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Heat conduction in semi-infinite solid in contact with linearly increasing mass of fluid

1956
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Quarterly of Applied Mathematics
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The boundary conditions implied by conditions (t) and (it) are: For Eq. (4): (a) ue = 0, ur finite, when 0 = 0. (b) ur = ue = 0, when 6 = a. For Eq. (5): (c) us = 0, ur finite, dur/dd finite, when 6 = 0.* These yield respectively the equations: Cj cos2 a + c2 cos a + c3 = 0, 2ci + c2 = 0. These have ct = c2 = c3 = 0 as their only solution. As Squire [5] has shown, the general solution of Eq. (4) with = c2 = c3 = 0 is: where a is an arbitrary constant. Referring again to the boundary condition

doi:10.1090/qam/79967
fatcat:dvl3d2gvcratrdob6m346nlvwa