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By Edwin Henry Barton

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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.

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