External Transient Convection

Another experiment of interest is that by El Wakil et al. (49), in which the center and peripheral temperatures were measured for a vaporizing droplet subjected to mild forced convection. The measurements show that there are essentially no differences between these two temperatures, not even during the initial transient heating period. Visual observations also revealed the existence of fairly rapid internal circulations. These imply that the assumption of a uniform droplet temperature may be quite realistic for droplet vaporization with some external convective motion. 

Conjugated eonduetion-convection problems are among the elassieal formulations in heat transfer that still demand exact analytical treatment. Since the pioneering works of Perelman (1961) [14] and Luikov et al. (1971) [15], such class of problems continuously deserved the attention of various researchers towards the development of approximate formulations and/or solutions, either in external or internal flow situations. For instance, the present integral transform approach itself has been applied to obtain hybrid solutions for conjugated conduction-convection problems [16-21], in both steady and transient formulations, by employing a transversally lumped or improved lumped heat conduction equation for the wall temperature. 

C.P. Naveira, M. Lachi, R. M. Cotta, and J. Padet, Hybrid Formulation and Solution for Transient Conjugated Conduction-External Convection, Int. J. Heat Mass Transfer, 52, 112-123 (2009). 

The temperature field in a tissue is determined by heat conduction and convection, metabolic heat generation, thermal energy transferred to the tissue from an external source or the surrounding tissue, and the tissue geometry. Thermal conduction is characterized by a thermal conductivity, k, at steady state and by a thermal diffusivity, a, in transient state. Thermal convection is characterized by the topology of the vascular bed and the blood flow rate, which is subject to the thermal regulation. 

We begin our treatment of transient heat conduction by analyzing a simplified case. In this situation we consider a solid which has a very high thermal conductivity or very low internal conductive resistance compared to the external surface resistance, where convection occurs from the external fluid to the surface of the solid. Since the internal resistance is very small, the temperature within the solid is essentially uniform at any given time. 

The slow, stable response of the GT-MHR to internally or externally initiated transients, in combination with passive safety features, provides a strong defence against internal or external threats to the plant. These characteristics arise from the inert coolant, large reactor heat capacity, low power density, strong negative reactivity feedback coefficients and passive decay heat removal by conduction, radiation and convection. 

The external force terms are retained in the given form to ensure that the effects of the interstitial fluid are included in a consistent manner. The two terms on the LHS denotes the transient term and the convective transport term. The terms on the RHS denote the rate of total energy input by conduction per unit volume, production of translational energy (fluctuations) by shear, production due to the interaction with fluid turbulence and dissipation due to interaction with fluid through the drag, and energy dissipation due to inelastic collisions, respectively. 

A scoping analysis of the hot leg piping was performed in ABAQUS to quantify the delay time of external temperature measurement, This model made the same material property assumptions, thermal radiation parameters, and wall thicknesses provided in Reference 9- 77. Additionally, an Inner wall convective heat transfer coefficient from the reactor plant transient model was assigned to provide the model conditions. 

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