Explore BrainMass

Explore BrainMass

    Heat Equation, Boundary Conditions, Steady State Condition and Initial-Value Problem

    Not what you're looking for? Search our solutions OR ask your own Custom question.

    This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

    Please help with the following problems involving numerical analysis.

    (a) Find all the separated solutions of the attached heat equation (satisfying the attached boundary condition)

    (b) Use these separated solutions to write a series solution for the initial value problem posed by the attached pde and the attached boundary conditions, with the initial condition given by {see attachment}

    (c) Find the steady state solution for the inital value problem, taking into account the initial condition.

    (d) Show that the series state solution for the initial value problem approaches the steady state solution of the initial value problem as {see attachment}

    (e) Give a brief physical interpretation of this limiting behaviour as {see attachment}

    © BrainMass Inc. brainmass.com December 24, 2021, 5:14 pm ad1c9bdddf


    Solution Preview

    Hello and thank you for posting your question to Brainmass!
    The solution is attached ...

    Solution Summary

    In this posting, heat Equations, Boundary Conditions, Steady State Conditions and an Initial-Value Problem are investigated. The solution is detailed and well presented.