The eye is an important organ of the human body, and its physiology can change mainly due to the ambient air temperature and velocity. In this study, a three-dimensional computational model for airflow around a full-scale manikin and the flow inside the eye is developed and used to evaluate the heat removal from the manikin eyes due to natural and forced convection under different environmental conditions. For natural convection, it was assumed that the movement of surrounding air was only due to the buoyancy effect in the body's thermal plume. Uniform air velocity and temperature far from the manikin were assumed for combined natural and forced convection. For simulating the velocity and temperature distribution, equations of continuity, momentum, energy, and turbulence transport model were solved numerically. The results for specific conditions were compared with the available experimental data reported in the literature and acceptable agreement was found. The validated computation model was used for several simulations of wind velocities and air temperatures. It was found that the eye surface temperature distribution predicted by the present model is closer to the experimental data than the earlier numerical studies for detached eyeballs using a constant convective heat transfer coefficient. The present results showed that the convective heat transfer coefficient over an eye surface depends strongly on the airflow velocity and temperature near the head.
Research Article
Heat Removal from a Human Eye for Different Environmental Conditions - A CFD Study Using a Full-Scale Manikin
https://doi.org/10.21203/rs.3.rs-3997744/v1
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eye
heat transfer
numerical modeling
manikin
natural convection
force convection
The eye is one of the most important organs of the human body. The changes in ambient temperature may affect the eye's physiology. Studying temperature distribution in the eye under different environmental conditions is important for understanding eye physiology and its interaction with the environment. Currently, an experimental facility for in vivo temperature measurement inside the eye is unavailable. However, some earlier experimental studies [1]–[4]measured the eye's surface temperature. Due to the limitations of in vivo measurement, researchers tried to evaluate the fluid flow and temperature distribution inside the eye by numerical simulation. Amara[5] investigated the effect of laser power and wavelength on the eye tissues by modeling a human eye exposed to laser irradiation. Heys and Barocas[6] studied the movement of pigment particles released near the iris tip to predict the formation of Krukenberg’s spindle. Ooi et al.[7] studied the effect of tumors on temperature distribution inside an eye. Karampatzakis and Samaras[8] studied the impact of an artificial intraocular lens on the eye temperature distribution. Li et al.[9] simulated the 2D and 3D models of an eye and investigated the effect of hyperthermia treatment on healthy eye tissues. Narasimhan and Jha[10] modeled Pan Retinal Photocoagulation (PRP), a retinal laser surgical process, and found eye temperature distribution under different conditions. Abouali et al.[11] used a computational modeling approach to study the unsteady flow in the vitreous cavity due to saccadic eye movement. They studied the flow dynamics of the vitreous after complete vitreous liquefaction and for post-vitrectomy eyes (Vitreous gel is substituted with silicon oil and balanced salt solution). Abouali et al.[12] also modeled the aqueous humor flow in the anterior chamber due to saccadic movements. They showed that mixing the aqueous humor due to the saccadic movements increased the heat transfer in the anterior chamber and through the cornea. Modareszadeh and Abouali[13] simulated the motion of vitreous humor for the real shape of a human vitreous chamber filled with the gel- with a viscoelastic model.
Bhandari et al. [14] have developed a computational model to investigate topical drug delivery in the aging human eye. Their research explores the impact of aging on various eye parameters, including heat transfer, aqueous humor flow, intraocular pressure, and drug distribution across different eye regions and orientations. Bayat et al. [15]–[17] studied partial vitreous liquefaction (PVL) flow dynamics as a two-phase viscoelastic-Newtonian fluid in 2D and 3D human eye models. Rahman et al. [18] studied the anatomical and physiological changes in the human eye as it ages. They have developed a model to analyze the thermos-fluid dynamics of the aging human eye, incorporating four physiological changes into their simulations: metabolism, blood perfusion, tear evaporation, and aqueous humor flow. Tang et al. [19] conducted simulations of the aqueous humor (AH) flow within human eyes, featuring diverse morphological structures and physical characteristics. They acquired the velocity distribution and temperature distribution of the aqueous humor flow.
All these earlier studies modeled the anterior chamber or the entire eyeball and the cornea as the boundary of the computational domain in contact with the ambient air. The heat transfer through the eyelid was not included in the earlier models. But when the eye is open, in addition to the cornea, a part of the sclera is also in contact with the ambient air. In some earlier studies, the temperature distribution obtained from the IR thermograph[6] is applied to the cornea as a boundary condition. In other research, the constant ambient convection heat transfer coefficient experimentally measured by Lagendijk[20] for a rabbit eye is used for the boundary condition at the cornea. Some researchers studied the effect of different parameters like ambient temperature and convection coefficient on the eye temperature distribution [21]–[25]) None of these earlier works investigated the corresponding environmental condition for the assumed convection coefficients.
Natural and forced heat transfer coefficients for different body parts under various environmental conditions were studied before in the literature. Dear et al.[26] reported experimentally measured convection and radiation heat transfer coefficients under natural and forced convection conditions for different parts of a seated and a standing manikin. Their measurement for force convection is performed for air velocities in the range of 0.1-5 m/s. They also reported some correlations for radiation and convection heat transfer coefficients for different body parts for different airflow velocities. Serensen and Voigt[27] found a seated manikin's natural heat transfer coefficient experimentally and numerically. They also investigated radiation heat transfer in their numerical simulation. Craven and Settles[28] provide particle image velocimetry (PIV) measurement of the thermal plume velocity at the top of the human head created due to the temperature difference between the body and ambient air in a standard room with moderate thermal stratification. They compared their experimental data with their CFD model and reported that the room thermal stratification significantly affected the thermal plume. Ono et al.[29] used a combined experimental and numerical approach to study the heat transfer coefficient of a standing manikin for different air velocities. They validated their CFD code by their experimental data and presented a correlation for body heat transfer coefficient for different air velocities and turbulence intensities. Kurazumi et al.[30] experimentally investigated the effect of postures on the conduction, convection, and radiation heat transfer of a manikin in an environmental chamber. Zhang et al.[31] reviewed manikins' experimental and numerical heat transfer studies. They considered three geometrical models (the first model was constructed using several cubes, the second one was developed using a sphere and cylinders and the third geometry resembles a standing human body). Their numerical results for the third model are more compatible with experimental measurements. Jia et al.[32] studied the details of a thermal plume created around a seated and heated manikin due to temperature differences with the environment. They used an LBM computational model for a rectangular-shaped manikin in a small room. Salmanzadeh et al.[33] numerically and experimentally investigated the effect of a thermal plume around a seated manikin on the particle transport in a cubicle. Ruzic and Bikic[34] simulated thermal conditions in vehicle cabins and studied natural and forced convection heat transfer between the manikin and the environment. Lee et al.[35] experimentally measured a seated manikin's natural convection[33] heat transfer coefficient. They validated their numerical results with experimental data and used their simulation to find the force heat transfer coefficient for different air velocities. Hasama et al.[36] studied the attributes of air circulation produced by ceiling fans around a thermal manikin and the convective heat exchange resulting from the airflow distribution through both experimental methods and CFD while considering both standing and seated positions.
In the present study, flow and heat transfer inside the eye of a three-dimensional manikin are simulated for both natural and mixed convection flows around the body. Particular attention was given to the variation of temperature inside the eye. In the present work, the manikin's surroundings were added to the computational model to study the heat transfer through the eye for different environmental conditions. Using this approach, the heat transfer coefficient over the cornea is obtained through the solution and it is not set with a rough approximation as a boundary condition.
To create a geometrical model of a human body, a 3D CAD model of a standing male manikin is used, shown in Fig. 1. The CAD model is converted to the STL file smoothed and scaled to 1.77 m height. To decrease numerical complexity, some simplifications are done on the model such as closing the lips and nostrils, removing eyelashes, ears, and nails, and smoothing the feet. The resulting simplified manikin model is shown in Fig. 2, which resembles a normal man and is more realistic than models used in the previous simulations [27], [28], [32], [34], [37]).
To model the eye with the dimensions presented by ([8], [38], [39]), a 3D computational model is created in GAMBIT 2.4.6 software by rotating a 2D model (shown in Fig. 3) around the optical axis. The axial diameter is 26 mm, and the vertical diameter is 23.65 mm, which leads to a total volume of 7.36 cm3 for the eye.
The developed eye model consists of a cornea, anterior chamber, posterior chamber, iris, lens, vitreous, and sclera. For simplification, the retina and choroid, which are very thin compared to the sclera, are not considered in the present model. Finally, the eye model is attached to the manikin using ANSYS 14.5 (ICEM,) as shown in Fig. 4.
The selected computational domain for the airflow is sufficiently large that the boundaries do not affect the thermal plume flow field around the manikin. Typically, the air far from the manikin is assumed to be stagnant for the natural convection case. Figure 5a shows the dimensions of the computational domain used for the airflow study. The domain independence study is performed by measuring heat transfer from the eye surface of the manikin. Table 1 shows the size of boxes used for various computational domains to study mixed convection. Table 1 also compares the heat flux and transfer coefficient for different domain sizes. It is seen that the simulation results for domains 2 and 3 are relatively close. Accordingly, the domain with a dimension of botwo 2 is selected for the rest of the analysis. Figure 5 illustrates the computational domain used for both the natural and mixed convection cases.
| Case number of computational domains | Number of grids | Size of the computational domain L×W×H (m3) | Average heat transfer coefficient (Wm− 2K− 1) | Average convective surface heat flux (W/ m2) |
|---|---|---|---|---|
| 1 | 1843365 | 0.95×0.76×1.79 | 20.2 | 308.2 |
| 2 | 5847579 | 4.95×7.76×3.80 | 17.8 | 270.6 |
| 3 | 7617363 | 7.5×12×6 | 17.6 | 267.8 |
The eyeballs and the space between the manikin and the surrounding cube (shown in Fig. 5) are considered a computational domain. To study the flow field, the following assumptions are made: The airflow is incompressible and steady and around the manikin is in turbulent regime. The experiment of Clark and Toy [40] showed that the flow is laminar around a standing nude human for height shorter than 0.9m with (Tskin =306 K, Tair=293 K, and Grashof number = 2×109) but the regime becomes fully turbulent for a manikin taller than 1.5 m (Grashof number = 1010). The eyes are located on the head; therefore, assuming a turbulent flow around the manikin head is especially justified. It is assumed that the liquid flow in the eye anterior chamber is laminar because of the low velocity in the small anterior chamber.
The physical properties of air are constant and determined at the film temperature. Boussinesq approximation is adopted for the density variation since the temperature difference is sufficiently small with βΔT < < 1 [41]. The body force in these flows is only due to gravity.
Governing Equations
a) Temperature distribution inside the solid part of the eyeball is obtained by solving the following heat conduction equation [8]:
$$-\nabla . \left(k\nabla T\right)=A-B\left(T-{T}_{bl}\right)$$
1
where T is temperature, k is thermal conductivity, Tbl is blood temperature, A is the metabolic heat generation rate and B is the term associated with the blood perfusion rate. Only aqueous humor (AH) in the anterior chamber is considered liquid).
Governing equations of conservation of mass, momentum, and energy for laminar flow of aqueous humor (AH) are expressed as:
| \(\nabla .\overrightarrow{v}=0\) | (2) |
|---|---|
| \(\rho (\overrightarrow{v}\bullet \nabla\)) | (3) |
| \(\nabla \bullet \left(k\nabla T\right)-\rho C\left(\overrightarrow{v } \bullet \nabla T\right)=0\) | (4) |
where the Boussinesq approximation is used for density variation. Here, β is the fluid's volume expansion coefficient, C is heat capacity, and Tref =34 ˚C is a reference temperature.
Several turbulence models are investigated to predict the thermal plume due to natural convection. The RNG k-ε model with three different types of boundary conditions (scalable wall function, enhanced wall treatment, low Reynolds) and the SST k-ω model were used in the present study. Among these models, the RNG k-ε model with enhanced wall treatment is better matched to the experimental data for the heat transfer coefficient over the body and no inconsistent jump over the contours. Therefore, this model was used for further simulations.
All the testing steps are repeated for mixed convection, and the RNG k-ε model combined with the enhanced wall treatment option is selected for the rest of the simulations.
The details of the continuity, momentum, energy, and the RNG k-ε turbulence model equations are not shown here for brevity, and they can be found in (ANSYS manual).
Boundary Conditions
To investigate mixed convection heat transfer from the manikin, uniform air velocity with 6% turbulent intensity and 0.7 m length scale (approximately similar to the experimental conditions of De dear et al. [26]) is applied on the inlet boundary. Zero gradients for flow parameters are considered at the outlet boundary condition. Enhanced wall treatment boundary condition is used on wall surfaces such as the computational domain's manikin surface, bottom, upper and side walls. In addition, the symmetry and uniform velocity boundary conditions are also tested on the upper face and sides of the computational domain. Due to the use of sufficiently large computational domains, the effects of these different boundary conditions on the heat transfer from the manikin were found to be negligible. Therefore, the results can also resemble the outdoor conditions. Air with different velocities and temperatures as summarized in Table 3, are used on the inlet boundary of the computational domain. Manikin surface temperature is assumed to be 34 ˚C.
When the ambient air speed is less than 0.2 m/s, the heat transfer from the human skin is mainly treated as natural convection. The force convection has also been simulated for a velocity higher than this. The selected range of air velocity (0.2-5 m/s) covers indoor and outdoor environmental conditions.
| Air velocity (m/s) | Environmental temperature (˚C) | |
|---|---|---|
| 0.0 | 0 | 20 |
| 0.3 | 0 | 20 |
| 1.0 | 0 | 20 |
| 5.0 | 0 | 20 |
To study natural convection conditions, a pressure inlet is applied on the side surfaces of the computational domain. Enhanced wall treatment is applied on the upper and lower surfaces of the domain.
Also, a zero gradient type boundary condition is considered an outlet boundary condition on the upper surface of the computational domain.
Numerical simulations are performed for two ambient air temperatures of 0, 20 ˚C. To consider heat flux between parts of the cornea and sclera that have contact with the inside of the body, the following equation is applied, respectively:
In this equation, the temperature of blood vessels Tbl, near the sclera is assumed to be constant, hs is the heat transfer coefficient between the inside of the body and the eye, B corresponds to the term associated with the blood perfusion rate, and A is the metabolic heat generation rate. Thermal properties and the quantities considered for Eq. (14) are summarized in Table 4 and Table 5.
| Material | Density ρ(hg m− 3) | Specific heat c(J kg− 1K− 1) | Thermal conductivity k(W m− 1K− 1) | Basal metabolism (W m− 3) | Blood perfusion power equivalent (W m-3 K-1) | |||
|---|---|---|---|---|---|---|---|---|
| Cornea | 1050a | 4178a | 0.58a | - | - | |||
| Sclera | 1050a | 3800b | 0.58b | 22000b | 80000b | |||
| Anterior chamber | 996a | 3997a | 0.58a | - | - | |||
| Iris | 1050a | 3600b | 0.52b | 10000b | 35000b | |||
| Lens | 1000a | 3000a | 0.4a | - | - | |||
| Vitreous chamber | 1100a | 4178a | 0.603a | - | - | |||
| a[38] | ||||||||
| b[42] | ||||||||
| Parameter | Description | Value | |
|---|---|---|---|
| hs | Body heat transfer coefficient (W m− 2 K− 1) | 65a | |
| Tbl | Blood temperature (˚C) | 37 | |
| E | Evaporation rate (W m− 2) | 40a | |
| σ | Stefan-Boltzmann constant (W m− 2 K− 4) | 5.67×10− 8 | |
| ε | Emissivity of corneal surface | 0.975a | |
| a [38] | |||
No slip boundary condition on the anterior chamber surface, which is assumed to be rigid and impermeable, is imposed. Mechanical properties of eye layers are considered homogenous and isotropic.
To consider radiation heat transfer from the eye surface, the heat flux given as
is added to each element of the eye surface that is in contact with the environment. A UDF (User-defined function) was developed and incorporated into the ANSYS-FLUENT.
According to the previous studies of [21], the evaporation rate from a normal eye ranges from 40–100 W/m2. Here, the lowest value of E = 40 W/m2 is used to obtain the highest temperatures in the eye. The evaporation heat loss is included using the same procedure used for the radiation heat transfer.
The commercial fluid dynamic software package ANSYS-FLUENT is used for numerical simulation. An unstructured grid is developed for the environmental chamber around the manikin using the ANSYS (ICEM) software. To resolve the boundary layer around the eye, five layers of extruded triangular prisms are used with an initial size of 0.01 cm and a growth rate of 1.1 between the layers. Since the focus of the present study is the heat transfer from the eyes, most grid elements are placed around the head, particularly near the eyes, as shown in Fig. 6. The grids are fine near the manikin and become course far from the manikin.
Since the enhanced wall treatment is used as the turbulent wall boundary condition, the value of y+ should be less than 5 for the grid points adjacent to the manikin surface as a requirement for the used turbulence model. In these simulations, it is made sure that this condition is satisfied. For the case of natural convection with a body temperature of 34˚C and environmental temperature of 22 ˚C, the average value of y+ for the first grid points near the manikin body is equal to 0.62.
To generate a computational grid for the anterior eye chamber, a structured grid is used for the 2D geometry shown in Fig. 7. Then, by rotating this grid around the optical axis, the 3D structured grid is created.
The eye grid is integrated with the manikin grid using an unstructured grid in the cornea and sclera. To have a smooth transition between the structured grid inside the eye and the unstructured grid outside, rectangular elements on the outer surface of the structured grid are separated into two triangles by ANSYS (ICEM) software to be a base for the unstructured grid of cornea and sclera as illustrated in Fig. 8.
The grid independence study is performed for various grid sizes, and finally, the cases with about 5 and 6 million cells are selected for natural and mixed convection cases, respectively.
There is no available experimental data for airflow around the manikin shown in Fig. 2. Therefore, to validate the computational model, the simulation results are compared with experimental and numerical data for airflow around another manikin and the liquid motion in a separate eye model.
a) Validation of the eye flow model
To validate the simulation model for the aqueous humor flow in the eye, the velocity field in the anterior chamber for the thermal boundary conditions of Karampatzakis and Samaras[8] is simulated and the predicted velocity profile along the pupillary axis is compared with the numerical results of [8]in Fig. 9. This figure shows good agreement of the predicted velocity distribution with earlier simulation. The deviation seen is due to a slight difference between the two geometries.
The maximum velocity reported for the numerical study of Karampatzakis and Samaras[8] is 3.36×10− 4 (m/s). In the current work, the maximum velocity is 3.39×10− 4 (m/s), which is quite close. But the second peak differs by a factor of 2. The details of the geometry of Karampatzakis and Samaras ([8], [28] ) are not available and it was impossible to compare more information on the flow field.
b) Validation for natural convection around manikin:
Two cases were studied for validating the natural convection flow simulations around the manikin.
1- The flow field and heat transfer of a manikin standing in the center of a box is investigated. A comparison of the present simulation results with the experimental data and numerical results of [28]for velocity magnitude along almost the plume centerline as a function of height from the floor is shown in Fig. 10. It is seen that there is an acceptable agreement of the present simulation results with the experimental measurements of [28].
The Maximum plume velocities reported by Craven and Settle[28] for the experimental data and their numerical model, respectively, were 0.24 m/s and 0.20 m/s. The present simulation predicts a maximum velocity of 0.25 m/s, which agrees with the experiment measurement.
2- de Dear et al.[26] reported the natural heat transfer coefficient of the head and the entire body for 12 K temperature differences, respectively, as 3.6 and 3.4 W/(m2.K). These values are close to the results of the present study of 3.36 and 3.12 W/(m2.K) to the heat transfer coefficients.
c) Validation for mixed convection flows around the manikin:
To validate the results for mixed convection around the manikin, the experimental condition of de Dear et al.[26] is applied to the present modeling and the results are shown in Fig. 11. In their experiment, the manikin surface temperature was equal to 34 ˚C and the ambient temperature was 20 ˚C. A general agreement between the present computational work and experimental measurements can be observed. The deviation is possibly due to different geometries for the manikins and experimental and numerical errors. The manikin in their work had hair and clothes. In addition, a large cylindrical drum (1.5 m tall and 0.5 m diameter) was installed upstream on the floor in the wind tunnel to generate large-scale eddies in the experiment. Also, Ono et al.[29] reported that the convective heat transfer coefficient of a seated manikin for 1 (m/s) air velocity and 10% turbulent intensity is hc =12.9 (W/m2.K). This value is close to that in the current study, which is hc=11.95 (W/m2.K).
The validated computational model is used and the airflow and temperature fields and heat transfer from a standing manikin with attached eyes for different environmental air velocities and temperatures are computed. Typical velocity distribution around the manikin for different air velocities and ambient temperatures are shown in Fig. 12. Although the thermal plume above the manikin head becomes different with an open-like boundary (like [27]), heat transfer and velocity around the eye does not change noticeably. Therefore, present results also can be used for outdoor conditions.
In the case of natural convection, the velocity in the thermal plume reaches 0.8 m/s. The velocity behind the head is higher than that in the front of the head. The velocity close to the eye, which is the focus of this study, is less than 0.1 m/s. The velocity field changes considerably when the wind blows toward the manikin. A plume formed over the head for free convection, while for wind-blowing conditions, a large separation zone is observed on the back of the manikin. The velocity increases compared to the free stream and reaches almost 1.5 m/s between the legs and 1.3 m/s over the head. The air velocity close to the eye is around 0.3 m/s, which is three times that in the case of free convection.
Figure 13 illustrates the velocity vectors in the vertical middle plane of manikin's left eye for different ambient air velocities and environmental temperatures. This figure shows that a circulation flow forms in the aqueous humor due to temperature differences across the anterior chamber. As expected, by increasing the air velocity and temperature difference between the body and the environment, the circulating flow in the anterior chamber becomes stronger due to increasing heat flux between the eye and the environment.
The effect of environmental air velocity and temperature on the average convective heat transfer coefficient and average heat flux over the eye is summarized in Tables 8 and 9. The data in these tables show that the heat transfer coefficient and heat flux over the eye change significantly when the airflow velocity increases. According to Baldwin and Maynard [43], air velocity in indoor conditions is approximately 0.3 m/s, and based on the current results, the convection heat transfer coefficient is h ̅ = 11 W/m2.K which is consistent with the values reported in [9], [21]–[25], [44]. This value, however, is valid only for indoor conditions and the heat transfer coefficient changes for different environmental conditions, as presented in Table 8. According to the results, some investigators used very large convection coefficients ([22], [24], [25]) such as 100 W m−2 K−1 which does not occur even in high air velocity and ambient temperature.
Table 8. Variation of average convective heat transfer coefficient (W/(m2.K)) of manikin eye.
Table 9. Variation of average convective heat flux (W/m2) of manikin eye.
Contours of convective heat transfer coefficient and heat flux over the manikin head for 1 m/s ambient airflow velocity at the temperature of 20˚C are shown in Fig. 14. As expected, in the bulge (gibbosity) parts of the manikin, heat transfer is higher.
Temperature contours on the surface of the eye for different air velocities are shown in Fig. 15. It is seen that the temperature distribution on the eye surface is not uniform. As expected, due to the convexity of the cornea, the maximum heat transfer occurs in this region, and hence, minimum eye temperature appears on the cornea. The isotherm contours of the eye are elliptical, similar to the observation of [3]. It is also seen that the far-field air temperature does not have a noticeable effect. This is because the thermal plume around the body controls the airflow and temperature fields near the head, and the temperature contours on the eye's surface do not change. For the mixed convection case, the far-field air temperature slightly affects the eye surface temperature, but the difference between far-field temperatures of 0˚C and 20˚small.
For a more comprehensive examination of the fluctuations in human eye temperature, a calibrated thermographic camera was employed to capture thermal images of the subjects. The room temperature was rigorously maintained within a narrow range of ± 0.1˚C by a control system comprising a computer, three thermocouples, and an air cooling and heating unit. Further details regarding the control room and the experimental procedures can be found in the work of Mahdavi and Yaghoubi [24]. The room temperatures selected for this study were 20, 23, and 25˚C, with the corresponding thermal image of the eye displayed in Fig. 16. Notably, the observed temperature variations on the surface of the eye were minimal, supporting the assumption that the eye's temperature could be considered relatively constant at T = 34˚C.
Figure 17 shows the temperature distribution at the eye vertical mid-plane for different environmental air velocities and temperatures. The surface temperature of the eye and anterior regions of the eye increases slightly for higher ambient temperatures and lower air velocities. For a 20˚C difference in the environmental temperature, the surface temperature of the eye differs by 1˚C for the natural convection case and about 3˚C for the mixed convection case with an airflow velocity of 1 m/s.
The convective heat transfer coefficient of the eye for manikin alone and manikin with attached eyes for different environmental air velocities and temperatures are presented in Table 10. When only the manikin without the eye globe is modeled, the temperature boundary condition is set on the uncovered surface of the cornea and sclera (34˚C). Table 10 depicts the differences which shows the importance of solving the eye coupled with the surrounding parts of the manikin.
Table 10. Average heat transfer coefficient (W/m2.K) of an eye for different models (T = 20 ˚C).
Table 11 compares the effect of convection and radiation on the eye for different ambient air velocities and temperatures. It is seen that the convection and radiation heat fluxes are in the same order for low air velocities which correspond to the indoor conditions. With the free stream air velocity increase, the convection dominates the heat transfer from the eye compared with the radiation.
Table 11. Convective and radiative heat transfer rate (W/m2) from an eye at different ambient air velocities and temperatures.
In the present study, the airflow velocity and temperature distribution of flow around a manikin and inside the eye were simulated using a model for eyes connected to a standing manikin. The convective heat transfer coefficient and heat flux over the eye were evaluated for different ambient air velocities and temperatures. The simulation results showed:
-
Modeling the airflow surrounding the manikin, including the face and the eyes and solving coupled system with the motion of aqueous humor inside the anterior chamber of the eye leads to more accurate results. The coupled simulations make the predicted eye temperature distribution more similar to the experimental data.
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The simulation results for air velocities in the range of 0 to 5 m/s and ambient temperatures of 0 and 20˚C showed that the convective heat transfer coefficient of the eye varied in the range of 4.7–43.1 W/m2.K and the heat flux varied in the range of 115.4 W/m2 to 1185.2 W/m2. Therefore, assuming a constant convective heat transfer coefficient irrespective of the environmental conditions is not appropriate for the thermal modeling of the eye. These results could be of interest to the reasons for the dryness of the eye due to an increase in heat transfer at high airflow velocities and low air temperatures.
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Natural convection due to temperature difference across the eye anterior chamber became markedly stronger by the increased air velocity and decreased air temperature. For the range of parameters studied, the maximum velocity of aqueous humor inside the anterior chamber of the human eye changed from 0.2 mm/s to 0.6 mm/s. That is, the variation in environmental conditions had a noticeable influence on the aqueous humor motion in the eyes.
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For high air velocities and low ambient temperature, the convective heat transfer became dominant compared to evaporation and radiation from the eye.
Author Contribution
F.F. wrote the main manuscript text, Conducted research, performed literature review andM.Y. , G.A, O.A mentored the research process, edited the manuscript, and provided guidance on research direction. All authors reviewed the manuscript.
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No competing interests reported.