Heat transfer to ultralarge-scale heat pipes placed in a geothermal reservoir. (4th report). Transient characteristics associated with axial fluid flows.:Transient Characteristics Associated with Axial Fluid Flows
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Heat transfer from convecting geothermal fluid to an extremely slender isothermal cylinder struck into a hydrothermal system is the center of concern in the development of thermal energy extraction technique with large heat pipes. A present study focuses on transient be-haviors of heat transport through permeable rock formation. The hydrothermal system is idealized as a water-saturated homogeneous porous medium with either forced or natural convection in the axial direction. The transient heat transfer process for both convection systems is analyzed when a cylinder surface temperature is suddenly lowered. Both numerical and analytical approaches are employed to delineate the heat transfer characteristics. The results reveal the presence of three distinct regimes along the course to achieve a steady state for a given set of parameters. Conductive regime, where the radial heat conduction is the dominant mode of transfer process, appears first. At large time the heat transfer becomes independent of time and steady state preveils, where the radial heat diffusion is balanced by the axially convecting heat. Between the two extremes there is a transitional regime, where the effect of convection is detected by the deviation of heat transfer rate from that predicted by the purely conductive solution. The time required for achieving steady state is found to be proportional to a nondimensional parameter indicating the surface curvature in the individual systems. More specifically, the time is proportional to the square of aspect ratio based on the cylinder radius and inversely proportional to the convective velocity. The time leading to steady state in the naturally converting system is, in general, much greater than that in the forced convection.
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