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A rectangular plate {0 x a, 0 y b} initially has a hot
Chapter 12, Problem 12(choose chapter or problem)
A rectangular plate {0 x a, 0 y b} initially has a hot spot at its center so that its initial temperature distribution is u(x, y,0)= M(x a 2, y b 2). Its edges are maintained at zero temperature. Let k be the diffusion constant. Find the temperature at any later time in the form of a series.
Questions & Answers
QUESTION:
A rectangular plate {0 x a, 0 y b} initially has a hot spot at its center so that its initial temperature distribution is u(x, y,0)= M(x a 2, y b 2). Its edges are maintained at zero temperature. Let k be the diffusion constant. Find the temperature at any later time in the form of a series.
ANSWER:Step 1 of 4
Series can be expressed as
It has to satisfy the initial condition
Multiply equation by ,