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Although convective heat transfer can be derived analytically through dimensional analysis, exact analysis of the boundary layer, approximate integral analysis of the boundary layer and analogies between energy and momentum transfer, these analytic approaches may not offer practical solutions to all problems when there are no mathematical models applicable.
In the field of thermodynamics the Bejan number is the ratio of heat transfer irreversibility to total irreversibility due to heat transfer and fluid friction: [1] [2] = ˙, ′ ˙, ′ + ˙, ′
Dimensionless numbers (or characteristic numbers) have an important role in analyzing the behavior of fluids and their flow as well as in other transport phenomena. [1] They include the Reynolds and the Mach numbers, which describe as ratios the relative magnitude of fluid and physical system characteristics, such as density, viscosity, speed of sound, and flow speed.
For a viscous, Newtonian fluid, the governing equations for mass conservation and momentum conservation are the continuity equation and the Navier-Stokes equations: = = + where is the pressure and is the viscous stress tensor, with the components of the viscous stress tensor given by: = (+) + The energy of a unit volume of the fluid is the sum of the kinetic energy / and the internal energy ...
where: = (), = = (), is the modified Reynolds number, is the packed bed friction factor,; is the pressure drop across the bed,; is the length of the bed (not the column), is the equivalent spherical diameter of the packing,
Darcy's law is an equation that describes the flow of a fluid through a porous medium and through a Hele-Shaw cell.The law was formulated by Henry Darcy based on results of experiments [1] on the flow of water through beds of sand, forming the basis of hydrogeology, a branch of earth sciences.
Fluid mechanics is the branch of physics concerned with the mechanics of fluids (liquids, gases, and plasmas) and the forces on them. [1]: 3 It has applications in a wide range of disciplines, including mechanical, aerospace, civil, chemical, and biomedical engineering, as well as geophysics, oceanography, meteorology, astrophysics, and biology.
where the eponymous μ(I) is a dimensionless function of I.As with Newtonian fluids, the first term -Pδ ij represents the effect of pressure. The second term represents a shear stress: it acts in the direction of the shear, and its magnitude is equal to the pressure multiplied by a coefficient of friction μ(I).