China
Africa
Explore chapters and articles related to this topic
Convection
Published in Greg F. Naterer, Advanced Heat Transfer, 2018
A useful approximate method for analyzing fluid flow and heat transfer problems is the method of scale analysis (or an order-of-magnitude analysis). This method is a powerful tool for a general understanding and simplification of governing equations with many terms. The magnitudes of individual terms in the equations are determined and then negligible small terms may be ignored. The objective of a scale analysis is to use the governing equations to estimate the order of magnitude of key variables of interest. Usually a scale analysis can be reliable within a factor of one order of magnitude. Sometimes this general level of accuracy is sufficient and can significantly reduce the computational costs relative to an exact or numerical solution. Scale analysis is also useful for quickly obtaining key trends, although a more detailed method of analysis is required to determine accurate numerical results.
Similitude
Published in Marian (Editor-in-Chief) Muste, Dennis A. Lyn, David M. Admiraal, Robert Ettema, Vladimir Nikora, Marcelo H. Garcia, Experimental Hydraulics: Methods, Instrumentation, Data Processing and Management, 2017
Marian (Editor-in-Chief) Muste, Dennis A. Lyn, David M. Admiraal, Robert Ettema, Vladimir Nikora, Marcelo H. Garcia
A necessary early step in experiment design is to determine parameters defining equivalence of dynamic similitude for process(es) of focal interest for the experiment. Three approaches are often used for taking this step: Scale analysis of the equations used to describe a flow or fluid-transport process;Direct comparison of the ratios of pertinent variables, such as forces or flux rates; and,Dimensional analysis, whereby pertinent variables are grouped without direct regard for their mathematical relationship. Approach 1 is the ideal and most rigorous approach, but requires that the equations be known, which often is not the case. Approach 2 involves understanding the critical processes in order to arrive at the main non-dimensional parameters needed for characterizing a process. Approach 3, dimensional analysis, based on the theory of dimensions, is a convenient and practical way to assemble dimensionless parameters from a listing of pertinent variables. The ensuing section of this chapter outlines Approach 1, and Appendix 3.A elaborates Approach 3. Approach 2 essentially relies on the judgment of the modeler to identify the main (or useful) parameters, and may be viewed as an informal or partial version of Approach 3.
Review of Basic Concepts
Published in Kleinstreuer Clement, Modern Fluid Dynamics, 2018
Scale analysis is a simple algebraic procedure whereby ratios of forces (or fluxes) are formed, based on selected terms of problem-specific equations and physical insight. Without going through elaborate schemes (e.g., Buckingham’s pi-theorem) or solving complex equations, scale analysis can provide directly dimensionless groups as well as their functional dependence on dependent variables. The derivations of the Reynolds number and the Strouhal number may serve as illustrative examples. The necessary physical insight is that both are (naturally) dimensionless ratios of selected forces appearing in the equation of fluid‑element acceleration.
Analytical solution of a heat transfer model for a tubular co-current diluted moving bed heat exchanger with indirect heating and thermal losses to the environment
Published in Chemical Engineering Communications, 2022
Richard Tribess, Sávio L. Bertoli, Carolina K. de Souza, Mercedes Gabriela Ratto Reiter, Maria I. L. Krautler, Marcel J. Gonçalves
In order to deepen the physical meaning of the parameters, a scale analysis is performed. As a first step, the following scales (Bertoli et al. 2012, 2016, 2017, 2019, 2020) are introduced: length scale for propagation of conductive effects at a distance within the particle, length scale associated with heating/cooling of the particle surface by convection between the dragging fluid and the particle, length scale associated with the cooling/heating of the dragging fluid by convection between the dragging fluid and the particle, length scale associated with the heating of the dragging fluid by the flue gas, length scale associated with the cooling of the flue gas by the dragging fluid, length scale associated with the cooling of the flue gas by the external environment: