Document Type

Thesis - Open Access

Award Date


Degree Name

Master of Science (MS)


Mechanical Engineering


Two recent papers [1,2] obtain formulas for temperature variations caused by the varying flow of solar heat through windows. These two works are used in the present study to develop a computer program for calculating the transient cooling load required to maintain the interior of a building at a given temperature. We assume that the building is standing by itself without surrounding radiating buildings or pavements. The heat gain through semi-transparent single or composite barriers is combined with the accompanying heat gain through the opaque walls; see Figure 1. The analytical solutions given in [1,2] cannot be represented directly as numerical terms in the cooling load. This is because the useful solutions in [1,2] exist as explicit solutions for the air temperature of the room; the solutions also exist in the form of a formal integral representation with the terms of the cooling load involved in the integrals. To obtain a solution of this part of the problem in numerical terms, two steps are involved: i. Numerical evaluations of the formal integral representation ii. Inversion of the indirect solutions to obtain the numerical results for the required cooling load. Two procedures can be followed to arrive at a· solution: One, we use the analytical solutions given in [1,2]; and two, we solve our problem directly from the differential formulation given in these references by numerical method. The mathematical representation of our problem was formulated into a computer program to perform the automatic calculations. This computer program is given in a separate volume available in the Department of Mechanical Engineering at South Dakota State University. Certain approximations are introduced in order to obtain the numerical results. The approximations associated with the numerical evaluations are discussed in Chapter III. The error induced due to the approximations can be reduced by using some of the more accurate approximation methods. However, the associated disadvantages in doing so are: 1. The flow chart for the automatic calculation system can be more complex in logic, and more difficult to understand. 2. The computer program associated with the flow chart can be more involved and larger in size to such an extent that it is not easily handled. Also, high accuracy can be attained by using smaller increments for each step of the calculations. But the required number of calculations will be greatly increased, and so will be the required computer time. For engineering applications, we prefer to have our methods simple and practical, so that they can be applied without difficulty by those who are interested.

Library of Congress Subject Headings

Solar heating



Number of Pages



South Dakota State University