A tool to minimize the need of Monte Carlo ray tracing code for 3D finite volume modelling of a standard parabolic trough collector receiver under a realistic solar flux profile

The energy collection element of a parabolic trough collector includes a selective coated metallic receiver tube inside an evacuated glass tube. Perpendicularly incident sun light on the parabolic trough mirror aperture is concentrated on the receiver tube highly nonuniformly along its circular direction. This solar energy is collected as thermal energy circulating a suitable heat transfer fluid (HTF) through the tube. This conjugate heat transfer phenomenon under nonuniform heat flux boundary condition is computationally studied applying 3D finite volume (FV) modelling technique of computational fluid dynamics coupled with Monte Carlo ray tracing (MCRT) optical data. The MCRT model simulates the actual flux profile around the receiver tube. Apart from a FV model, this coupled study requires expertise in, and access to, a suitable MCRT code. A combination of polynomial correlations and user‐defined function (UDF) is introduced in this article in order to minimize the need of MCRT codes from subsequent FV modelling of the receiver tube of the Luz Solar 2 (LS2) collector. The correlations are developed from a verified 3D MCRT model, which is equivalent to the local irradiation data as a function of receiver circular location. The UDF includes two algorithms: one to develop solar flux profile from the correlations around the receiver, and the other to calculate heat loss from the receiver. Interpreting the UDF into ANSYS Fluent, a 3D FV model of the LS2 receiver is developed and validated with experimental results. The effectiveness of the UDF as an alternative to MCRT code is verified. The FV model is capable to investigate the heat transfer characteristics of the LS2 collector receiver at different solar irradiation level, optical properties of the collector components, glass tube conditions, HTFs, inserts or swirl generators, collector length, and internal diameter of the tube.


| INTRODUCTION
Rapid depletion of fossil fuel, global warming, and ecological imbalance act as driving factors to use green and renewable alternatives of energy like solar. Efficient harnessing of this literally in-exhaustive energy has the capacity to fulfill world's energy demand. 1,2 Significant amount of research already been undertaken to develop technologies for harnessing this abundant energy. [3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22] Concentrating solar power (CSP) technologies including the parabolic trough collector (PTC), parabolic dish, linear Fresnel reflector, and heliostat field are competitive candidates to the conventional sources in terms of carbon emissions though the investment cost is still higher. 23 The PTC is one of the most efficient CSP technologies for medium temperature application ranging between 50°C and 400°C. 1,[24][25][26] A PTC consists of a parabolic trough mirror and an energy collection element (ECE) placed along the focal line of the mirror as shown in Figure 1. The PTC can be either east-west oriented, tracking the sun from north to south collecting maximum energy in winter, or north-south oriented, tracking the sun from east to west collecting maximum energy in summer employing a single-axis tracking system. 1,26,27 Perpendicularly incident light rays on the aperture of a solar pointed collector are reflected from the trough and concentrated on to the ECE. The concentrated radiation heats up the continuously circulated heat transfer fluid (HTF) through the receiver tube (see Figure 1), and, by this way, incident solar energy is converted into useful thermal energy. Thus, the overall energy performance of the collector directly depends on the optical performance of the collector and heat transfer performance of the ECE. 25,28,29 The optical performance of the collector involves parameters including solar concentrated irradiance distribution on the outer surface of the receiver tube, average light concentration, optical efficiency, and light intercept factor. Different optical and physical factors like solar irradiance intensity, ECE geometry, optical properties of the collector components, "dirt and dust" on the components, receiver defocus, and tracking error [29][30][31] affect the optical and thermal performance of the collector. The irradiance distribution around the receiver tube is highly nonuniform, which can be determined experimentally applying flux mapping 32,33 and theoretically applying cone optics, 30,34,35 and, most popularly, applying Monte Carlo ray tracing (MCRT) technique. 29,[36][37][38][39][40][41][42][43] On the other hand, thermal performance of the collector depends on the ECE design, optical and thermal properties of the receiver material, flow characteristics of the HTF, heat removal factor, heat loss coefficient, and operating and ambient condition of the collector. 1,26,27,31,37,[44][45][46][47][48][49][50][51][52][53] The receiver tube is usually coated with selective coating in order to absorb most of the concentrated light. A glass tube envelop around the receiver tube is usually placed to reduce convection loss. The loss can be further reduced evacuating the annular space between the glass tube and the receiver tube. Most of the spectral energy of the radiation is absorbed in the selective coating that increases the temperature and heat flux density at the outer surface of the receiver tube. Due to the temperature gradient, thermal conduction occurs in the tube material, and heat fluxes become available at the inner surface of the tube. The heat flux from the inner surface is absorbed into the HTF, transferred by means of mass transfer of the fluid, and released into a heat exchanger for storage or desired application. Heat conduction at the solid-fluid interface and heat convection in the bulk fluid take place. The energy transfer from the tube surface to the HTF is a coupled heat and mass transfer phenomenon with complex geometry condition. 26 With technological advancement in computing tools, modelling and simulation of PTC system provide useful information on the collector performance and optimization with less uncertainty, effort, and cost than their experimental counterpart. 3 The collector systems were studied numerically by many researchers. 3,12 Applying 1D approach, Forristall 31 investigated the effect of design conditions and operating parameters on the thermal performance of the ECE of a PTC. Luz black chrome, cermet, and solel cermet selective coatings were studied, and the ECE showed improved thermal performance. Gercia and Velazquez 54 developed a 1D mathematical model considering the geometrical, optical, thermal, and fluid dynamic aspects of a single-pass and double-pass of the HTF through the ECE. They obtained improvement in heat transfer operating the solar PTC with external recycle or with a double-pass without recycle. Padilla et al 55 57 summarized the 1D mathematical models under different assumptions and proposed a simple algorithm to make the control equations linear and solve easily. All of these 1D models are suitable for a single-piece short ECE under the assumptions that the solar radiation flux, wall temperature, and physical properties are uniform for the whole ECE circumference. However, 1D model is unable to capture nonlinearity in temperature along the ECE axis and, therefore, may underestimate heat losses. 31 Forristall 31 implemented a 2D mathematical model of the ECE of Luz Solar 2 (LS2) collector in engineering equation solver (EES) to investigate its heat transfer characteristics. The model was verified with test result obtained by Dudley et al. 47 Tao and He 58 presented a unified 2D numerical model for the coupled heat transfer process in PTC receiver tube. Both of these studies assumed constant heat flux on the outer surface of the receiver tube. On the contrary, Hachicha et al 59 36 also coupled a FV solver with MCRT model to study solar flux nonuniformity effect on the radiative exchange between the participating surfaces, and heat loss and gain.
The overall goal of these early studies was to explore the conjugate heat transfer characteristics of the ECE under realistic solar flux profile relying on coupled MCRT and CFD model. This coupled study is computationally expensive, and relied on access to, and expertise in MCRT codes, and prohibitive to many CFD researchers. No study could be found in the literature that attempted to either eliminate or minimize the need of this MCRT code for the study. The authors attempted to address this research gap and made endeavor to provide a tool to minimize the need of an MCRT code.
The MCRT simulates the optical interactions among the participating surfaces, which is a surface phenomenon and temperature independent, whereas the FV model accounts for volumetric effect of the heat flux and temperature dependent. Depending on the glass envelop condition, the annuli space between the receiver tube and the glass tube is either evacuated, filled with air, or open to environment. As the solar heat flux boundary condition is the direct input to the FV model from the MCRT model, for each variation in optical conditions including daily normal irradiance, glass tube conditions, and optical properties of the collector materials, the MCRT needs to be executed in parallel to the FV model. By this way, the process becomes computationally highly expensive.
Therefore, studying the optical characteristics of a standard PTC using MCRT technique, the authors have developed optical design data in the form of polynomial correlations and MCRT-FV coupling algorithm. The correlations and the coupling algorithm altogether replace the MCRT for further CFD study using FV model of the receiver of the collector.
The correlations for nonuniform solar flux were developed in terms of local concentration ratio (LCR) from a verified MCRT model developed earlier by the authors. 29 LCR is a nondimensional value, which is a function of receiver angular location, and product of daily normal irradiation, optical properties of the collector components and other factors that have linear effect on the optical properties of the collector. A user-defined function (UDF) was then written using Fluent-specific programming language incorporating the correlations and heat loss functions, and was interpreted in the ANSYS Fluent.
It is assumed that the solar incidence is perpendicular to the collector aperture, and the receiver diameter and the trough width are fixed to those of the modelled standard collector. Based on these assumptions, the UDF is capable to produce realistic nonuniform solar flux profile around the wall boundary of the receiver and calculate heat loss from the outer surface of receiver adopting the following variations in: 1. optical conditions include daily normal irradiance, optical properties of the collector components and linear optical loss factors such as tracking error, and effect of dirt and dust on the participating surfaces; 2. collector geometry that include collector length and internal diameter of the receiver; 3. glass envelop conditions including evacuated, filled of air or removed; and 4. internal design of the receiver, HTFs, and ambient conditions.
In order to be able to validate the MCRT and FV models directly, the LS2 parabolic trough collector from Dudley et al 47 was modelled. Zemax optical ray-tracing software for MCRT modelling 29 and ANSYS Fluent 15.0 63 for FV modelling were employed.

| PHYSICAL MODEL
The LS2 collector was used in the Solar Energy Generating System III-VII 150 MW plants, Kramer Junction, California, USA. It was tested on the AZTRAK rotating platform at SNL. 47 Figure 2A,B show the cross-sectional views of the collector and the ECE. The geometry and the optical properties of the collector are given in Table 1. A closed-end plug was inserted in the tube of the collector to increase the flow velocity of the HTF, Syltherm800 silicone oil. Thermal performances of the collector for evacuated, lost evacuated, and removed glass envelop conditions were measured using black chrome or cermet selective coatings for varying weather conditions. For the MCRT modelling, the trough and the ECE with and without glass tube envelop excluding the support structure of the LS2 collector were modelled, whereas only the HTF domain was modelled for the current FV simulation as discussed in the following sections.

| MCRT modelling
The detail MCRT simulation technique is available in, 29 and a brief description is given in this section as follows. The Cartesian coordinate system, XYZ, was used for the trough and the cylindrical coordinate system, and rβZ was adopted for the ECE system. The LS2 collector was modelled as per the geometry as presented in Table 1. A biconic surface for the parabolic trough and two concentric annular volume objects for the receiver tube and the glass tube from the object library of the software package were adapted to model the collector system. The ECE was 100 mm larger than the trough at both ends. Ideal coating system was enabled, and desired specular reflectance of the mirror, glass transmittance with antireflection coating, and ECE absorptance with spectral selective coatings were developed. The ray tracing algorithm and the light interaction among the components are presented in Figure 3A,B, respectively.
The steps in Figure 3A are self-explanatory. The rhombuses and rectangles in the flow chart represent the arguments and Monte Carlo decision of the arguments, respectively. The Monte Carlo decision was based on the sunshape, optical properties and geometry of the collector components, and the laws of reflection and refraction. The azimuth angle and the deflection angle of the sunshape, I (φ), see Equation (1), were 2π and 0.266°, respectively. The incident location and the direction vectors of the rays were denoted by P(P x , P y , P z ) and D(D x , D y , D z ), respectively. Considering the computational expense and an average absolute error of 0.1 to 0.08% in the concentrator reflectance and the glass transmittance, 5 × 10 7 to 10 × 10 7 rays/m 2 of aperture area of the collector were traced for the model. Light reflection on the mirror and transmission through the glass was followed by Fresnel's law, Equation (2), and Snell's law, Equation (3). where is the deflection angle.
where D, N, n GT , and n air are the direction vector, normal vector, and refractive indices of the glass and air, respectively. The normal vectors, N PT and N GT , were calculated from Equations (4) and (5), respectively.
Cross-sectional views of (A) the Luz Solar 2 (LS2) collector and (B) the ECE geometry where P is the incident points of the rays in Cartesian coordinate system and f is the focal length of the mirror.

| MCRT model validation
The MCRT model was validated against the measured optical efficiency of the LS2 collector 47 and analytical irradiance distribution developed by Jeter for his exemplary collector. 30,34,35 Several test conditions of the LS2 collector (see Table 2) were modelled, and optical efficiencies were calculated using the current MCRT model (shown in Figure 4A). Jeter's published analytical model is able to predict local irradiance intensity, I(β), in angular direction of the ECE as local concentration ratio (LCR) using Equation (6). The factors product, C opt, was assumed unity. The LCR profiles of an ideal collector of 20 × geometric concentration (GC) and 90° rim angle with a 3 mm thick glass tube envelop and without glass tube were calculated using the current MCRT model and compared against Jeter's one as shown in Figure 4B. The light intensity was one sun (1 kW/m 2 ), and angular radius of the solar disk was 7.5 mrad. Figure 4 shows very good agreement between the MCRT calculated results and literature.

| Correlations to calculate irradiance distribution around the bare ECE
Extensive MCRT investigation confirms that the LCR profile of the ECE of an ideal PTC is bisymmetric with respect to the geometric symmetry of the collector, that is, the global YZ plane (see Figure 4B). Refer to Figure 4B, normal LCR profile is symmetric about the geometric symmetry of the collector and assumed uniform along the length of the ECE. As presented in Figure 5, the profile can be divided as (A) ECE shadowing zone within 0°≤β ≤ 15°, (B) concentration increasing zone within 15°<β ≤ 48°, (C) concentration falling zone within 48°<β ≤ 90°, and (D) direct sun zone within 90°<β ≤ 180°. Moreover, the LCR was found proportional to the DNI and optical properties of the collector components including the mirror reflectance, glass transmittance, and the receiver tube absorptance. 29 Ignoring the effect of glass envelop refraction on the flux profile, a set of polynomial correlations for the collector to calculate the LCR as a function of angular location, β (°), of the receiver tube was developed as given in Table 3. From the LCR, the local irradiance profile, I β , around the ECE can be calculated using Equation (6), (7), and (8) as shown in Figure 6.

| The computational domain and its physical properties
Selected test conditions, in which the glass envelop was either broken or removed, are presented in Table 4. Since the LCR profile was bisymmetric with respect to the global YZ plane, characteristics of physical symmetry in the HTF domain were utilized to minimize the computational expense with fewer grids. The computational domain between the close-end plug and the receiver tube is a semicylindrical horizontal annulus, see Figure 2B, as presented in Figure 7. Kelvin temperature (K)-dependent thermal conductivity of the ECE material, stainless steel, is given by Equation (9a), 64 and thermo-physical properties include density (ρ), heat capacitance (C P ) and thermal conductivity (k), and dynamic viscosity (μ) of the HTF, Syltherm800 oil, are adapted from reference, 65 and given by Equations from (9a) to (9e).

| Boundary conditions
The boundaries are showed in Figure 7. As the HTF was viscous, the wall surfaces formed by the ECE and the plug were considered no-slip, that is, near the wall, Launder and Spalding standard wall functions were used for near wall treatment. 66 The wall was not modelled. However, a thickness of 3 mm was considered for the wall, and the shell conduction was checked in the model.
At steady-state condition, the plug wall was assumed adiabatic in radial direction, that is, where r Z is cylindrical coordinate system.
Since, the light is concentrated on the ECE surface, at steady-state condition, this surface was assumed as constant heat flux wall, that is, where R is the radius of the receiver tube.
As the computational domain was essentially a part of a long pipe flow, at the inlet and outlet, the flow was considered fully developed velocity inlet and fully developed pressure outlet, respectively, that is, the flow along the tube (Z direction) at the inlet and outlet was characterized as: A "symmetry" boundary condition was assumed along the YZ plane, such as: The rest of the HTF flow line beyond the computational domain was assumed perfectly thermally insulated. The edges of the walls at the inlet and outlet of the domain were assumed adiabatic. Heat loss from the frame and bracket of the domain was neglected.

F I G U R E 6
Calculation of the irradiance flux profile, I(β), across the surface of the ECE employing the correlations given in Table 3.
(In the legend of the figure, TC1, TC2, etc, refer the test conditions of Table 4. C opt and C opt_1 are defined by Equations (7) and (8), respectively. The values of the factors are given in Table 1) Angular locationon the receiver ( ) β°

| Grid generation
The generated grids were structured and hexahedral in shape as shown in Figure 8. As the flow was turbulent and viscous, the grid size was uniform along the flow (Z direction) and inflated across the flow (radial direction). The inflation rate from wall to the center of the flow was 10%, and the y + value near the wall was reasonably small to capture the physics near the walls.

| Governing equations
Considering the critical Reynolds number, Re c , is 4000 for close channel flow through a tube or annulus, the flow of the HTF of the selected test conditions of Table 4 at steady-state condition was categorized as steady-state and incompressible turbulent flow. The governing equations for this particular flow criterion are given below. 63 As the flow was assumed incompressible, the volume continuity equation replaced the mass continuity equation.
The momentum equations were as follows while the gravity was acting along the -YY axis: where µ and µ t were the molecular viscosity and turbulent eddy viscosity, respectively.

Adiabatic no-slip wall
The energy balance was given by Equation (17) where S r was the concentrated solar radiation source term. The turbulent energy production, κ, and the turbulent energy dissipation, ε, for RNG κ-ε model were given by Equation (18) and (19), respectively.
where C 1ε = 1.42, C 3ε = 1.68, G κ was turbulent kinetic energy generation for mean velocity gradient, G b was the same for buoyancy, α κ is inverse effective Prandtl number for κ, and α ε was the same for ε.
The modified eddy viscosity for swirl generation for the RNG model was given by Equation (20) where C µ = 0.0845 and α s ≈ 0.07 were two swirl constants, and Ω was a characteristic swirl number.

| Heat loss from the ECE wall
The radiation heat loss was calculated by Equation (21) where ε was the emissivity of the ECE coating which was given by Equation (22), 31 σ was the Stefan-Boltzmann constant, and F gr and F Sky were the radiation view factors of the ECE with the ground and the sky, respectively, that were calculated as function of ECE angular location, β (see Eq. 23).
T w and T Sky were the average face temperature of each wall cell and sky temperature, respectively. They were calculated by Equation (24). 31 where T amb is ambient temperature.
Since there was strong wind during the collector testing as Table 4 shows, natural convection heat loss from the ECE was neglected. Heat loss due to forced convection was given by Equation (25).
where h was convection coefficient, which was given by the average effect of leeward (h lee ) and windward (h wind ) convection heat transfer coefficients as the wind flow directions were not known 67 and T wall is the cell average temperature of the heat flux wall surface of the computational domain.

| Algorithm for nonuniform solar energy input and heat loss calculation
The source term, S r , of Equation (17) was highly nonuniformly distributed concentrated solar irradiation on the wall boundary of the HTF domain (see Figure 7). This was the only constant heat flux source to the domain, and the exact profile of the solar flux, I β , across the wall surface as shown in Figure 6 was developed in FV model using a source code. At ideal condition for the bare ECE, the C opt included the trough reflectance and the ECE absorptance. However, to make the simulation more realistic, factors like tracking error, geometry error, general error, and dust and dirt on the trough and the ECE were also considered in the C opt . Tracking error and geometry error have directional effect on the LCR profile. For simplification, the directional effect on the conjugate heat transfer was neglected, and linear effect on the overall energy efficiency was considered. The values of these loss factors are given in Table 1. Heat loss algorithm was also incorporated in the source code as explained in Figure 9. The rhombuses and the rectangles in the flow chart represent arguments and decisions to the arguments, respectively. The meanings of signs and symbols are either given in the nomenclature or they have usual meaning for the FLUENT subroutine. As the ECE of the LS2 collector was 200 mm larger than the trough, the light was assumed to be concentrated between Z = 0.1 m and 7.9 m, and the rest of the ECE was shaded as shown in the last argument of the flowchart.

| Solution technique
Built-in segregated finite volume method of ANSYS Fluent 14.5 software package was enabled to solve coupled-nonlinear governing equations. As the domain was specified clearly from upstream to downstream, and the cells were hexahedron, convection-diffusion was solved employing a higher order differencing scheme, the QUICK scheme. 68 The "PRESTO!" pressure interpolating scheme and "SIMPLE" pressure-velocity coupling technique were adopted for the current FV model. Under relaxation factor was 0.75 for most of the parameters. However, it was 0.3 for pressure and momentum, and 0.8 for turbulent dissipation rate. Convergence criteria set to maximum 10 −6 for energy equation and 10 −4 for the rest of the parameters.

| Grid sensitivity test
Static temperature of the receiver wall and plug wall near the HTF outlet for different grid resolutions was recorded from the model as presented in Figure 10. The variation in the temperatures from the grid system 20 × 80 × 800 onward F I G U R E 9 Algorithm of the user-defined function. (In the figure, Z is the longitudinal axis of the ECE domain from inlet to outlet. The rest of the notations either are given in the nomenclature, or have their usual meaning in FLUENT subroutine) was negligible. Nonetheless, grid structure 20 × 80 × 3200 (=5 120 000 hexahedral cells) was used for this model to obtain a better accuracy in the theoretical results.

MCRT coupling algorithm
A test run of the FV model was executed to verify the UDF macro considering 1000 W/m 2 DNI, and the collector was in ideal optical conditions and no heat loss from the outer surface of the computational domain. The residual heat flux profiles across the receiver wall at 0.35 m, 4 m, and 7.23 m length locations from the inlet were calculated and presented in Figure 11. This flux profile is comparable with the input solar flux profile as presented in Figure 6, which confirms the accuracy of the macro, and coupling between the MCRT and the current FV model. The flux profiles were found coincident at all three locations because of the fact that the solar flux profile was considered uniform along the length of the ECE.

| Validation of the FV model with experimental results
The HTF outlet temperatures for the selected test conditions (see Table 4) were calculated and compared against the experimental results as shown in Figure 12. The figure shows that the computational results agree very well with their experimental counterparts. The maximum, minimum, and average absolute deviations between the experimental and computational results were found to be 2.92%, 0.23%, and 1.11%, respectively. It could be noted that the maximum deviation was found for the second test condition with lowest DNI (867.6 W/ m 2 ), and so the lowest heat flux density around the no-slip heat flux wall. The DNI for the rest four test conditions was much higher than the second one, DNI varied between 919 and 961 W/m 2 , and the ambient air flow was between as low as 0.1 m/s and as high as 9.3 m/s. Average absolute deviation between the experimental and computational results for these four test conditions was only 0.66%. This infers that the heat loss algorithm of this current model is highly capable to predict heat loss at wide range of air speed for high heat flux condition than low heat flux condition. The heat loss algorithm overestimates the heat loss at lower heat flux density. Overall, the current FV model is quite accurate for the simulated PTC.

| Verifying fully developed velocity inlet
For this simulation, the HTF domain was considered a part of a continuous fluid line; therefore, the flow must be fully developed throughout the domain. Comparative velocity profile of the HTF at the symmetry of the computational domain for the fully developed flow at the inlet in opposed to an average bulk fluid flow and the resultant velocity profile at the inlet are shown in Figure 13.

| T YPICAL APPLICATION OF THE FV MODEL
Using the present FV model, the temperature profile across and heat loss from the receiver tube were calculated as explained below.

| Temperature profile along the angular direction of the receiver
Static temperature profiles across the receiver wall at 0.35 m, 4 m, and 7.23 m length locations from the inlet were calculated and presented in Figure 14. The temperature profiles were found highly nonuniform and reasonably similar to corresponding input solar flux profile (see Figure 6). The local temperatures were found increasing almost linearly from inlet to the outlet.

| Convection and radiation heat loss from the receiver wall
At outdoor condition, while wind was blowing, the receiver without glass envelop was experiencing forced convection heat loss from its outer surface, as well as radiation heat loss due to high temperature gradient with the ambient. Employing the current FV model, outlet temperatures for the test conditions shown in Table 4 were further modelled assuming: (a) no heat loss, (b) radiation heat loss, (c) convection heat loss, and (d) total (radiation + convection) heat loss. HTF outlet temperatures were recorded as presented in Figure 15.
As Figure 15A shows, HTF outlet temperature for the radiation heat loss model is very close to that of no heat loss model. On the other hand, HTF outlet temperature for the convection heat loss model is very close to that of the total heat loss model. That means convection heat loss from the ECE was accounted for most of the energy loss and was dominated almost linearly by the ambient wind speed (see Figure 15B). Radiation loss on the contrary was very low and dependent on the inlet temperature. Total radiation and convection heat loss were found to be between 18% and 62% of the input energy for the range of ambient wind velocity between 0.1 m/s and 9.3 m/s. The convection heat loss was accounted for 13.5%-57.3% of the total heat loss, which indicates that protection of this convection heat loss from the collector in harsh outdoor condition is extremely important.

| CONCLUSIONS
Perpendicularly incident sun light on the trough aperture of a parabolic trough collector (PTC) is concentrated highly nonuniformly along the circular direction of the receiver tube of the energy collection element (ECE). Luz Solar II (LS2) is a 8 m long standard PTC, which was used in the Solar Energy Generating System III-VII 150 MW plants, Kramer Junction, California, USA, and tested on the AZTRAK rotating platform at SNL. 47 Analysis of conjugate heat transfer mechanism of the ECE of the LS2 collector using three dimensional (3D) finite volume (FV) technique of computational fluid dynamics (CFD) coupled with Monte Carlo ray-tracing (MCRT) is a popular technique. However, this coupled study is computationally expensive and requires expertise in, and access to, a suitable MCRT code, and thus, prohibitive to many CFD researchers. Open literature lack of any study that attempted to either eliminate or minimize the need of this MCRT code for the conjugate study. In this paper, the authors attempted to provide a tool in a form of user-defined function (UDF) that will minimize the need of MCRT code and will serve as a built-in function to the FV model. The current study can be summarized as: 1. The UDF contains an algorithm to calculate and populate local irradiance, I(β), data as heat flux boundary condition around the receiver tube and heat loss from the receiver of the PTC. 2. I(β) is calculated multiplying local concentration ratio (LCR) by daily normal irradiance (DNI) and optical factors. The heat loss algorithm accounts for the radiation loss and the convection loss depending on the glass envelop condition. 3. The LCR is a function of angular location, β, of the receiver, derived as polynomial correlations from a validated 3D MCRT model. The optical factors include the optical properties of the collector components and the optical error factors such as tracking error, general error, geometry error, and effect of dirt on the optical surfaces of the collector. 4. The MCRT coupling algorithm of the UDF is verified, and the FV model is validated with experimental results. 5. Typical application of the model was performed by checking temperature profile around the ECE, and radiation and convection heat losses from the ECE. Convection heat loss from the outer surface of the receiver tube (assumed bare or no glass envelop) was dominant over the radiation heat loss and varies almost linearly with ambient wind velocity. For wind velocity ranges between 0.1 and 9.3 m/s, and convection heat loss was observed to be accounted for 13.5%-57.3% out of 18%-62% of total heat loss. 6. The UDF has the capacity to accommodate and use for various a. optical conditions include daily normal irradiance, optical properties of the collector components, and optical loss factors with average effect, such as, tracking error, effect of dirt and dust on the participating surfaces, general error, and geometry error; b. collector geometry that include collector length and internal diameter of the receiver; The test conditions of Table 4 Wind and HTF flow velocities (m/s)