For a one dimensional steady state variable thermal conductivity heat conduction with uniform internal heat generation, develop

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For a one dimensional steady state variable thermal conductivity heat conduction with uniform internal heat generation, develop a generalized finite difference formulation for the interior nodes, with left surface boundary node exposed to constant heat flux and right surface boundary node exposed to convective environment. The variable conductivity is modeled such that the thermal conductivity varies linearly with the temperature as k(T) = ko(1 + βT) where T is the average temperature between the two nodes.

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