hi pf!(adsbygoogle = window.adsbygoogle || []).push({});

i was reading a sample problem in a text on ode's and came across a boundary condition that didnt really make sense to me.

the physical scenario is: a liquid ##L## measured in moles/cubic meter (##mol / m^3##) is injected into a stream of water. ##L## is being injected at a rate ##W## measured in (g-moles)/sec (##(g-mol) / s##). the following boundary condition is presented: $$s \to 0 \implies -4 \pi s^2 C \frac{\partial L}{\partial s} \to W$$ where ##s^2 = x^2 + y^2 + z^2##. this boundary condition physically represents that the injection rate at ##s=0## is ##W## (the coordinate system is centered at the injection site). ##C## is a constant, who's units are square meters per second (##m^2 / s##)

now i know ##4 \pi r^2## is the surface area of a sphere. also, we are given that molar flux, ##\vec{n}## is ##\vec{n}=-C\nabla L## which has units ##mol / (m^2 \times s)##.

thanks for any help on the help!

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Boundary conditions

**Physics Forums | Science Articles, Homework Help, Discussion**