Question

Two conductors A and B given in previous problem are connected in parallel as shown in Fig.
i. Determine the equivalent thermal resistance.
ii. Determine the heat current in each rod.

Answer 1

i. The thermal resistance of the two rods are
`R_A=(l)/(3kA)`,`R_B=(l)/(kA)`
The equivalent resistance is
`(1)/(R )=(1)/(R_A)+(1)/(R_B)=(3kA)/(l)+(kA)/(l)=(4kA)/(l)`
or `R=(l)/(4kA)`
ii. The heat current through each rod is
`I_A=(T_1-T_2)/(R_A)=(100-0)/(l//3kA)=300((kA)/(l))`
`I_B=(T_1-T_2)/(R_B)=(100-0)/(l//kA)=100((kA)/(l))`
Total heat current is
`I=I_A+I_B=400(kA)/(l)`