Mathematical modeling and analysis of thermodynamic performance parameters of tubular solar still

ABSTRACT

Mathematical modeling of the tubular solar still (TSS) has been carried out. The MATLAB code has been developed for calculating the performance parameters like tubular glass cover temperature, rectangular basin liner temperature, basin water temperature, and productivity and efficiency. The results obtained from mathematical modeling has been compared with the benchmark results of experimental work of various research work related to present study for the validation of present work . Different heat transfer coefficients have been calculated on hourly basis. Heat transfer coefficient values increase from minimum at early in the morning and reaches the maximum at afternoon then it starts decreasing near the evening time. The maximum evaporative heat transfer coefficient, convective heat transfer coefficient, and radiative heat transfer coefficient are 33.28 $\frac{W}{{m^2}^{\circ }\mathrm{C}}$, 2.90 $\frac{W}{{m^2}^{\circ }\mathrm{C}}$, and 6.49 $\frac{W}{{m^2}^{\circ }\mathrm{C}}$, respectively. Evaporative heat transfer coefficient is dominating amongst others. Basin water temperature and hourly yield of TSS have been calculated for 1 cm, 2 cm, 3 cm, and 4 cm water depth, respectively. The tubular glass cover temperature and basin water temperature for different climatic zone of India have been calculated. Various cities such as Nagpur, Chennai, Jaipur, Srinagar, and Guwahati are considered for studying the effect on tubular glass cover temperature, water temperature stored in rectangular basin liner, hourly yield for these geographical locations of India. The tubular glass cover temperature for three absorptivity values 0.04, 0.08, and 0.16 (of glass materials) has also been calculated. As a result, 5.8 kg of fresh water cumulative yield have been obtained from 6 am to 6 pm for whole day. From the economic analysis study of TSS, it is found that cost for producing fresh water per kg depend on annual interest rate. Higher value of interest rate results in higher cost for producing fresh water. In the study, annual rate considered are 5%, 10%, and 15% for which cost of producing fresh water are 0.255, 0.521, and 0.786 $\mathrm{\$}/\mathrm{k}\mathrm{g}$, respectively. Efficiency of TSS increases from morning and reaches maximum at the noon when solar intensity is highest for a day then it starts decreasing toward the end of day in the evening. The maximum thermal efficiency of TSS is 43.78% at 12 noon where solar intensity is maximum for the day. The maximum exergy efficiency obtained at 11 am is 50.88% then it decreases as the temperature and solar intensity decreases with the time.

KEYWORDS:

• Tubular solar still
• thermodynamic performance of solar still
• solar distillation
• mathematical modeling of solar still
• renewable energy

Nomenclature

$I\left(t\right)$	=	Solar intensity
$m$	=	Mass
$A$	=	Area
$\mathrm{\Delta }t$	=	Time difference between initial and final
$Q$	=	Heat transfer
$T$	=	Temperature
$h$	=	Heat transfer coefficient
$p$	=	Partial saturated vapor pressure
${\xi }_{eff}$	=	Effective emissivity
$\sigma$	=	Stephan-Boltzmann constant
$v$	=	Wind velocity
$k$	=	Thermal conductivity
$\mathrm{\Delta }{q}_L$	=	Enthalpy of vaporization of water
${\dot{m}}_e$	=	Hourly yield
$M_e$	=	Total production of fresh water
$\mathrm{k}\mathrm{g}$	=	kilograms
$\eta$	=	Efficiency of TSS
$\alpha$	=	Absorptivity
$R$	=	Reflectivity
$a$	=	Ambient
$g$	=	Tubular glass cover
$b$	=	Rectangular basin
$w$	=	Water
$gi$	=	Inner side of tubular glass cover
$go$	=	Outer side of tubular glass cover
$g-a$	=	Tubular glass cover to air
$b-w$	=	Rectangular basin to water
$w-g$	=	Water to tubular glass cover
$c$	=	Convection
$e$	=	Evaporation
$r$	=	Radiation
$\mathrm{\$}$	=	United states dollar currency

Acknowledgments

Authors heartily acknowledge National Institute of Technology Raipur (CG), India for providing permission to access library and other resources for writing research manuscript.

Disclosure statement

No potential conflict of interest was reported by the author(s).