Eleven identical rods are arranged as shown in Fig. Each rod has length l, cross sectional area A and thermal conductivity of material L. Ends A and F are maintained at temperatures T_1 and T_2(ltT_1), respectively. If lateral surface of each rod is thermally insulated, the rate of heat transfer ((dQ)/(dt)) in each rod is

Eleven identical rods are arranged as shown in Fig. Each rod has len

1.	Eleven identical rods are arranged as shown in Fig. Each rod has length l, cross sectional area A and thermal conductivity of material L. Ends A and F are maintained at temperatures T_1 and T_2(ltT_1), respectively. If lateral surface of each rod is thermally insulated, the rate of heat transfer ((dQ)/(dt)) in each rod is
Answer» `((DQ)/(dt))_(AB)=((dQ)/(dt))_(CD)` `((dQ)/(dt))_(BE)=(2)/(7)((T_1-T_2)KA)/(l)` `((dQ)/(dt))_(CH)ne((dQ)/(dt))_(DG)` `((dQ)/(dt))_(BC)=((dQ)/(dt))_(DC)` Solution : Resistance of each ROD `R=(l)/(kA)` In STEADY state `T_B=T_D` `T_E=T_G` Thermal current `((dQ)/(dt))=i` `i_1R+i_3R+i_1R=(T_1-T_2)` `2i_1+i_3=((T_1-T_2))/(R )` ..(i) `2i_1+i_3=(T_1-T_2)/( R)`.(ii) `i_1=i_2` For the path ABCHGF `i_1R+(i_1-i_3)R+2(i_1+i_3)R+(i_1-i_3)R+i_1R=(T_1-T_2)` `6i_i-4i_3=((T_1-T_2))/(R )=2i_i+i_3`.(iv) `4i_i=5i_3impliesi_3=(4)/(5)i_i`.(v) From eqs (ii) and (v) `2i_i+(4)/(5)i_1=((T_1-T_2))/(R )` `(14i_i)/(5)=((T_1-T_2))/(R )` Equivalent thermal resistance `((T_1-T_2))/(2i_i)=(7)/(5)R` `((dQ)/(dt))_(AB)=i_1=(5(T_1-T_2)KA)/(14l)` `((dQ)/(dt))_(BE)=(2)/(7)((T_1-T_2)KA)/(l)` `((dQ)/(dt))_(BC)=((T_1-T_2)KA)/(14l)` `((dQ)/(dt))_(CH)=((T_1-T_2)KA)/(7l)`