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describes heat transfer across a surface = Here, is the overall heat transfer coefficient, is the total heat transfer area, and is the minimum heat capacity rate. To better understand where this definition of NTU comes from, consider the following heat transfer energy balance, which is an extension of the energy balance above:
The basic mechanisms and mathematics of heat, mass, and momentum transport are essentially the same. Among many analogies (like Reynolds analogy , Prandtl–Taylor analogy) developed to directly relate heat transfer coefficients, mass transfer coefficients and friction factors, Chilton and Colburn J-factor analogy proved to be the most accurate.
Just like "conventional" or "macro scale" heat exchangers, micro heat exchangers have one, two or even three [12] fluidic flows. In the case of one fluidic flow, heat can be transferred to the fluid (each of the fluids can be a gas, a liquid, or a multiphase flow) from electrically powered heater cartridges, or removed from the fluid by electrically powered elements like Peltier chillers.
Figure 1: Thermal pressure as a function of temperature normalized to A of the few compounds commonly used in the study of Geophysics. [3]The thermal pressure coefficient can be considered as a fundamental property; it is closely related to various properties such as internal pressure, sonic velocity, the entropy of melting, isothermal compressibility, isobaric expansibility, phase transition ...
The suitable relationship that defines non-equilibrium thermodynamic state variables is as follows. When the system is in local equilibrium, non-equilibrium state variables are such that they can be measured locally with sufficient accuracy by the same techniques as are used to measure thermodynamic state variables, or by corresponding time and space derivatives, including fluxes of matter and ...
The macroscopic energy equation for infinitesimal volume used in heat transfer analysis is [6] = +, ˙, where q is heat flux vector, −ρc p (∂T/∂t) is temporal change of internal energy (ρ is density, c p is specific heat capacity at constant pressure, T is temperature and t is time), and ˙ is the energy conversion to and from thermal ...
As noted, a Biot number smaller than about 0.1 shows that the conduction resistance inside a body is much smaller than heat convection at the surface, so that temperature gradients are negligible inside of the body. In this case, the lumped-capacitance model of transient heat transfer can be used. (A Biot number less than 0.1 generally ...
For the case of flow without heat transfer, the non-dimensionalized Navier–Stokes equation depends only on the Reynolds Number and hence all physical realizations of the related experiment will have the same value of non-dimensionalized variables for the same Reynolds Number. [3]