. Heat transfer occurs at a lower rate in materials of low thermal conductivity than in materials of high thermal ...
of the fluid, ''L'' is the
characteristic length In physics, a characteristic length is an important dimension that defines the scale of a physical system. Often, such a length is used as an input to a formula in order to predict some characteristics of the system, and it is usually required by ...
with respect to the direction of gravity, Ra''L'' is the
Rayleigh number In fluid mechanics, the Rayleigh number (, after Lord Rayleigh) for a fluid is a dimensionless number associated with buoyancy-driven flow, also known as free (or natural) convection. It characterises the fluid's flow regime: a value in a certain ...
with respect to this length and Pr is the
Prandtl number The Prandtl number (Pr) or Prandtl group is a dimensionless number, named after the German physicist Ludwig Prandtl, defined as the ratio of momentum diffusivity to thermal diffusivity. The Prandtl number is given as: : \mathrm = \frac = \frac ...
. (Note: The Rayleigh number can be written as the product of the Grashof number and the Prandtl number) :h \ = \frac\left(\right)^2 \, \quad \mathrm_L < 10^ 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 Ra''L'' exceeds around 109. :h \ = \frac \left(0.68 + \frac\right) \, \quad \mathrm10^ < \mathrm_L < 10^9


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 :\frac\ge \frac where \mathrm_L is the Grashof number.


External flow, horizontal plates

W. H. McAdams suggested the following correlations for horizontal plates. 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: :h \ = \frac \, \quad 10^5 < \mathrm_L < 2\times 10^7 and for turbulent flow: :h \ = \frac \, \quad 2\times 10^7 < \mathrm_L < 3\times 10^ . For a hot surface facing down, or a cold surface facing up, for laminar flow: :h \ = \frac \, \quad 3\times 10^5 < \mathrm_L < 3\times 10^. 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 ''θ'' 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^<\mathrm_D<10^. :h \ = \frac \left(\right)^2


External flow, spheres

For spheres, T. Yuge has the following correlation for Pr≃1 and 1 \le \mathrm_D \le 10^5. :_D \ = 2 + 0.43 \mathrm_D^


Vertical rectangular enclosure

For heat flow between two opposing vertical plates of rectangular enclosures, Catton recommends the following two correlations for smaller aspect ratios. The correlations are valid for any value of Prandtl number. For 1 <\frac < 2 : :h \ = \frac0.18 \left(\frac \mathrm_L \right)^ \, \quad \mathrm_L \mathrm/(0.2 + \mathrm) > 10^3 where ''H'' is the internal height of the enclosure and ''L'' is the horizontal distance between the two sides of different temperatures. For 2 < \frac < 10 : :h \ = \frac0.22 \left(\frac \mathrm_L \right)^ \left(\frac \right)^ \, \quad \mathrm_L < 10^. For vertical enclosures with larger aspect ratios, the following two correlations can be used. For 10 < ''H''/''L'' < 40: :h \ = \frac0.42 \mathrm_L^ \mathrm^ \left(\frac \right)^ \, \quad 1 < \mathrm < 2\times10^4, \, \quad 10^4 < \mathrm_L < 10^7. For 1 < \frac < 40 : :h \ = \frac0.46 \mathrm_L^ \, \quad 1 < \mathrm < 20, \, \quad 10^6 < \mathrm_L < 10^9. For all four correlations, fluid properties are evaluated at the average temperature—as opposed to film temperature—(T_1+T_2)/2, where T_1 and T_2 are the temperatures of the vertical surfaces and T_1 > T_2.


Forced convection


Internal flow, laminar flow

Sieder and Tate give the following correlation to account for entrance effects in laminar flow in tubes where D is the internal diameter, _ is the fluid viscosity at the bulk mean temperature, _ is the viscosity at the tube wall surface temperature. :\mathrm_=\cdot For fully developed laminar flow, the Nusselt number is constant and equal to 3.66. Mills combines the entrance effects and fully developed flow into one equation :\mathrm_=3.66+\frac


Internal flow, turbulent flow

The Dittus-Bölter correlation (1930) is a common and particularly simple correlation useful for many applications. This correlation is applicable when forced convection is the only mode of heat transfer; i.e., there is no boiling, condensation, significant radiation, etc. The accuracy of this correlation is anticipated to be ±15%. For a fluid flowing in a straight circular pipe with a
Reynolds number In fluid mechanics, the Reynolds number () is a dimensionless quantity that helps predict fluid flow patterns in different situations by measuring the ratio between inertial and viscous forces. At low Reynolds numbers, flows tend to be domin ...
between 10,000 and 120,000 (in the
turbulent In fluid dynamics, turbulence or turbulent flow is fluid motion characterized by chaotic changes in pressure and flow velocity. It is in contrast to a laminar flow, which occurs when a fluid flows in parallel layers, with no disruption between t ...
pipe flow range), when the fluid's
Prandtl number The Prandtl number (Pr) or Prandtl group is a dimensionless number, named after the German physicist Ludwig Prandtl, defined as the ratio of momentum diffusivity to thermal diffusivity. The Prandtl number is given as: : \mathrm = \frac = \frac ...
is between 0.7 and 120, for a location far from the pipe entrance (more than 10 pipe diameters; more than 50 diameters according to many authors) or other flow disturbances, and when the pipe surface is hydraulically smooth, the heat transfer coefficient between the bulk of the fluid and the pipe surface can be expressed explicitly as: := \, \left(\right)^ \, \left(\right)^n where: :d is the
hydraulic diameter The hydraulic diameter, , is a commonly used term when handling flow in non-circular tubes and channels. Using this term, one can calculate many things in the same way as for a round tube. When the cross-section is uniform along the tube or channel ...
:k is the
thermal conductivity The thermal conductivity of a material is a measure of its ability to conduct heat. It is commonly denoted by k, \lambda, or \kappa. Heat transfer occurs at a lower rate in materials of low thermal conductivity than in materials of high thermal ...
of the bulk fluid :\mu is the fluid
viscosity The viscosity of a fluid is a measure of its resistance to deformation at a given rate. For liquids, it corresponds to the informal concept of "thickness": for example, syrup has a higher viscosity than water. Viscosity quantifies the inter ...
:j
mass flux In physics and engineering, mass flux is the rate of mass flow. Its SI units are kg m−2 s−1. The common symbols are ''j'', ''J'', ''q'', ''Q'', ''φ'', or Φ ( Greek lower or capital Phi), sometimes with subscript ''m'' to indicate mass is t ...
:c_p isobaric
heat capacity Heat capacity or thermal capacity is a physical property of matter, defined as the amount of heat to be supplied to an object to produce a unit change in its temperature. The SI unit of heat capacity is joule per kelvin (J/K). Heat capacity i ...
of the fluid :n is 0.4 for heating (wall hotter than the bulk fluid) and 0.33 for cooling (wall cooler than the bulk fluid). The fluid properties necessary for the application of this equation are evaluated at the
bulk temperature In thermofluids dynamics, the bulk temperature, or the average bulk temperature in the thermal fluid, is a convenient reference point for evaluating properties related to convective heat transfer, particularly in applications related to flow in pip ...
thus avoiding iteration.


Forced convection, external flow

In analyzing the heat transfer associated with the flow past the exterior surface of a solid, the situation is complicated by phenomena such as boundary layer separation. Various authors have correlated charts and graphs for different geometries and flow conditions. For flow parallel to a plane surface, where x is the distance from the edge and L is the height of the boundary layer, a mean Nusselt number can be calculated using the Colburn analogy.


Thom correlation

There exist simple fluid-specific correlations for heat transfer coefficient in boiling. The Thom correlation is for the flow of boiling water (subcooled or saturated at pressures up to about 20 MPa) under conditions where the nucleate boiling contribution predominates over forced convection. This correlation is useful for rough estimation of expected temperature difference given the heat flux: \Delta T_ = 22.5 \cdot ^ \exp (-P/8.7) where: :\Delta T_ is the wall temperature elevation above the saturation temperature, K :''q'' is the heat flux, MW/m2 :''P'' is the pressure of water, MPa Note that this empirical correlation is specific to the units given.


Heat transfer coefficient of pipe wall

The resistance to the flow of heat by the material of pipe wall can be expressed as a "heat transfer coefficient of the pipe wall". However, one needs to select if the heat flux is based on the pipe inner or the outer diameter. Selecting to base the
heat flux Heat flux or thermal flux, sometimes also referred to as ''heat flux density'', heat-flow density or ''heat flow rate intensity'' is a flow of energy per unit area per unit time. In SI its units are watts per square metre (W/m2). It has both a ...
on the pipe inner diameter, and assuming that the pipe wall thickness is small in comparison with the pipe inner diameter, then the heat transfer coefficient for the pipe wall can be calculated as if the wall were not curved: :h_ = where ''k'' is the effective
thermal conductivity The thermal conductivity of a material is a measure of its ability to conduct heat. It is commonly denoted by k, \lambda, or \kappa. Heat transfer occurs at a lower rate in materials of low thermal conductivity than in materials of high thermal ...
of the wall material and ''x'' is the wall thickness. If the above assumption does not hold, then the wall heat transfer coefficient can be calculated using the following expression: :h_ = where ''d''i and ''d''o are the inner and outer diameters of the pipe, respectively. The thermal conductivity of the tube material usually depends on temperature; the mean thermal conductivity is often used.


Combining convective heat transfer coefficients

For two or more heat transfer processes acting in parallel, convective heat transfer coefficients simply add: :h = h_1 + h_2 + \cdots For two or more heat transfer processes connected in series, convective heat transfer coefficients add inversely: : = + + \dots For example, consider a pipe with a fluid flowing inside. The approximate rate of heat transfer between the bulk of the fluid inside the pipe and the pipe external surface is: :q=\left( \right) \cdot A \cdot \Delta T where :''q'' = heat transfer rate (W) :''h'' = convective heat transfer coefficient (W/(m2·K)) :''t'' = wall thickness (m) :''k'' = wall thermal conductivity (W/m·K) :''A'' = area (m2) :\Delta T = difference in temperature.


Overall heat transfer coefficient

The overall heat transfer coefficient U is a measure of the overall ability of a series of conductive and convective barriers to transfer heat. It is commonly applied to the calculation of heat transfer in
heat exchanger A heat exchanger is a system used to transfer heat between a source and a working fluid. Heat exchangers are used in both cooling and heating processes. The fluids may be separated by a solid wall to prevent mixing or they may be in direct contac ...
s, but can be applied equally well to other problems. For the case of a heat exchanger, U can be used to determine the total heat transfer between the two streams in the heat exchanger by the following relationship: :q = UA \Delta T_ where: :q = heat transfer rate (W) :U = overall heat transfer coefficient (W/(m2·K)) :A = heat transfer surface area (m2) :\Delta T_ = logarithmic mean temperature difference (K). The overall heat transfer coefficient takes into account the individual heat transfer coefficients of each stream and the resistance of the pipe material. It can be calculated as the reciprocal of the sum of a series of thermal resistances (but more complex relationships exist, for example when heat transfer takes place by different routes in parallel): :\frac = \sum \frac + \sum R where: :''R'' = Resistance(s) to heat flow in pipe wall (K/W) :Other parameters are as above.Coulson and Richardson, "Chemical Engineering", Volume 1, Elsevier, 2000 The heat transfer coefficient is the heat transferred per unit area per kelvin. Thus ''area'' is included in the equation as it represents the area over which the transfer of heat takes place. The areas for each flow will be different as they represent the contact area for each fluid side. The ''
thermal resistance Thermal resistance is a heat property and a measurement of a temperature difference by which an object or material resists a heat flow. Thermal resistance is the reciprocal of thermal conductance. * (Absolute) thermal resistance ''R'' in kelvi ...
'' due to the pipe wall (for thin walls) is calculated by the following relationship: :R = \frac where :''x'' = the wall thickness (m) :''k'' = the thermal conductivity of the material (W/(m·K)) This represents the heat transfer by conduction in the pipe. The ''
thermal conductivity The thermal conductivity of a material is a measure of its ability to conduct heat. It is commonly denoted by k, \lambda, or \kappa. Heat transfer occurs at a lower rate in materials of low thermal conductivity than in materials of high thermal ...
'' is a characteristic of the particular material. Values of thermal conductivities for various materials are listed in the
list of thermal conductivities In heat transfer, the thermal conductivity of a substance, ''k'', is an intensive property that indicates its ability to conduct heat. For most materials, the amount of heat conducted varies (usually non-linearly) with temperature. Thermal cond ...
. As mentioned earlier in the article the ''convection heat transfer coefficient'' for each stream depends on the type of fluid, flow properties and temperature properties. Some typical heat transfer coefficients include: * Air - ''h'' = 10 to 100 W/(m2K) * Water - ''h'' = 500 to 10,000 W/(m2K).


Thermal resistance due to fouling deposits

Often during their use, heat exchangers collect a layer of fouling on the surface which, in addition to potentially contaminating a stream, reduces the effectiveness of heat exchangers. In a fouled heat exchanger the buildup on the walls creates an additional layer of materials that heat must flow through. Due to this new layer, there is additional resistance within the heat exchanger and thus the overall heat transfer coefficient of the exchanger is reduced. The following relationship is used to solve for the heat transfer resistance with the additional fouling resistance: :\frac = \frac+\frac+\frac where :U_ = overall heat transfer coefficient for a fouled heat exchanger, \textstyle \rm \frac :P= perimeter of the heat exchanger, may be either the hot or cold side perimeter however, it must be the same perimeter on both sides of the equation, \rm m :U = overall heat transfer coefficient for an unfouled heat exchanger, \textstyle \rm \frac :R_ = fouling resistance on the cold side of the heat exchanger, \textstyle \rm \frac :R_ = fouling resistance on the hot side of the heat exchanger, \textstyle \rm \frac :P_C = perimeter of the cold side of the heat exchanger, \rm m :P_H = perimeter of the hot side of the heat exchanger, \rm m This equation uses the overall heat transfer coefficient of an unfouled heat exchanger and the fouling resistance to calculate the overall heat transfer coefficient of a fouled heat exchanger. The equation takes into account that the perimeter of the heat exchanger is different on the hot and cold sides. The perimeter used for the P does not matter as long as it is the same. The overall heat transfer coefficients will adjust to take into account that a different perimeter was used as the product UP will remain the same. The fouling resistances can be calculated for a specific heat exchanger if the average thickness and thermal conductivity of the fouling are known. The product of the average thickness and thermal conductivity will result in the fouling resistance on a specific side of the heat exchanger. :R_f = \frac where: :d_f = average thickness of the fouling in a heat exchanger, \rm m :k_f = thermal conductivity of the fouling, \textstyle \rm \frac.


See also

* Convective heat transfer *
Heat sink A heat sink (also commonly spelled heatsink) is a passive heat exchanger that transfers the heat generated by an electronic or a mechanical device to a fluid medium, often air or a liquid coolant, where it is dissipated away from the device, t ...
*
Convection Convection is single or multiphase fluid flow that occurs spontaneously due to the combined effects of material property heterogeneity and body forces on a fluid, most commonly density and gravity (see buoyancy). When the cause of the convecti ...
* Churchill–Bernstein equation *
Heat In thermodynamics, heat is defined as the form of energy crossing the boundary of a thermodynamic system by virtue of a temperature difference across the boundary. A thermodynamic system does not ''contain'' heat. Nevertheless, the term is al ...
*
Heat pump A heat pump is a device that can heat a building (or part of a building) by transferring thermal energy from the outside using a refrigeration cycle. Many heat pumps can also operate in the opposite direction, cooling the building by removing h ...
*
Heisler Chart Heisler charts are a graphical analysis tool for the evaluation of one-dimensional transient conductive heat transfer in thermal engineering. They are a set of two charts per included geometry introduced in 1947 by M. P. Heisler which were suppleme ...
*
Thermal conductivity The thermal conductivity of a material is a measure of its ability to conduct heat. It is commonly denoted by k, \lambda, or \kappa. Heat transfer occurs at a lower rate in materials of low thermal conductivity than in materials of high thermal ...
* Thermal-hydraulics * Biot number * Fourier number * Nusselt number


References


External links


Overall Heat Transfer CoefficientsCorrelations for Convective Heat Transfer
{{DEFAULTSORT:Heat Transfer Coefficient Convection Heat transfer Heat conduction