What is thermal conductivity connected in parallel and series?

Hint:The rate of heat energy flow through a solid material is related to the temperature differential between the rod's two ends. The rate of heat flow is inversely proportional to the combination of length area and thermal conductivity coefficient. Thermal resistance is defined as the ratio of a material's length to its thermal conductivity coefficient and cross-sectional area.

Complete answer:
Series: We can compute the effective coefficient of heat conductivity when different materials are linked with varying coefficients of thermal conductivity. When the rods are linked in series, the flow rate through both sections is the same. However, because the different connections get varying amounts of heat energy, the temperature differential between them will be varied.

The total of the temperature differences between the junctions equals the temperature difference between the first and last ends. When two materials are linked in series and their physical dimensions are the same,
\[{k_s} = \dfrac{{2{k_1}{k_2}}}{{{k_1} + {k_2}}}\]

Parallel: When two materials are linked in a parallel configuration, the entire available heat energy per second is divided between them. In any case, the temperature will be the same at the end. When the rods are linked in parallel, the effect on thermal resistance is identical to the effect on electric resistance.

We may construct a simple equation for the influence on coefficient of heat conductivity when two distinct rods have the same length and cross-section area, as shown below.
${k_p} = \dfrac{{{k_1} + {k_2}}}{2}$

Note: Low thermal conductivity materials transmit heat at a slower pace than high thermal conductivity materials. Metals, for example, have a high thermal conductivity and are extremely effective at transferring heat, whereas insulating materials like Styrofoam are the polar opposite. High thermal conductivity materials are commonly utilised in heat sink applications, while low thermal conductivity materials are used as thermal insulation. Thermal resistance is the counterpart of thermal conductivity.