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The Laws of Nuclear Heat Transfer
Published in Robert E. Masterson, Nuclear Reactor Thermal Hydraulics, 2019
Here TWALL is the temperature at the outer surface of the object, which is also called the temperature of the wall and TFLUID is the “average” temperature of the fluid passing over the wall. The average temperature of the fluid is also called its bulk temperature. In Equation 10.15, q is the heat flow rate (in W/s or kW/s), A is the cross-sectional area over which this flow occurs (in cm2), and h is a constant of proportionality called the convective heat transfer coefficient. In the SI system of units, the convective heat transfer coefficient is expressed in W/m-°K, and in most nuclear applications, it is also expressed in W/cm-°C. In other words, the value of h depends upon both the thermal conductivity of the fluid and the speed that the fluid is flowing past the wall. In Chapter 20, we will find that we can express h as the product of two additional parameters called the Reynolds number Re and the Prandtl number Pr. The Reynolds number is a function of the way we choose to operate a reactor, and the Prandtl number is a function of the type of coolant the reactor uses. In other words, we can express the convective heat transfer coefficient as
Nanoscale Thermal Phenomena
Published in C. B. Sobhan, G. P. Peterson, Microscale and Nanoscale Heat Transfer, 2008
To better understand the reasons for the improved thermal conductivity of nanoparticle suspensions, it is important to understand the physical situation that exists in these suspensions. Envision a nanoparticle suspension enclosed in a rectangular container with one wall heated and the opposite wall cooled. As noted by Keblinski et al. (2002), the thermal diffusion in the base fluid is typically much faster than the Brownian diffusion of the nanoparticles in the suspension. As a result, heat transferred through the base liquid by thermal diffusion will be much faster than the heat transfer resulting from the movement of the nanoparticles. This implies that when heat is conducted from the heated surface into the nanoparticle suspension, the temperature of the base fluid will be higher than, or at least the same as, the temperature of the nanoparticles at any given location. Further, as the bulk temperature increases, the thermal conductivity of most base fluids, e.g., water, increases, while the thermal conductivity of most nanoparticles, e.g., aluminum or copper oxide, decreases. Hence, if the thermal conductivity of the nanoparticle is initially higher than that of the surrounding fluid, the thermal conductivity difference will decrease with increasing temperature, and as a result, the contribution resulting from the combined thermal conductivity will decrease with increasing temperature. In addition, the temperature difference between nanoparticle and the fluid molecules around it will be decreasing and, in turn the contribution from the microconvection heat transfer between the nanoparticles and the base fluid will decrease. This is quite different from what has been observed experimentally, where the higher the bulk temperature, the greater the enhancement of the effective thermal conductivity. Finally, based on the computational simulation of Wang et al. (2004), it appears that the presence of the nanoparticles will enhance the effective thermal conductivity of the suspension, even if the nanoparticle has a very low thermal conductivity, indicating that it is the movement of the particle alone, that enhances the overall effective thermal conductivity in nanoparticle suspensions. For these reasons, it seems unlikely that the enhancement observed in a number of experimental investigations, is due to the heat transfer relationships between the nanoparticles and the base fluid alone, as described in several previous investigations (Jang and Choi 2004, Prasher et al. 2005).
Thermodynamic and thermophysical effects enabling high-forced convection heat transfer coefficients in supercritical fluids
Published in Numerical Heat Transfer, Part A: Applications, 2020
Olivia C. da Rosa, Gustavo M. Hobold, Alexandre K. da Silva
Therefore, the existence of a peak in the heat transfer coefficient along the heat exchanger would require the bulk temperature to increase faster than the wall temperature. Because the thermal diffusivity of supercritical fluids is typically small, this condition can be approximately met when the specific heat of the fluid adjacent to the wall is much larger than the specific heat of the bulk fluid. In fact, when Tin = 301 K or 307 K, the wall quickly reaches a peak in the heat capacity and most of the flow is under low wall heat capacity. These effects can be observed in Figure 4b, where the wall and the bulk specific heats are plotted along the heat exchanger. However, note that for Tin = 289 K, the wall reaches a peak in the specific heat just after entrance length effects start becoming negligible, which causes the temperature difference between the wall and the bulk fluid to be small along most of the heat exchanger, hence triggering the proposed mechanism of heat transfer intensification in supercritical fluids.