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**3. A rectangular bar as shown in Fig below is connected between two walls. The bar generates heat at 3500 W/m 3 and is exposed to gas at 18 C with convection coeff. 34 W/m2.K. The wall surface temperatures are kept at 120 C. The bar is divided into 7 divisions with node numbered from 0,1,2.. to 7. The initial temperatures are TO-120 T1-91.11 T2-72.02 T3-62.72 T4-63.22 T5-73.52 T6-93.61 T7-120 C. For t>0 TO and T7 is kept at 120 Data: Bar density 8000 kg/m3, c-400 J/kg.K, k-56 WIm.K Bar length-14 cm and the rectangular section is 5 cm x 4 cm Gas density 1.18 kg/m ^3-K, c-1000 J/kg.K, k-00253 W/m.? The walls are maintained at a temperature of 120 C. (Prob2is 50%) (A) Use the explicit finite difference method and derive the nodal energy balance equation for node 6 with symbols. (B) Substitute numbers for all symbols and find the new temperature for the node with time step dt-65 s. (i.e. find T for node 6 at time -65 s. Do only one node.) Wall wall 0 4 6 Fig. prob. 2

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