# A new design of a solar water storage wall: a system-level model and simulation

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## Abstract

Some configurations have been proposed as passive solar wall, but nearly all of them suffer from common shortcomings such as high heat loss flux and low thermal capacity. In this paper, a modified design for building passive solar wall is proposed and a detailed computerized model for its dynamic behavior was developed as a triplet (S, Q, M) from first principles and empirical equations, such that the designer is able to alter any of the variables. Hence, the wall-room properties can be adjusted to improve the wall performance. In this model, S is a solar water wall which is designed on the south wall of a building with a water storage tank as the sensible thermal storage placed inside to passively heats the space with controlled heat transfer and a sufficiently sized storage. Also, Q is a question relating to S which is the performance evaluation of the proposed system including annual and monthly performance along with the room and storage temperatures. Finally, M is a set of mathematical statements \(\hbox {M}=\left\{ {\Sigma \_\hbox {1},\Sigma \_\hbox {2},\Sigma \_\hbox {3},\ldots } \right\} \) which can be used to answer Q. The statements M are based on the lumped capacitance approach which utilizes solar optocalorics, solar thermal conversion and convective heat transfer to simulate passive space heating of a small building. A code was developed to solve the problem and to evaluate parametric sensitivity for design features. A new TrnSys model was introduced and the code results were compared with TrnSys outcome.

## Keywords

Thermal Storage Solar Simulation TRNSYS Building## List of symbols

- \(R_i \)
Thermal resistance (\(\mathrm{m}^{2}\,{^\circ \mathrm{C}}/\mathrm{W})\)

- \(C_m \)
Specific heat (\(\mathrm{J/m}^{2}\,{^\circ \mathrm{C}})\)

- \(Q_r \)
Radiant source term (\(\mathrm{J/m}^{2})\)

- \(m_i \)
Mass of i\(\mathrm{th}\) node (kg)

- \(C_{p,i} \)
Specific heat of the i\(\mathrm{th}\) node (\(\mathrm{J/m}^{2}\,{^\circ \mathrm{C}})\)

- \(T_i \)
Temperature of the i\(\mathrm{th}\) node (\({^\circ \mathrm{C}})\)

- \(k_{nm} \)
Thermal conductance between the nodes m and n (\(\hbox {W/m}^{2}\,{^\circ \mathrm{C}})\)

- \(q_{nm} \)
Energy flow between two nodes (\(\mathrm{J/m}^{2})\)

- \(E_i \)
Rate of heat transfer with external source at the i\(\mathrm{th}\) node

- \(\Delta t\)
Simulation step time (s)

*l*Characteristics length (m)

- \(L_{tank} \)
Tank wall thickness (m)

- \(k_{tank} \)
Tank wall conductivity (\(\hbox {W/m}^{2}\,{^\circ \mathrm{C}})\)

- \(A_{tank} \)
Tank wall area (\(\mathrm{m}^{2})\)

*Nu*Nusselt number

*Pr*Prandtel number

- \(Ra_l \)
Rayleigh number

*P*Perimeter (m)

- \(A_s \)
Surface area (\(\mathrm{m}^{2})\)

*ET*Equation of time

- \(T_g \)
Glass cover temperature (\({^\circ \mathrm{C}})\)

- \(T_a \)
Absorber temperature (\({^\circ \mathrm{C}})\)

- \(T_{amb} \)
Ambient temperature (\(\,{^\circ \mathrm{C}})\)

*N*Number of covers

- \(\beta \)
Collector tilt

- \(\varepsilon _g \)
Glass cover emissivity

- \(\varepsilon _a \)
Absorber emissivity

*h*Wind heat transfer coefficient (\(\hbox {W/m}^{2}\,{^\circ \mathrm{C}})\)

- \(L_h \)
Cube root of the house volume (\(\mathrm{m}^{3})\)

*V*Wind speed (m/s)

- \(\varvec{G}_{\varvec{d,t}} \)
Diffuse irradiance on the tilted surface (\(\hbox {W/m}^{{2}})\)

- \(\varvec{G}_{\varvec{iso}} \)
Sky component (\(\hbox {W/m}^{{2}})\)

- \(\varvec{G}_{\varvec{cir}} \)
Circumsolar diffuse component (\(\hbox {W/m}^{{2}})\)

- \(\varvec{G}_{\varvec{hor}} \)
Horizon diffuse component (\(\hbox {W/m}^{{2}})\)

- \(\varvec{G}_{\varvec{gro}} \)
Ground diffuse component (\(\hbox {W/m}^{{2}})\)

- \(\varvec{G}_{\varvec{t}} \)
Total radiation on the tilted surface (\(\hbox {W/m}^{{2}})\)

- \(\varvec{F}_{\varvec{1}} \)
Circumsolar coefficient

- \(\varvec{F}_{\varvec{2}} \)
Horizon brightness coefficient

- \(\phi \)
Latitude

- \(\varvec{\rho } _{\varvec{g}}\)
Ground reflectance

- \(\varvec{a,b}\)
Constants in Perez model

- \(\varvec{G}\)
Total radiation on horizontal surface (\(\hbox {W/m}^{{2}})\)

- \(\varvec{G}_{\varvec{b}} \)
Beam radiation on horizontal surface (\(\hbox {W/m}^{{2}})\)

- \(\varvec{G}_{\varvec{d}} \)
Diffuse radiation on horizontal surface (\(\hbox {W/m}^{{2}})\)

- \(G_{sc} \)
Solar constant (\(\hbox {W/m}^{2})\)

- \(G_{on} \)
Extraterrestrial radiation incident on the plane normal to the radiation (\(\hbox {W/m}^{2})\)

- \(R_b \)
Beam radiation tilt factor

- \(\varvec{\epsilon }\)
Clearness

- \(\Delta \)
Brightness

- \(L_{st} \)
Local standard time

*L*Longitude

*ET*Equation of time

- \(\left( {\tau \alpha } \right) \)
Transmittance-absorptance product

- \(\gamma \)
Surface azimuth angle

- \(\omega \)
Hour angle

*n*Number of day

- \(\delta \)
Declination

- \(f_{ij}\)
Constants in calculation of brightness coefficients \(F_1 \) and \(F_2 \)

- \(q_{abs}\)
Absorbed energy in the system (\(\mathrm{J}{/}\mathrm{m}^{2})\)

- \(\theta _b\)
Angle of incidence

- \(\theta _z\)
Zenith angle

- \(\theta _d\)
Effective incidence angle of isotropic diffuse radiation

- \(\theta _g\)
Effective incidence angle of ground-reflected radiation

- \(\theta _r\)
Angle of refraction

- \(n_a\)
Index of refraction for aerogel

- \(n_g\)
Index of refraction for glass

- \(\tau _r\)
Transmittance based on the refraction losses only

- \(\tau _a\)
Transmittance in regard with absorption losses only

- \(\tau \)
Transmittance

- \(r_\parallel \)
Parallel component of the unpolarized radiation

- \(r_{\bot }\)
Perpendicular component of the unpolarized radiation

- \(\alpha _n\)
Absorptivity at normal incidence

- \({\upalpha }\)
Absorptivity

- \(Q_{aux,\,j}\)
Monthly auxiliary heating (\(\mathrm{J}{/}\mathrm{m}^{2})\)

- \(Q_{dem,\,j}\)
Monthly heating demand (\(\mathrm{J}{/}\mathrm{m}^{2})\)

- \(\mathcal{F}\)
Annual solar fraction

- \(T_{min}\)
Set point temperature (lower comfort limit) (\({^\circ \mathrm{C}})\)

- \(W_{tank}\)
Tank width (m)

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