Spherical shell

In geometry, a spherical shell is a generalization of an annulus to three dimensions. It is the region of a ball between two concentric spheres of differing radii. Volume The volume of a spherical shell is the difference between the enclosed volume of the outer sphere and the enclosed volume of the inner sphere: : V=\frac{4}{3}\pi R^3- \frac{4}{3}\pi r^3 : V=\frac{4}{3}\pi \left(R^3-r^3\right) : V=\frac{4}{3}\pi (R-r)\left(R^2+Rr+r^2\right) where r is the radius of the inner sphere and R is the radius of the outer sphere. Approximation An approximation for the volume of a thin spherical shell is the surface area of the inner sphere multiplied by the thickness t of the shell: : V \approx 4 \pi r^2 t, when t is very small compared to r (t \ll r). The total surface area of the spherical sh

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Spherical shell

Finite Element Approximation to Infinite Prandtl Number Boussinesq Equations with Temperature-Dependent Coefficients - Thermal Convection Problems in a Spherical Shell

Finite Element Approximation to Infinite Prandtl Number Boussinesq Equations with Temperature-Dependent Coefficients - Thermal Convection Problems in a Spherical Shell