# Studying thermal stresses of a solar absorber in single and two-phase regimes and effects of various coatings on the absorber

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## Abstract

In the solar parabolic trough collectors, functioning based on direct steam generation system, heat transfer system and appropriate thermal stress are indicated as two most important thermal parameters. High amount of the critical heat flux creates an extensive application range for the system so heat transfer systems can function without being subjected to high thermal stresses. In this regard, by using a coat on the external surface of the absorber thermal stresses can be reduces in single-phase, sub-cooled, boiling flow regimes and even at the critical heat flux point. In this study, by considering a numerical model of heat transfer, the input heat flux of the absorber which is considered to be a boundary condition for the absorber’s external surface is calculated. Energy conservation is assessed for three different zones of the fluid flow, single-phase, sub-cooled and boiling. Obtaining the temperature profile of the absorber’s surface from the beginning of the fluid flow to the critical heat flux point, leads to calculation of thermal stresses, which has been accomplished by finite element modeling of Misses and Tresca Model, and these two criteria have been compared. Mentioned analyses are performed and compared for coated and uncoated tubes. Three different coats (zinc, chromium and tungsten) are considered. It is shown that zinc is much more preferred than the two other coats, due to 39% and 83% reduction of thermal stress at the onset of critical thermal flux in both Mises and Tresca, respectively.

## Nomenclature

*c*_{p}Specific heat at constant pressure, J/kg.K

*D*Diameter, m

*E*Module of elasticity (Gpa)

*F*_{rad}Fraction of blackbody radiation in a wavelength band

*h*Convection heat transfer coefficient, W/m

^{2}.K*h*_{L}Convection heat transfer coefficient in one-phase, W/m

^{2}.K*h*_{lv}Latent heat of fusion, J/kg

*k*Thermal conductivity, W/m.K

*l*Element length of pipe, m

*m*Mass, kg

- \( \dot{m} \)
Mass flow rate, kg/s

*Nu*Nusselt number

*p*Pressure, N/m

^{2}*Pr*Prandtl number

*pr*Rate between saturate pressure and critical pressure

*q*Heat transfer rate, W

- \( \dot{q} \)
Heat transfer rate per unit length, W/m

*Ra*Rayleigh number

*Re*Reynolds number

*T*Temperature, K

*V*Volume, m

^{3}- \( \overline{\boldsymbol{\nu}} \)
Poisson number

*x*Vapor quality, percent (%)

## Greek letters

*β*_{c}Volumetric thermal expansion coefficient, K

^{−1}*μ*Viscosity, kg/s.m

*π*Pi number, 3.14

*ρ*Mass density, kg/m

^{3}*σ*Stefan-Boltzmann constant, W/m

^{2}.K^{4}- \( \overline{\sigma} \)
Stress, Mpa

- Δ
Difference

## Subscripts

*a*Absorber

*c*Cavity

*cond*Conduction

*conv*Convection

*crit*Critical

*e*Environment

*eff*Effective

*ex*External

*f*Fluid

*g*Glass

*in*Internal (for temperature), Inlet (for fluid flow)

*l*Liquid

*m*Middle

*nb*Nucleate boiling

*out*Outlet

*rad*Radiation

*s*Sun

*Sat*Saturate

*tp*Two-Phase

*v*Vapor

## Notes

## References

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