Effectiveness of a thermal protective coating for automotive components.
Management of the thermal environment of a component can be achieved by altering the contact with surrounding objects (conduction), changing the fluid flow (speed or temperature) around the component (convection), altering the properties of the surface, modifying the orientation of surfaces and altering the temperature of the surroundings (radiation). Examples of thermal management in an automotive environment are use of a thermally insulating gasket between an EGR valve and the intake manifold (conduction), ducting cooling air to brake components (convection) and use of a so-called heat shield around an exhaust manifold (radiation) to protect nearby components.
Heat shields (radiation shields) reduce the rate of radiation heat transfer between two objects by virtue of an intervening presence in the line of sight between the two objects. The way in which these shields function (ref. 2) is not intuitively obvious, but is related to the common experience of being comfortably warmed by a bonfire until someone steps in between you and the bonfire. Radiation for most solid objects is treated as a surface phenomenon, since most solids are opaque (intuitively similar to opacity to visible light) to the wavelengths of radiation involved in heat transfer. A common example is the use of a high emissivity coating (e.g., flat black paint) on a normally shiny surface when measuring the surface temperature using infrared thermography. Since it is the surface of an opaque solid that is important in how that solid interacts with incident radiation, a property to describe this interaction is defined ([epsilon], emissivity) which varies from zero to one. An emissivity of unity defines a surface that absorbs all of the thermal radiation incident on that surface, a so called black body. This terminology can be misleading since the color of the surface does not determine the emissivity directly (i.e., flat white paint typically has a high emissivity). Since radiation is essentially a surface phenomenon for opaque materials, one can modify the radiation heat transfer to an object by modifying only the surface emissivity, such as in the case of applying a coating (refs. 3-6) with an emissivity different than that of the substrate. In the context of the present work, the usual situation is that a lower emissivity surface is desired relative to the emissivity of the substrate. An example of a coating for elastomeric substrates to reduce the emissivity of the surface is HRC coating, which is part of the family of Lord HPC coatings (refs. 7-9) that impart fluid and ozone resistance to the underlying elastomeric substrates. Special pigmentation enables the coatings to impart lower surface emissivity to the elastomeric substrate.
[FIGURE 1 OMITTED]
Model and solution method
For illustration purposes, consider a small object of interest suspended inside of a very long tube which is at a higher temperature than the object and through which cooler air flows. Assume further that the object has reached steady state and there are no thermal gradients within the object. The steady state temperature of the object is then determined by the solution to the energy balance (equation 1):
0 = hA(T-[T.sub.air]) + [epsilon][sigma]A([T.sup.4] - [T.sup.4.sub.source]) (1)
Where h is the convective heat transfer coefficient, A is the surface area of the object, [epsilon] is the emissivity, [sigma] is the StefanBoltzmann constant, T is the steady-state temperature of the object, [T.sub.source] is the temperature of the tube wall and [T.sub.air] is the ambient air temperature. For any combination of parameters in this simple energy balance, one could solve for the resulting steady state operating temperature. A primer on radiation heat transfer relevant to this work is contained in the appendix. A more complete background is available in standard heat transfer texts (ref. 3).
The thermal environment for automotive components is quite complex, with multiple sources of radiation involved as well as both conduction and convection. The approach taken in this study is to simplify the model to the essential elements so as to be able to understand the effects of key model parameters with particular emphasis on the emissivity of the surface. In this model, energy is exchanged via convection with the ambient air with a presumed convection coefficient, and energy is exchanged by radiation with both a hot object of concern and the collection of other surfaces that are at a temperature different than the ambient air in most cases. Conduction is neglected in this model. The radiation is thus considered to be a three surface enclosure with one surface being the component, another being the hot object ([T.sub.source]), and the remaining surface being the totality of remaining surfaces ([T.sub.surr]) which are presumed to have a single temperature. Geometrically, one can envision this as a component suspended inside a very long, two-sided duct where one side of the duct represents the hot object and the other side represents the surroundings while air flows through the duct exchanging energy by convection only with the component (figure 1).
Several assumptions are needed to simplify the model (see appendix for background):
* Kirchoff's Law is valid so that the emissivity [epsilon] and absorptivity ct of the surface are the same.
* The source and surrounding objects behave as black bodies ([epsilon] = 1) with known constant temperatures.
* The component is convex or flat ([F.sub.11] = 0).
* Air is not involved in radiation.
* Convection occurs only between the component and the air.
A steady state energy balance on the component of interest yields (equation 2):
0 = [F.sub.12][epsilon][sigma]([T.sup.4] - [[T.sup.4.sub.source]) + [F.sub.13][epsilon][sigma]([T.sup.4] - [T.sup.4.sub.surr]) + h(T - [T.sub.air]) (2) Where [F.sub.12] represents the view factor between the component to the hot object and [F.sub.13] = 1-[F.sub.12] is the view factor between the component and the remaining surrounding surfaces, [epsilon] is the emissivity of the surface of the component, and [T.sub.surr] represents the temperature of surrounding surfaces other than the hot object with which the component may exchange energy by radiation. For the situation of an engine mount, there are three relevant temperatures: [T.sub.source] represents the temperature of a hot object such as an exhaust manifold, [T.sub.surr] represents the temperature of other underhood surfaces, and [T.sub.air] represents the temperature of the air flowing through the engine compartment. Equation 2 is easily solved for the steady state object temperature T. However, it is not the steady state temperature of the component that is of primary interest in this work; rather it is the reduction in steady state temperature that results from changing the surface emissivity of the component to a lower value that is desired. This is meant to simulate the effect of coating the component with a lower emissivity material. The energy balance is thus solved twice for each condition, once for [epsilon] = 1 to represent an uncoated component, and again with a lower value ore to represent a component coated with a lower emissivity material.
Of course, if one were investigating a specific component, the attention would shift to the actual steady state operating temperature. This type of analysis would require more specific information about the geometry, material properties, airflow and boundary conditions, and is beyond the scope of this work. As a point of reference, it should be kept in mind that a frequently used rough rule of thumb is that the rates of degradation reactions are assumed to be cut approximately in half for every 10[degrees]C reduction in temperature if the degradation is controlled thermally and not by diffusion.
[FIGURE 2 OMITTED]
[FIGURE 3 OMITTED]
To explore the behavior of this system over a range of values of the independent variables, the experimental design approach was used. A central composite design (ref. 10) with three independent variables at five levels was used. This design is shown in table 1 in terms of coded variable levels. The actual levels of the independent variables are linearly related to the coded variable levels. The idea was to choose conditions that would illustrate the general trends and magnitudes of the reduction in steady state temperature ([T.sub.red]). An "experiment" was run in two different situations; one of an underhood component, and one of an underbody component. The rationale for these two different scenarios is that the heat transfer coefficient and air temperature would be expected to vary more significantly for underbody components, and the view factor is envisioned to vary more significantly for underhood components. Table 2 shows the experimental design for an underbody situation, and table 3 shows the experimental design for an underhood component situation. The dependent variable is taken to be the difference between the predicted steady state temperature of the component with a surface emissivity of 1 ([T.sub.uncoated]) and the same result with a lower surface emissivity ([T.sub.coated]). A value of [epsilon] = 0.55 is used unless otherwise indicated to approximately represent a practical lower emissivity coating. The dependent variable is thus the reduction in steady state temperature predicted by the model due to the application of a surface coating with [epsilon] = 0.55. The results thus obtained were then fitted to quadratic models in the independent variables and their interactions ([x.sub.i] and [x.sub.ij] where i and j vary from 1 to 3). These quadratic models were then used to generate contour plots.
[FIGURE 4 OMITTED]
[FIGURE 5 OMITTED]
Analysis results and discussion
In the underbody simulation, the three independent variables were taken to be the convection heat transfer coefficient ([x.sub.1]), the ambient air temperature ([x.sub.2]) and the temperature of the hot object ([x.sub.3]). The view factor [F.sub.12] was chosen to be a fixed value of 0.2, while the heat transfer coefficient h was varied from 16 to 184 W/[m.sup.2][degrees]C, [T.sub.air] was varied from - 11 [degrees]C to 141 [degrees]C, and [T.sub.source] was varied from 100 to 600[degrees]C. The values of the independent variables and the steady state temperature reduction [T.sub.red] = [T.sub.uncoated] - [T.sub.coated] results are shown in table 2. Note that a positive value of [T.sub.red] indicates that the coating caused a lower steady state operating temperature to occur compared to an uncoated component with an assumed [epsilon] = 1. These results were then fitted to a quadratic model ([r.sup.2] = 0.979) and the model was used to plot contour plots shown in figure 2. The third independent variable is held constant at the center point value in all contour plots. From figure 2 it is evident that the coating is predicted to be most effective under conditions of low convective heat transfer coefficients and high temperature sources. Note that under conditions of low h and low [T.sub.source], it is possible to have the situation where [T.sub.coated] > [T.sub.uncoated].
In order to understand this somewhat counter-intuitive result, the conditions under which the steady state operating temperature does not depend on the surface emissivity (no effect of a coating) can be determined by using equation 2. This is done by writing equation 2 for two different values of [epsilon] and solving for the common value of T (equation 3):
T = [sup.4] [square root of ([T.sup.4.sub.surr] - [F.sub.12] ([T.sup.4.sub.surr] - [T.sup.4.sub.surr]))] (3)
Substituting this result back into the model yields the additional conclusion that in this situation T = [T.sub.air]. Figure 3 is a plot of the [T.sub.air] required for the emissivity to have no effect on the temperature of the component using equation 3. It can be seen that the trivial solution of no effect of emissivity for the case [T.sub.air] = [T.sub.surr] = [T.sub.source] is contained in the plot. If the value of [T.sub.air] exceeds the value determined from the right side of equation 3 then [T.sub.coated] > [T.sub.uncoated] and in addition T [not equal to] [T.sub.air]. Conversely if [T.sub.air] is less than the value determined from the right side of equation 3 then [T.sub.coated] < [T.sub.uncoated] and T [not equal to] [T.sub.air].
[FIGURE 6 OMITTED]
[FIGURE 7 OMITTED]
Returning to the model described by equation 2, the effect of reducing surface emissivity is examined for simulated underhood conditions. The conditions for the independent variables and the simulation results are shown in table 3. In this simulation, the three independent variables were taken to be the view factor [F.sub.12] ([x.sub.1]), the air temperature [T.sub.air] ([x.sub.2]) and the source temperature [T.sub.source] ([x.sub.3]). In this simulation, [T.sub.surr] was taken to be 125[degrees]C, h was 35 W/[m.sup.2][degrees]C, while [F.sub.12] was varied from 0.032 to 0.37, [T.sub.air] was varied from 65 to 140[degrees]C, and [T.sub.source] was varied from 100 to 600[degrees]C. These results were then fitted to a quadratic model ([r.sup.2] = 0.999) and the model was used to plot contour plots shown in figure 4. The third independent variable is again held constant at the center point value in all contour plots. From this plot it is evident that a reduction in surface emissivity is predicted to be quite effective at higher view factors and high source temperatures. Protection from radiation heat transfer is not needed for [T.sub.source].
Equation 2 was used to predict the isolated effect of surface emissivity on the steady state temperature reduction [T.sub.red] using the center point conditions from the two central composite experiment designs. The effect of surface emissivity on [T.sub.red] is shown in figure 5. The extrapolated value of [T.sub.red] at [epsilon] = 0 represents the elimination of radiation heat transfer and the equilibration of the component with the ambient air at [T.sub.air]. A monotonic increase in [T.sub.red] is noted as the [epsilon] of the coated component is decreased. The magnitude of[T.sub.red] and the sensitivity to [epsilon] depends on the other parameters in the model, as can be observed by the difference between the underhood and under-body simulations.
In order to explore the effect of emissivity more fully, including interactions with other variables, another central composite design simulation was run with [x.sub.1] = h, [x.sub.2] = [epsilon], 3 = [T.sub.source]. In this experiment, [T.sub.red] is the difference between the solution to equation 2, with [epsilon] = 1 and the value of [epsilon] listed as the experimental condition. The conditions used and the results that were obtained are shown in table 4. The results were fitted to a quadratic polynomial model ([r.sup.2] = 0.985) which was used to create contour plots. Figure 6 indicates that the sensitivity of [T.sub.red] to emissivity decreases as the value of [T.sub.source] decreases.
It is also possible to use these same data to examine the effect of emissivity and heat transfer coefficient, as shown in figure 7. The value of [T.sub.red] increases as the value of [epsilon] decreases over most of the region, with the steepest dependence at low values of h. A reduction in [epsilon] is most effective at low h as can occur in a location where airflow is restricted.
The operating temperature of an automotive component that is in proximity to another high temperature component can be reduced by application of a coating that has an emissivity that is lower than that of the component. This is most effective under conditions of low convective cooling, high source temperatures and low coating emissivity. Further work is needed to experimentally verify the simulations.
Energy is exchanged between bodies which are at different temperatures by three mechanisms: conduction, convection and radiation. Generally conduction and convection are what one considers as most obvious, but radiant heat transfer can be significant as well. Conduction heat transfer is the energy that is transferred between bodies via direct contact between the bodies (e.g. warming one's hands by wrapping them around a hot cup of coffee). Heat transfer by convection adds the element of fluid movement to the mechanism of transfer of heat. This fluid movement can be driven by buoyancy forces arising from differences in fluid density caused by temperature changes (termed natural or free convection in this situation) or by mechanical means such as the air forced to flow through a radiator by virtue of the motion of the vehicle or the operation of an electric cooling fan (so called forced convection). The third mechanism of heat transfer is thermal radiation which is usually viewed as the most complex.
Heat transfer by radiation is distinguished from the other two by the fact that radiation heat transfer occurs between two bodies without the need for an intervening medium. The energy from the sun that warms the earth arrives through the vacuum of outer space. The observation that is fundamental to radiation heat transfer is that all objects emit thermal radiation that is proportional to the 4th power of the absolute temperature. This mode of heat transfer is different from the other two in that the wavelength of the thermal radiation, the direction or orientation from a radiating surface, and the geometric arrangement of two surfaces exchanging radiation are important considerations as are unfamiliar properties such as emissivity, absorptivity, reflectivity, and transmissivity. The transmissivity is assumed to be 0 for an opaque material. It is tempting to rationalize that this complex mode of heat transfer is only important in the case of very high temperatures such as a piece of metal that is visibly glowing "red hot" or the surface of the sun. The truth is that radiation heat transfer is always present but is not always significant in magnitude relative to the other heat transfer mechanisms operative in a given situation.
The three mechanisms of heat transfer have different constitutive relations governing the basic behavior. Heat transfer by way of conduction is proportional to the temperature gradient within the body, heat transfer by convection is proportional to the difference in temperature between a surface and the fluid flowing over that surface, and heat transfer by radiation is proportional to the difference between two surface temperatures each raised to the 4th power.
[??]= kAdT [dT/dx] conduction [??] = hA(T-Ts) convection [[??].sub.1-2] = [epsilon][sigma][F.sub.12][A.sub.1]([T.sub.1.sup.4]- [T.sub.2.sup.4]) radiation
The property [epsilon] is defined as the emissivity of the surface and is the ratio of the energy emitted from the surface relative to that of a blackbody at the same temperature. When considering the radiation energy absorbed by a surface one needs to consider a different property called the absorptivity [alpha] which is defined as the fraction of incident radiation that is absorbed by a surface. A surface that is a blackbody would absorb all incident radiation and thus would have an absorptivity of 1. A frequently used simplification is that [epsilon] = [alpha] which follows from the assumptions delineated in Kirchoff's Law (ref. 2). To account for the size, shape, and geometrical arrangement of any two surfaces a so called view factor [F.sub.ij] is defined. Formally, [F.sub.ij] is the fraction of the radiant energy that leaves surface i that falls on surface j directly.
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by Russell L. Warley, Penn State Erie, The Behrend College School of Engineering, and Tejbans S. Kohli, Lord
Table 1--central composite experiment design [X.sub.1] [X.sub.3] [X.sub.3] 1 -1 -1 -1 1 -1 1 1 -1 -1 -1 1 1 -1 1 -1 1 1 1 1 1 0 0 0 0 0 1.682 0 1.682 0 1.682 0 0 0 0 -1.682 0 -1.682 0 -1.682 0 0 Table 2--underbody model simulation. results h [W/([m.sup.2] [T.sub.surr] [T.sub.source] [T.sub.red] [degrees]C)] ([degrees]C) ([degrees]C) ([degrees]C) [x.sub.1] [x.sub.2] [x.sub.3] y 50 20 200 3.7 150 20 200 1.39 50 110 200 -2.04 150 110 200 -0.86 50 20 500 28.16 150 20 500 11.29 50 110 500 29.06 150 110 500 11.51 100 65 350 5.18 100 65 602.3 23.95 100 140.69 350 1.37 184.1 65 350 3 100 65 97.7 -0.77 100 -10.69 350 7.56 15.9 65 350 15.4 Table 3--underhood model simulation results [T.sub.air] [T.sub.source] [T.sub.red] [F.sub.12] ([degrees]C) ([degrees]C) ([degrees]C) [X.sub.1] [X.sub.2] [X.sub.3] y 0.1 80 200 5.8 0.3 80 200 8.1 0.1 125 200 1.1 0.3 125 200 3.1 0.1 80 500 19.1 0.3 80 500 40.9 0.1 125 500 12.9 0.3 125 500 32.6 0.2 102.5 350 12.9 0.2 102.5 602.3 39.8 0.2 140.345 350 8 0.3682 102.5 350 20.7 0.2 102.5 97.7 1.8 0.2 64.655 350 17.7 0.0318 102.5 350 4.1 Table 4--emissivity experiment h [epsilon] [T.sub.source] [T.sub.red] [W/([m.sup.2] ([degrees]C) ([degrees]C) [degrees]C)] [x.sub.1] [x.sub.1] [x.sub.1] y 50 0.202735 200 6.86 150 0.202735 200 2.5 50 0.797265 200 1.62 150 0.797265 200 0.62 50 0.202735 500 53.32 150 0.202735 500 20.34 50 0.797265 500 12.04 150 0.797265 500 5.02 100 0.5 350 7.52 100 0.5 602.3 29.62 100 1 350 0 184.1 0.5 350 4.27 100 0.5 97.7 0.6 100 0 350 15.54 15.9 0.5 350 26.24
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|Author:||Warley, Russell L.; Kohli, Tejbans S.|
|Date:||Apr 1, 2012|
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