| Summary: | The heat transfer characteristics of a viscous, low Peclet number fluid entering a circular duct from an isothermal reservoir is considered. A technique for realistically modeling the constant temperature entrance condition in the presence of axial conduction is described. Graphs of the local Nusselt number and the local temperature profile are given for each case of constant temperature and constant heat flux at the duct wall.
The energy equation is solved numerically using a finite difference scheme; Langhaar's solution for developing flow is used to describe the fluid dynamics. The results were tested by assuming either uniform or parabolic velocity profile. The results compared favorably with those reported in the literature. The classical Graetz problem was also solved, and the numerical result agreed to within 1% with the known analytical solution.
An analysis of heat transfer in a shell and tube energy device having a phase change material (PCM) on the shell side is presented for the case of energy recovery from the PCM. The PCM is initially liquid, and at its freezing point. The working fluid originates from an isothermal reservoir. Developing, laminar Newtonian flow is assumed. The coupled energy equations written for the fluid and the PCM fully account for the effects of axial conduction. Finite difference methods are employed in solving the equations. Alternating direction procedures are applied to the energy equations, and the nonlinear heat balance equation written for the interface is solved by the Newton-Raphson method.
The numerical results were obtained by assuming the ratio of the conductivity of the PCM to that of the fluid to be 4.0, and the ratio of the diffusivities to be 2.5. Physically, this could represent an n-octadecan wax water system.
Certain assumptions that have been made in the literature have been checked for validity. This work supports the assumption that axial conduction can be neglected in the PCM. However, the heat capacity of the PCM can not be neglected even for small Stefan numbers. In addition the bulk temperature of the fluid is shown to be a function of the Stefan number and therefore can not be imposed a priori until the general form of the problem (coupled energy equation for PCM and fluid) has been solved.
Graphs of the temperature distribution for the fluid and the PCM, the bulk temperature of the fluid, the interface position and the Biot number are presented.
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