Clifton W. D r a ~ e r ' The Pennsylvania State University Unwersity Park, 16802
11
Classroom/Laboratory Simulation of Periodic ~em~erature Fluctuations in Soil
Current concerns about energy utilization and its conservation emphasize the need to introduce students to the concept of heat transfer, particularly conduction and the role it plays in overall energy loss in everyday problems. The outermost crust of the earth and the roughly periodic temperature fluctuations that the surface is exposed to offer an ideal "practical application" of Fourier's heat equation. The classical works of Forbes ( 1 ) and Lord Kelvin (2).along with numerous other studies ( 3 ; 4 )have shown that (1) diurnal waves resulting from daily heating and nightly cooling of the surface do not penetrate to a depth of more than about 3 feet, (2) yearly fluctuations from the seasonal heating and cooling of summer and winter penetrate considerably deeper, and (3) that thermophysical properties (thermal diffusivity ( a ) and conductivity (K)) of the soil can he determined from measurements of the periodic fluctuations in the earth. The Fourier heat equation in one dimension is
Application of the boundary condition that a t the surface ( x = 0) the temperature he periodic T = An sin w t
(2)
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leads, after mathematical manipulation, to the solution
which gives the temperature T, a t time t, a t a depth x down from the wridrtt. A , is rhr tempt,r>iture amplitude at the surface. L, rhv itnguliir irequenq I.., = L ' r v l utoscilli~t~m, and ., th(. tlterlnal d ~ i i u s ~ v i111 t ) the matwi:il the heat W:IWS arc propagating in. (Fur ;I complrn. d6w\.at:w1 r,t eqn. 1;11 s w ret. f.i I
