Purchase Solution

Temperature distribution within a hemisphere exposed to a hot gas stream.

Not what you're looking for?

Ask Custom Question

See the attached file.

Please see the attached file for the fully formatted problem.

L .M. Chiappetta and D.R. Sobel ("Temperature distribution within a hemisphere exposed to a hot gas stream," SIAM Review 26, 1984, p. 575?577) analyze the steady- state temperature in the rounded tip of a combustion-gas sampling probe. The tip is approximately hemispherical iii shape, with radius a. Its outer surface is exposed to hot gases at a temperature Tc, and its base is cooled by water at temperature Tw circulating inside the probe. Let the temperature inside the tip he T. Because of the symmetry of the problem, there is no azinnitha.1 variation in T. In other words, if we are using spherical coordinates, T = T(r, 0), where U is the colatitude. So, T is governed by the differential equation
inside the domain ... (the upper hemisphere with radius a). Let us use a Dirichlet condition at the base of the tip.
and a Robin boundary condition at the outer surface of the tip,
As usual, we will also assume that tile temperature is bounded at the origin and along the north pole. Let .... and solve for it using separation of variables.
Hints: You will need to figure out the orthogonality condition for the eigenfunctions, but you can assume that tile eigenfunctions will he orthogonal with respect to the appropriate weight function because the eigenvalue problem is in Sturm-Liouville form.

Purchase this Solution

Solution Summary

Temperature distribution within a hemisphere exposed to a hot gas stream is investigated. The solution is detailed and well presented.

Purchase this Solution

Free BrainMass Quizzes
Probability Quiz

Some questions on probability

Exponential Expressions

In this quiz, you will have a chance to practice basic terminology of exponential expressions and how to evaluate them.

Solving quadratic inequalities

This quiz test you on how well you are familiar with solving quadratic inequalities.

Multiplying Complex Numbers

This is a short quiz to check your understanding of multiplication of complex numbers in rectangular form.

Graphs and Functions

This quiz helps you easily identify a function and test your understanding of ranges, domains , function inverses and transformations.