Date of Award

Spring 1991

Document Type


Degree Name

Doctor of Philosophy (PhD)


Mechanical & Aerospace Engineering


Mechanical Engineering

Committee Director

A. Sidney Roberts, Jr.

Committee Member

Surendra N. Tiwari

Committee Member

Robert L. Ash

Committee Member

John J. Swetits

Committee Member

Ronald N. Jensen


The heat loss from a building slab was investigated. The continuity equation, Darcy's Law and the energy equation were formulated to include the temperature dependence of viscosity and density of water. The governing equations and appropriate boundary conditions were transformed into dimensionless variables. A finite difference numerical scheme was constructed based on the Gauss-Seidel method by lines and solved iteratively in alternating directions. A correlation between the geometrical characteristics of the domain, the convective surface heating parameters, and the total nondimensional slab heat loss in two dimensions was discovered. Furthermore, the correlation was extended to three-dimensional slabs and produced good agreement with analyses by other workers using different methods. Numerical results were validated by comparison with a proprietary finite element solver in two dimensions. Moreover, a scaled laboratory simulation of building slab heat loss was conducted. The agreement between the numerically predicted heat loss and the experimental results was good for solid media. For porous media, the apparent thermal conductivity for both dry and saturated media was measured and found to be in consonance with data produced by others. The observed dye tracer positions in the flow visualization confirmed the predicted positions. The results of the experiments indicated that: the volume averaged method of computing apparent thermal conductivity of the porous media was inadequate and experimentally determined conductivity should be used; and, the time required for a particle to transit a fixed path in the porous media is independent of the thermal conductivity of the media. Finally, the numerical model was extended to include surface evaporation at the earth interface. Surface evaporation increased slab heat transfer by approximately ten percent compared to a non-evaporating surface condition.


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