Optimum thermo-hydraulic performance of solar air heater provided with cubical roughness on the absorber surface

ABSTRACT

Heat transfer augmentation in solar air heaters (SAHs) can be achieved economically and conveniently using artificial roughness elements on the absorber surface. Cubical roughness elements used in this investigation produces better heat transfer characteristics. However, this enhancement is particularly accompanied by increased pumping power due to increased friction. This study presents the results of the experiments carried out to determine the optimum design and operating conditions which gives a better thermohydraulic performance. Efficiency index ($\eta$) is often used as thermohydraulic performance parameter which is evaluated using correlation $\eta$ = (($N{u}_{av}/N{u}_s$)/($f_{av}/f_s$)). Experiments are conducted within the limits of Reynolds number ($Re$) from 3000 to 8000, relative roughness pitch ($p/e$) of 10 to 20 and relative roughness gap ($w/e$) of 4 to 8. Relative roughness height ($e/D_h$) of 0.06 and aspect ratio ($W/H$) of 5 is maintained constants. Substantial enhancement in the Nusselt number (59.1–72.7%) accompanied by a large increase in the friction factor (138.7–179.4%) over SAH with smooth absorber plate is achieved. Optimum thermohydraulic performance is obtained for lower values of the Reynolds number, relative roughness pitch ($p/e$) value 20 and relative roughness gap ($w/e$) of 8.

KEYWORDS:

• Thermohydraulic performance
• efficiency index
• Nusselt number
• friction factor
• cubical roughness

Nomenclature

$A_c$	=	Area of absorber surface $(m^2)$
$a_o$	=	Area of the orifice $(m^2)$
$a_1$	=	Area of the pipe $(m^2)$
$C_p$	=	Specific heat of air $(J/kgK)$
$C_d$	=	Coefficient of discharge
$D_h$	=	Hydraulic diameter of duct $(m)$
$e$	=	Height of the element (m)
$e/D_h$	=	Relative roughness height
$f$	=	Friction factor
$f_{av}$	=	Average friction factor
$f_r$	=	Friction factor of roughened duct
$f_s$	=	Friction factor of smooth duct
$g$	=	Acceleration due to gravity $(m/s^2)$
$H$	=	Height of the duct $(m)$
$h$	=	Convective heat transfer coefficient $(W/m^{2}K)$
$h_m$	=	Manometer reading $(m)$
$k$	=	Thermal conductivity of air $(W/mK)$
$L$	=	Test length $(m)$
$m$	=	Mass flow rate of air $(kg/s)$
$N{u}_{av}$	=	Average Nusselt number
$N{u}_s$	=	Nusselt number of four sided smooth duct
$Pr$	=	Prandtl number
$p$	=	Rib pitch $(m)$
$p/e$	=	Relative roughness pitch
$q$	=	Rate of heat transfer to air $(W)$
$R_{av}$	=	Average radial distance of the duct $(m)$
$Re$	=	Reynolds number
$t_f$	=	Average temperature of fluid ${(}^{o}C)$
$t_i$	=	Average inlet temperature of air ${(}^{o}C)$
$t_o$	=	Average outlet temperature of air ${(}^{o}C)$
$t_p$	=	Average temperature of absorbing surface ${(}^{o}C)$
$V$	=	Average velocity of air in the duct $(m/s)$
W	=	Width of the duct $(m)$
$W/H$	=	Aspect ratio
$w$	=	Gap between roughness elements $(m)$
$w/e$	=	Relative roughness gap
$\mathrm{\Delta }p$	=	Pressure drop in the test length $(N/m^2)$
$\rho$	=	Density of air $(kg/m^3)$
${\rho }_w$	=	Density of water $(kg/m^3)$
$\mu$	=	Viscosity of air $(Ns/m^2)$