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Convection is the form of heat transfer that occurs when a fluid (liquid or gas) flows over a surface at a different temperature.
By comparing Eqs. 1 and 3, it is apparent that the convective heat transfer coefficient is equivalent to the thermal conductivity of the fluid divided by the thermal boundary layer thickness. The thermal boundary layer thickness (δt), however, is a result of the geometry and size of the solid, flow conditions (such as velocity, flow direction, forced vs. natural, laminar vs. turbulent, etc.), and fluid properties. This means that the convective heat transfer coefficient is not a simple material property that can be tabulated but is a variable that must be evaluated.
Non-dimensional Numbers and Evaluation of Convective Heat Transfer Coefficient
There are two ways to evaluate the convective heat transfer coefficient. In some rare and simple cases, it can actually be calculated from first principles (see the isothermal flat plate in parallel flow discussion below). This involves solving the conservation equations for mass, momentum, and energy in the fluid flow. For forced convection, the mass and momentum conservation equations are solved first for the velocity profile of the fluid flow. This velocity profile is then used to solve the energy equation for the temperature profile. This temperature profile is then used to evaluate the temperature gradient at the surface and thus the heat transfer rate. For natural convection, however, the flow is a result of a density gradient in the fluid usually caused by a temperature gradient. This means that the mass, momentum, and energy equations are coupled and must be solved simultaneously. As one can imagine, this process is challenging for both forced and natural convection and can only be done in a handful of situations and only in laminar flow. Because of this, the convective heat transfer coefficients are most often measured experimentally. These experimental measurements are often made for a given flow configuration under a wide range of conditions and correlated with four common dimensionless numbers. These dimensionless numbers can be found by non-dimensionalizing the conservation equations.
When selecting an empirical correlation for the convective heat transfer, there are several things to take note of. The first is to make sure that the flow configuration of your problem matches the configuration the correlation was developed for. Remember that thermal properties will vary with temperature, and different correlations account for this in different ways. Many will have you calculate the thermal properties at an average or “film” temperature, but others will have you calculate the thermal properties at the bulk or free-stream fluid temperature and include a ratio inside the correlation to adjust. You will also need to pay attention to whether the correlation is for average heat transfer rates or for local heat transfer rates. Average values are typically denoted by an overbar. Because both the velocity and thermal boundary layer develop as the fluid flows over the surface, so will the heat flux. Typically, the heat flux will be the largest at the place the fluid first contacts the surface (the leading edge) because the velocity and temperature gradients are the largest. As the fluid continues the flow over the surface, the boundary layer gets thicker, shrinking the gradients and reducing the heat flux. Correlations for the average heat transfer coefficient are good for the entire length of the solid whereas correlations for the local heat transfer correlation are good for the surface starting from the leading edge to some point of interest downstream. Another thing to note is if the correlation provides limitations. Sometimes they are developed for only certain fluids or over a limited range of Reynolds numbers.
Effect of Turbulence
Convective heat transfer from turbulent flow tends to be larger than from laminar flow. Turbulent eddies in the flow enhance mixing so that the turbulent velocity and thermal boundary layer are more uniform at the core. This results in a sharper or larger temperature gradient at the surface, increasing the heat transferred. Note that because larger amounts of momentum and energy are transported by these turbulent eddies, the momentum diffusivity (kinematic viscosity) and thermal diffusivity are somewhat meaningless. In turbulent flows, the thermal boundary layer thickness is always about the same as the velocity boundary layer thickness, regardless of the Prandtl number.
Effect of Blowing
Isothermal Flat Plate in Laminar Parallel Flow
This relationship indicates that the local heat transfer coefficient is infinite at the leading edge of the plate and decreases as x−1/2 along the plate. The average Nusselt number can be found from Eq. 13 by integrating over the length of the plate.
Importance to Wildland and WUI Fires
Convection is the form of heat transfer that occurs when a fluid (liquid or gas) flows over a surface at a different temperature. The amount of heat transferred is proportional to the temperature difference between the solid and fluid. Solving for the proportionality constant, known as the convective heat transfer coefficient, is the fundamental problem of convective heat transfer. Though it can be solved for from fundamental theory in a few rare cases, it is most often measured experimentally and correlated with dimensionless numbers. Several factors will influence this heat transfer coefficient. These include the fluid velocity; the thermal properties of the fluid; whether the flow is laminar or turbulent, forced, or naturally (buoyantly) induced; and, perhaps most important in wildland and WUI fires, the surface size and shape. With all else held constant, solids with small length scales, such as needles and grasses, will transfer much more heat convectively than solids with large length scales, such as tree trunks and siding on structures. This not only makes measuring relevant convective heat transfer with traditional sensors challenging but will also likely shift the dominant heat transfer mechanism for ignition and fire spread between convection and radiation depending on the fuel size and shape.
- Bergman TL, Lavine AS, Incropera FP, DeWitt DP (2011) Fundamentals of heat and mass transfer, 7th edn. Wiley, HobokenGoogle Scholar
- Le Fevre EJ, Ede AJ (1956) Laminar free convection from the outer surface of a vertical circular cylinder. In: Proceedings of the 9th international congress applied mechanics, Brussels, vol 4, pp 175–183Google Scholar