Chapter 17, Problem 17.54P

Interpretation Introduction

Interpretation:

Thermal conductivity of laminatefor parallel and perpendicular to the layer should be calculated.

Concept introduction:

The relationship of thermal conductivity, parallel to fiber is defined as:

Thermal conductivity is defined as the ability of material to conduct heat per unit surface area.

Relation of thermal conductivity for parallel condition is given as:

  $k_{material}=f_{Al}{k}_{Al}+f_{foam}{k}_{foam}$

Where,

  ${\text{k}}_{material}=$ Thermal conductivity of material.

  ${\text{f}}_{\text{Al}}=$ Volume fraction of aluminum.

  ${\text{k}}_{\text{Al}}=$ Thermal conductivity of aluminum.

  $f_{foam}=$ Volume fraction of polystyrene foam.

  ${\text{k}}_{\text{foam}}=$ Thermal conductivity of polystyrene foam.

Relation of thermal conductivity, perpendicular to fiber is given as:

  $\frac{1}{k_{material}}=\frac{1}{f_{Al}{k}_{Al}}+\frac{1}{f_{foam}{k}_{foam}}$

Where,

  ${\text{k}}_{material}=$ Thermal conductivity of material.

  ${\text{f}}_{\text{Al}}=$ Volume fraction of aluminum.

  ${\text{k}}_{\text{Al}}=$ Thermal conductivity of aluminum.

  $f_{foam}=$ Volume fraction of polystyrene foam.

  ${\text{k}}_{\text{foam}}=$ Thermal conductivity of polystyrene foam.

Volume fraction of composite is defined as the ratio of volume of one component to sum of volume of all components.

The relationship of volume fraction with volume is stated as:

  $\begin{array}{l}f=\frac{V_1}{V_1+V_2}\\ f=\text{volume}\text{fraction}\\ V_1=\text{volume}\text{of}\text{first}\text{component}\\ V_2=\text{volume}\text{of}\text{second}\text{component}\end{array}$