The temperature of the two outer surface of a composite slab...

The temperature of the two outer surface of a composite slab consisting of two materials having cocflicient of thermal conductivities $K$ and $2 K$, thickness $x$ and $4 x$ respectively are $T_{3}$ and $T_{1}\left(T_{2}>T_{1}\right) .$ The rate of heat transfer through the slab, in a steady state is $F\left[\frac{A\left(T_{2}-T_{1}\right) K}{x}\right]$, the value of $F$ is (a) 1 (b) $1 / 2$ (c) $2 / 3$ (d) $1 / 3$

Key Concepts

Composite Slab Conduction

Composite slab conduction involves analyzing heat transfer across slabs made of two or more different materials. In such cases, the overall heat transfer is determined by the individual thermal resistances of each layer, which are considered in series. The effective resistance and resulting temperature drops across each layer can be calculated by summing the individual resistances, allowing for determination of the overall rate of heat transfer.

Thermal Resistance

Thermal resistance is a concept used to quantify how strongly a material resists the flow of heat. It is analogous to electrical resistance and is calculated by dividing the thickness of the material by its thermal conductivity and cross?sectional area. This concept is crucial for analyzing complex heat transfer problems involving multiple layers of different materials.

Thermal Conductivity

Thermal conductivity is a material property that measures a material's ability to conduct heat. It is a key factor in determining the rate at which heat energy is transferred through a material when a temperature gradient is applied.

Fourier's Law of Heat Conduction

This is the fundamental law governing heat transfer by conduction, which states that the heat flux through a material is proportional to the negative gradient of temperatures and the material’s thermal conductivity. It provides the basis for quantifying the rate of heat transfer across a medium given a temperature difference and material properties.

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