A composite rod consists of two different materials, A and B, each of length \(0.5 L\).

The thermal conductivity of Material A is half that of Material B, that is, \(k_{\mathrm{A}} / k_{\mathrm{B}}=0.5\). Sketch the steady-state temperature and heat flux distributions, \(T(x)\) and \(q_{x}^{\prime \prime}\), respectively. Assume constant properties and no internal heat generation in either material.

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T T