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Suppose Fluid (say, water) occupies a domain D and has velocity field V=V(x, t). A substance (say, a day) is suspended into the fluid and will be transported by the fluid as well as diffused within it; let u= u(x,t) be the concentration of the substance( mass per unit volume). Let be the concentration flux (mass per unit area per unit time, analogous to heat flux). Let B(x) be a ball of radius r > 0 contained in D. Derive the conservation law.
Fick's law for diffusion states that the concentration flux due to diffusion is proportional to the gradient of the concentration flux due to diffusion is proportional to the gradient of the concentration. Deduce that .
Apply the divergence theorem to the conservation law and substitute the flux formula to arrive at the diffusion- transport equation:
this is the higher- dimensional transport equation. If the fluid is motionless, it is called the diffusion equation.
Determine the causality principle for the Klein- Gordon equation in one dimension. Deduce that the speed of propagation is at most c.
1). A ring of outer diameter 80 cm is made from square of cross -section steel bar size(8 *8 cm) . If relative permeability 1200 for steel . calculate the current needed to produce
An element exists in two solid phases (labelled P1 and P2). The standard molar entropies of P1 and P2 are 21.9 J mol -1 K -1 and 23.3 J mol -1 K -1 respectively. The
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The variable period of a moon of Jupiter, which is the basis of measurement of the speed of light in Roemer's method (whoever heis), is regarded as the Doppler affect. The period o
A wooden ring stand The bottom for this ring stand is made from a piece of wood 40 cm long, 15 cm wide and 1 cm thick. A whole 1 cm in diameter is bored by the centre of the ba
Q. Illustrate what is ntu in thermodynamics? Answer:- The ntu is nothing but number of transfer units it is one of the method utilized to find the heat transfer of hot and
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An atom which has lost one electron would be: (1) Negatively charged () Positively charged (3) Electrically neutral (4) Carry double positive charge Ans: Elec
Ask question #whether s component or p component present in the reflected light of Biot''s polariscope# Minimum 100 words accepted#
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