Two bars of equal length and the same cross-sectional area but of different thermal conductivities k 1 and k 2 are joined end to end as shown in Figure 4.36. One end of the composite bar is mainta

Question

Two bars of equal length and the same cross-sectional area but of different thermal conductivities $k_{1}$ and $k_{2}$ are joined end to end as shown in Figure 4.36. One end of the composite bar is maintained at temperature $T_{h}$ , whereas the opposite end is held at $T_{c}$ . If there are no heat losses from the sides of the bars, the temperature $T_{j}$ of the junction is given by:

TestHub · Accepted Answer

The heat current is equal: k 1 ​ ( T h ​ − T j ​ ) = k 2 ​ ( T j ​ − T c ​ ) . So T j ​ = k 1 ​ + k 2 ​ k 1 ​ T h ​ + k 2 ​ T c ​ ​ . D.

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