Question

What is thermal conductivity connected in parallel and series?

Answer 1

Thermal conductance:

1. The law of heat conduction states that the rate at which heat is transferred through a material is proportional to the negative of the temperature gradient and is also proportional to the area through which the heat flows.
2. The differential form of this law can be expressed through the following equation as

$\mathrm{q}=-\mathrm{k}.\nabla \mathrm{T}$

Where, $\nabla \mathrm{T}$ refers to the temperature gradient, $\mathrm{q}$ denotes the thermal flux or heat flux, and, $\mathrm{k}$ refers to the thermal conductivity of the material.

Let ${\mathrm{k}}_1$ and ${\mathrm{k}}_2$ be thermal conductivities of two resistors.

Series combination:

1. Whenever the two rods are joined throughout the series, this same effective thermal resistance is equal to the total of the respective thermal resistances.
2. The equivalent conductivity in series combination is given as follows:

${\text{k}}_{\mathrm{eq}}=\frac{2{\mathrm{k}}_1{\mathrm{k}}_2}{{\mathrm{k}}_1+{\mathrm{k}}_2}$

Parallel combination:

1. Whenever two materials have been linked in parallel, the whole attainable heat generated per second is divided between them
2. The equivalent conductivity in series combination is given as follows:

${\mathrm{k}}_{\mathrm{eq}}=\frac{{\mathrm{k}}_1+{\mathrm{k}}_2}{2}$