A wellmixed fluid is heated by a long iron plate of conductivity \(k=10 \mathrm{~W} / \mathrm{m} /{ }^{\circ} \mathrm{C}\) and thickness \(t=0.12 \mathrm{~m}\). Heat is generated uniformly in the plate at the rate \(Q_{g}=5,000 \mathrm{~W} / \mathrm{m}^{3}\). If the surface convection coefficient \(h=5 \mathrm{~W} / \mathrm{m}^{2} /{ }^{\circ} \mathrm{C}\) and fluid temperature is \(T_{f}=45^{\circ} \mathrm{C}\), determine the temperature at the center of the plate, \(T_{c}\), and the heat flow rate to the fluid, \(q\), using three onedimensional elements.

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Tf h 0.12 m k Tf h