Passive solar heating of buildings continues to be a great interest of renewable energy applications. Part of this interest focuses on solar heating walls. A solar heating wall (SHW) is a part of building walls that receive, store, and transfer solar thermal energy into the building. SHW sensitivity analysis is often performed to guide optimum designs. For the sensitivity analysis, the methodology used so far is numerical simulations. This work presents a new approach, regression analysis, and develops a general regression model. To show how to develop a specific model for a given SHW from the general one, how to do the regression, and how to validate the model, the lattice solar heating wall (LSHW) is selected as a case study. Detail heat transfer analysis is performed to develop the specific regression model for the LSHW sensitivity analysis. Four side-by-side test cells are constructed to obtain experimental data. The data are then used to determine the regression constants and coefficients and the time series numbers. Validation of the regression analysis shows that the model has very high confidence. The model is also used for LSHW optimization, yielding the same results as those from the simulation with the numerical simulation program, which further demonstrates that the proposed model is reliable.
Passive solar heating of buildings is a great interest of renewable energy applications. Part of this interest focuses on the thermal performance study of new materials and configurations of solar heating walls [1], [2], [3], [4] and [5].
The solar heating wall (SHW) is a part of building walls that is designed to receive, store, and transfer solar thermal energy into the building. SHW examples are Trombe walls [6], [7] and [8], phase-change-material solar walls [9] and [10], lattice solar walls [11], composite wall solar collectors [2], and honeycomb insulation walls [12] and [13].
Factors that influence SHW thermal performances can be classified as two categories: (a) design parameters, such as shading, orientation, insulation, glazing, wall configurations, and thermal properties, and (b) climate conditions, mainly solar radiation and ambient temperature.
To analyze the influence of design parameter changes on SHW thermal performances, sensitivity analysis is performed [14] and [15]. When analyzing the influence of a chosen design parameter on SHW thermal performances, the sensitivity analysis is performed by hour-by-hour calculations in a given climate pattern, allowing only this design parameter to change while keeping the rest constant.
To the author’s best knowledge, methodology used so far for SHW sensitivity analysis is numerical simulations. Experimental measurements are only used to validate the simulation program.
Regression analysis, a powerful tool for solar energy applications [16], [17], [18] and [19], is scarcely used for SHW study. There are only two papers found out in the author’s extensive literature search [20] and [21], and both of them are only for SHW thermal performance study.
The methodology of regression is especially useful for the study of new SHW materials and/or configurations where numerical solutions are not available in a period of time. The objectives of this study are: (a) to propose a general regression model for SHW sensitivity analysis; (b) to take the lattice solar heating wall (LSHW) as an example to show how to develop a specific model from the general one, how to arrange test matrix, and how to perform regression analysis; and (c) to validate the concretized model by comparing the predicted values with experimental measurements and those obtained from numerical simulation program.
The only methodology used for SHW sensitivity analysis is numerical simulations. The present work proposes a new approach, regression analysis. A general regression model is developed. To validate the model and to show how to concretize the general regression model for a given SHW, the LSHW is selected as a case study. Detailed heat transfer analysis for developing the specific regression model for LSHW sensitivity analysis is conducted.
The four side-by-side test cells were constructed to conduct LSHW experiments. With hour-by-hour measurements, more than 500 data cases were obtained, among which 285 valid cases were chosen for the regression to determine the regression constants and coefficients and the time series numbers in the specific LSHW regression model.
The regression result has very high confidence. The standard error is 0.0286, and the coefficient of determination, R2 = 0.992, indicating that the calculated results agree with the measurements very well. The resulted correlation is also used for LSHW optimization, yielding the same results as those from the numerical simulation program, which further demonstrated that the general regression model proposed is reliable.
The process using the regression methodology can be summarized as the following:
(a)
Build test cells with the size as proposed by ASTM C236 [23] or other equivalent guidelines. Using more test cells causes higher initial cost but saves experimental time.
(b)
Set text matrix based on the f function and winter weather conditions.
(c)
Conduct experiments following the text matrix to obtain the data cases for determining the regression constants and coefficients and the time series numbers M’s and N’s. An experimental period lasts at least 50-h, measuring both cell temperatures and ambient conditions hour-by-hour. More than 250 data cases should be taken down in order to obtain at least 120 valid cases.
(d)
Perform regression analysis to determine the regression constants and coefficients and the time series numbers M’s and N’s, as the example described in Section 5.
(e)
Then extrapolate the results to a full scale system that operates in a different climate but within the ambient condition ranges the experiments covered. This allows performing SHW sensitivity analysis.
