(Solved): Consider a simple heat exchanger made of a long rectangular enclosure contain ...

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Consider a simple heat exchanger made of a long rectangular enclosure containing a number of aluminium rods running from one passage of fluid 1 at \( T_{f 1} \) through a thin adiabatic membrane into another passage of fluid 2 at \( T_{f 2} \). The cross section of the enclosure is shown in Figure 1. The enclosure is made of an insulation material, and the membrane is located at the middle of the rod. Both ends of the rod of thermal conductivity \( k \) are in contact with the enclosure with contact resistance \( R^{\prime \prime} \) c. It is estimated that the heat transfer coefficients between the two fluids and the rod are \( h_{l} \) and \( h_{2} \) corresponding to fluid 1 and fluid 2, respectively. The diameter and the total length of the rod are denoted by \( D \) and \( L \), respectively. For the following conditions:- - \( T_{f 1}=125^{\circ} \mathrm{C}, T_{f 2}=65^{\circ} \mathrm{C} \) - \( \quad h_{1}=20 \mathrm{~W} / \mathrm{m}^{2} \cdot \mathrm{K}, h_{2}=250 \mathrm{~W} / \mathrm{m}^{2} \cdot \mathrm{K} \) - \( k=185 \mathrm{~W} / \mathrm{m} \cdot \mathrm{K}, D=25 \mathrm{~mm}, L=60 \mathrm{~cm} \) - \( R_{c t}^{n}=2.8 \mathrm{~cm}^{2} \cdot{ }^{\circ} \mathrm{C} / \mathrm{W} \) (a) Draw a schematic of the problem. (b) Provide a list of assumptions complete with validation whenever applicable. (c) Provide a corresponding thermal resistance network, and clearly indicate all the relevant notations. (d) Compute the equivalent total resistance of the thermal network. (e) Compute the total heat transfer rate through each rod.