Ex. The temperature u(x.t) in a strip of metal of width L is govemed by the heat equation au =u, for 05XSL and t>0. Use separation of variables method to find the unsteady state temperature distribution in the strip given that the initial condition is u(x,0) =x and the boundary conditions u, (0.1) =u(Lt)=0 for t>0. The condition u, (0,1)=0 expresses mathematically the constraint that no heat flows through the left boundary (insulated end condition).

Q: Solve the heat transfer equation for a metal rod in one dimension, assuming a constant cross-section…

A: Method of Separation of variables

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A: In this,we cam find the expression for the temperature using given initial temperature distribution.

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A: please comment if you need any clarification. I done lots work for you.. please put thumbs up.thank…

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A: In this question, we solve the heat equation by using the separation of varibale. U(x,t)=X(x)T(t).

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Contingency Table

A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.

Binomial Distribution

Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.