Open parallelogrammic enclosures to improve Trombe wall performance by enhancing free convection. An experimental approach

ABSTRACT

A version improving the efficiency of the Trombe-type assembly is proposed in this study. It consists in equipping the wall with a series of inclined fins forming open cavities of parallelogram section affecting the aerodynamics of the active cavity. The natural convective flow leads to an increase in natural convective heat transfer and improves the overall performance of the assembly. The experimental study is performed with a 0.2 scale assembly. The wall generates a heat flux in a wide range corresponding to the solar radiation while the glass cover is maintained isothermal at cold temperature. The distance between the hot and cold walls compared to the height of the cavity leads to three aspect ratio values (0.1, 0.2 and 0.3). The study performed for a Rayleigh number ranging from 2.81 × 10⁸ to 4.14 × 10⁹ confirms the effectiveness of the new version proposed in this work. With the finned wall, the average natural convective heat transfer increases from 7 to 23% compared to the conventional version without fins, according to the considered configuration. The average Nusselt number is determined for all the tested configurations with a maximum uncertainty of 5%, taking into account the uncertainties of the measured physical parameters. A Nusselt-Rayleigh type correlation is proposed, obtained by means of the least squares optimization method.

KEYWORDS:

• Free convective heat transfer
• performance enhancement
• trombe-wall
• high Rayleigh number
• experimental heat transfer
• thermal measurements

Nomenclature

A	=	Aspect ratio of the active cavity A = L/H (-)
A'	=	Aspect ratio of the parallelogrammic cavity A’ = L’/H’ (-)
a	=	Thermal diffusivity (m2s−1)
E	=	Thickness (m)
g	=	Gravity acceleration (m.s−2)
H	=	Height of the active cavity (m)
H’	=	Height of the parallelogrammic cavity (m)
I	=	Current intensity (a)
k	=	Coefficient in the correlation $\overline{Nu}$ = k Ran (-)
L	=	Distance between the hot and cold walls of the active cavity (m)
L'	=	Right distance of the parallelogrammic cavity (m)
n	=	Exponent in the correlation $\overline{Nu}$ = k Ran (-)
$\overline{Nu}$	=	Average nusselt number for the wall without fins (-)
${\overline{Nu}}_m^{\hspace{0.17em}}$	=	Average nusselt number for the finned wall (-)
P	=	Generated power, P = RI2 (w)
r*	=	Improvement factor r* = 100(${\overline{Nu}}_m^{\hspace{0.17em}}$-$\overline{Nu}$)/$\overline{Nu}$ (-)
R	=	Resistance (W)
Ra	=	Rayleigh number (-)
S	=	Surface of the wall’s central band (m2)
T	=	Temperature (k)
$\overline{T_h^{\hspace{0.17em}}}$	=	Average surface temperature of the hot active wall (k)

Greek symbols

$\beta$	=	Volumetric expansion coefficient (K−1)
Δm/m	=	Relative uncertainty of a given parameter m (-)
$\varphi$	=	Generated heat flux (Wm−2)
$\lambda$	=	Thermal conductivity (Wm−1K−1)
$\mu$	=	Dynamic viscosity (Pa.s)
$\rho$	=	Density (kg.m−3)

Subscripts

a	=	Air
c	=	Cold
f	=	Fin
g	=	Thermal insulator
h	=	Hot
v	=	Glass
w	=	Wall