By G. K. Batchelor
First released in 1967, Professor Batchelor's vintage paintings remains to be one of many most suitable texts on fluid dynamics. His cautious presentation of the underlying theories of fluids remains to be well timed and acceptable, even today of just about unlimited laptop energy. This reissue guarantees new new release of graduate scholars reports the beauty of Professor Batchelor's writing.
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Additional resources for An Introduction to Fluid Dynamics
It is evident that molecular transport will still lead to a net transfer across an element of surface in the material when the distribution of intensity in the neighbourhood of the surface element is non-uniform, but, instead of representing this local non-uniformity as a difference between the values of the intensity on the two sides of the element, we must take a more general point of view and represent it as a vector gradient of intensity at the position of the surface element. The linear relation between flux and the gradient of a scalar intensity Consider first the cases in which the relevant intensity is a scalar quantity (viz.
KHVT). 10) that the term on the far left can also be written as the rate of change of enthalpy I, in these circumstances of constant pressure. When the thermal conductivity kH is approximately uniform throughout the material, the equation for T becomes aT at = where V2T, (6 I. 13) KH this' heat conduction equation' is thus identical in form with the diffusion equation for media at rest. The parameter KH here may be termed the thermal dijJusivity, being sometimes known also as the thermometric conductivity.
6] Transport phenomena 29 element of surface drawn in the fluid is larger than that on the other side, random migration of marked molecules in both directions across the surface element will lead in general to a non-zero flux of marked molecules across the element, of such a sign as to tend to make the proportion of marked molecules more nearly equal on the two sides. t This non-zero flux of a constituent of the fluid due to migration of molecules constitutes diffusion of matter. Our discussion of this rather complex phenomenon will be limited to cases of small concentration of the diffusing constituent.
An Introduction to Fluid Dynamics by G. K. Batchelor