By Edwin Henry Barton
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Microcontinuum box theories represent an extension of classical box theories --- of elastic solids, viscous fluids, electromagnetism, and so forth --- to microscopic size and time scales. fabric our bodies are considered as collections of a giant variety of deformable debris (sub-continua), appropriate for modeling blood, porous media, polymers, liquid crystals, slurries, and composite fabrics.
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However, if we took a boat that was so light that it moved at the ﬂow speed, then a thermometer glued to it would be registering the temperature of the (approximately) same ﬂuid particle. In this case we would be using the Lagrangian description because we would be describing the temperature of the same ﬂuid particle with time. Obviously it is much simpler and much more accurate to ﬁx the thermometer at a spatial point. 3 Arbitrary Lagrangian-Eulerian Description (ALE) This description ﬁnds application in modern computational tools developed for analysis in engineering and sciences.
The direction of the force that the pressure causes is determined by the normal to the surface n. The minus sign indicates that pressure is a negative normal stress, also called compression, that acts in the opposite direction to the exterior normal. When the normal stress is positive, then it acts in the direction of the exterior normal, producing traction. 4. This type of tensor, proportional to the identity tensor, is called an isotropic tensor. 5. For a ﬂuid in motion, the stress tensor is the sum of the action due to the pressure plus a contribution from the motion, called the viscous stress tensor τ , which is introduced in Chapter 7.
Note that for a positive ρφ, the convective ﬂux is positive for outgoing ﬂow (v · n > 0) and negative, for incoming ﬂow (v · n < 0). 11 (Flux). In general, the ﬂux of a vector Φ equals the integral of Φ · n over the surface S Φ · n dS F = S where n is the exterior normal to the surface. 13 (Heat ﬂux across a surface). The heat ﬂow or heat ﬂux across a surface can be calculated by setting Φ = q, where q is the vector of heat per unit surface per unit time [W/m2 ]. 1. Examples of ﬂuxes across a surface S.