# Plate Cooling Model of the Lithosphere

Mean oceanic geotherm determined from Equation (4–125) with t =60.4 Myr. proaches an equilibrium, time-independent thermal structure. This result requires heating of the base of the continental lithosphere by mantle convection. The surface heat flow data from the ocean basins given in Figure 4–25 show that there is also basal heating of the oceanic lithosphere. To account for this basal heating, we introduce the plate cooling model.

Consider the instantaneous heating or cooling of a finite thickness plate. Since our application is to the lithosphere, we take the plate thickness to be yL0, the thickness of the lithosphere at large times. The infinitely long plate

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fills the region 0 ≤ y ≤ yL0. The temperature in the plate is a solution of the one-dimensional unsteady heat conduction equation (4–68). Initially at t = 0 the plate is at the temperature T1; for t > 0, the surface

of the plate y = 0 is maintained at the temperature T0. The base of the plate y = yL0 is maintained at the temperature T1. These conditions can be written as T = T1 at t = 0, 0 ≤ y ≤ yL0 T = T0 at y = 0, t > 0