Rework Example 16.4, now assuming the house has 10 single-glazed windows, each measuring 2.5 ft

Rework Example 16.4, now assuming the house has 10...

Key Concepts

R-Value

R-Value is a measure of a material’s resistance to conductive heat flow. In building science, it quantifies how well a component such as a window, wall, or insulation medium resists heat transfer. A higher R-value indicates lower heat loss, and it is a critical parameter when analyzing energy efficiency and thermal performance of building envelopes.

Heat Transfer Through Windows

Heat transfer through windows involves conduction through the glazing material. This process is determined by the window’s area, the temperature difference between interior and exterior, and the R-value of the window. Understanding conductive heat loss via windows allows engineers and architects to assess how much thermal energy is lost during colder periods, directly impacting overall heating requirements and energy consumption.

Solar Heat Gain

Solar heat gain refers to the energy added to a building from sunlight, as solar radiation passes through windows and other openings. The amount of solar gain is influenced by factors such as window orientation, glazing properties, and the intensity of solar radiation. This concept is essential when evaluating the thermal performance of a building because it can reduce the demand for additional heating energy in the winter by providing free, natural heat.

Energy Cost Analysis

Energy cost analysis involves quantifying the financial impact of energy consumption or savings associated with heat losses or gains in a building. By calculating the heat lost through windows and the heat gained from solar radiation, one can estimate the heating cost for a given period. This analysis is crucial for designing energy-efficient buildings and for making informed decisions about investments in insulation or window upgrades.

Transcript

00:01 In this problem, we're asked to essentially redo the example problem 16 .4, but we are assuming that our house has 10 windows, each measuring 2 .5 feet by 5 feet.

00:21 Four of those windows are south -facing, and so they admit solar energy at a rate of 30 btu per hour per hour per.

00:30 Her foot squared.

00:33 However, all of the windows will lose heat and the r factor for the windows is 0 .9.

00:41 And the question is then in part a, what would be the heating cost for an entire month in this house? and in part b, what is the solar gain from the south -facing windows worth? so following the example 16 .4, we know that in order to figure out what the total cost is, we first want to find the heat flow rate through the walls, the roofs, and now the windows in order to figure out the total flow rate that's lost and compare that to then how much oil we would need to burn to account for that loss.

01:43 So we'll start with the walls.

01:47 In the example problem, we're told that the r factor for the walls is 12 .65.

01:56 We are told that the walls have an area.

02:00 I'm going to label these sub -ws, so we know those are walls.

02:04 The walls have an area of 1 ,506 square meters.

02:11 However, we're replacing some of those walls with windows.

02:18 So we're going to need to subtract off the area that the windows take up.

02:25 So first, let's figure out the area that the windows take up.

02:30 We're told that there are 10 windows and they measure 2 .5 feet by 5 feet.

02:39 And so we can just multiply all of that together and get 125 feet squared for the area of the windows.

02:51 And now i'm realizing i wrote meters squared here, but this should be feet squared.

02:59 So then that means that the area taken up by the walls is 1 ,381 square feet.

03:08 So then now knowing that, we can find h for the walls.

03:13 H is generally equal to k -a -d delta -t over delta -x.

03:25 However, in this problem, we're not going to quite do it that way because we don't know necessarily k, but we are given the r -factors.

03:41 So instead, we are going to note that, r is equal to delta x over k, so we can instead do this as a delta t over the r factor.

04:00 Anyway, plugging that in for the walls, we get a value of 5 ,458 btu per hour.

04:13 We're going to repeat this process for the roof, but the roof doesn't change at all from the example problem.

04:23 So we can just go ahead and note that in the example problem, it was 1 ,839 btu per hour for the roof.

04:35 And then we need to also find now for the windows...

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