Apple is famous for its glass store buildings and is considering a similar structure in Los Angeles (LA). The first schematic design of this building together with surroundings are provide in the figures below:
Apple hired a design firm, which offered you an energy consulting position. So, you decided to build a simplified energy model that should show the impact of large glass areas on the energy performance of this building. Since you just need rough numbers that compare a glass roof with a regular roof, you can simplify this building geometry to a square box with the geometry provided below. Also, the schematics below provide info about the walls, ceiling, and slab structure, as well as the details about the surrounding buildings.
To do this analysis, you will need to build an energy model that includes all relevant building components that are major contributors in the cooling load since LA has a warm climate. certain assumptions (simplifications) are listed below, and most probably you will need to provide more assumptions to solve this problem.
Assumptions:
- Roof glass is flat, even though there is a small curvature in the architectural drawings.
- Steel beams that support glass roof do not participate in the heat transfer.
- Side concrete walls span all the way to the front façade (side glass walls are negligibly small).
- The exterior walls of the three surrounding buildings have the same height as the Apple store and wall temperature of these surrounding building is the same as the outdoor air temperature.
- The store HVAC system keeps the indoor temperature constant at 23°C.
- Assume that roof glass has no shading.
- The frequent door opening provides constant infiltration of outdoor air that provide 2 ACH.
- Below concrete floor insulation prevents heat transfer to the ground.
- Internal heat source (from occupants, electronics and lighting) is constant equal to 5 kW. Assume that 50% of this energy is convection and 50% is radiation.
- Assume that you know all physical and material properties and the geometry for your model.
- Assume that view factor from sky to the glass roof to the sky is 1.
(a) Identify the major elements and explain the physical properties and parameters which you need to have as inputs in your model. You do not need to substitute numerical values.
(b) Among the assumptions listed above pick 2 that are most important and 2 that are the least important. Briefly explain the reasons.
(c) Construct your thermal network with all building elements that you introduce to the model. Distribute the nodes (discretize the elements that you model) according to your assumptions. Provide a clear schematic that shows all the nodes and display heat transfer (connection) between the nodes. List the assumptions that you introduced to solve the problem.
(d) Write the 3 most important energy balance equations (please justify your selection). Please explain what each term represents. Please do not write the matrix representation for the solution, but the initial form of the equations.
(e) Then show the equations in explicit form (finite difference method). You do not need to substitute numerical values.
(f) List 3 other possible factors not included in the assumptions listed above but that will affect the energy consumption.
(g) Considering the assumptions which were defined and those that you introduced, identify the one which creates the largest inaccuracy in the model. How would you correct this inaccurate assumption?
(h) Which suggestion in the design would you propose for reduction of energy consumption? Explain why.