One Dimensional Steady State Heat conduction Composite Systems

ONE DIMENSIONAL STEADY STATE HEATCONDUCTION COMPOSITE SYSTEMS:

Composite Surfaces

There are many practical situations where different materials are placed m layers to form composite surfaces, such as the wall of a building, cylindrical pipes or spherical shells having different layers of insulation. Composite surfaces may involve any number of series and parallel thermal circuits.

Heat Transfer Rate through a Composite Wall

Let us consider a general case of a composite wall as shown m Fig. 1.5 The different materials of thicknesses L₁, L₂, etc and having thermal conductivities k_l, k₂, etc. On one side of

the composite wall, there is a fluid A at temperature T_A and on the other side of the wall there is a fluid B at temperature T_B. The convective heat transfer coefficients on the two sides of the wall are h_A and h_B respectively. The system is analogous to a series of resistances as shown in the figure.

Fig 1.4   Heat transfer through a composite wall

The Equivalent Thermal Conductivity

The process of heat transfer through compos lie and plane walls can be more conveniently compared by introducing the concept of 'equivalent thermal conductivity', k_eq. It is defined as:

And,  its  value  depends  on  the  thermal  and  physical  properties  and  the  thickness  of  each constituent of the composite structure.

An Expression for the Heat Transfer Rate through a Composite Cylindrical System

Let us consider a composite cylindrical system consisting of two coaxial cylinders, radii r₁, r₂ and r₂ and r₃, thermal conductivities k_l and k₂ the convective heat transfer coefficients at the inside andoutside surfaces h₁ and h₂ as shown in the figure. Assuming radial conduction under steady state

conditions we have: Fig 1.5

R₁ =1/ h₁A₁   =1/ 2  ₁ pLh₁

R₂ =ln (r₂ / r₁ )2 pLk₁

R₃ =ln (r₃ / r₂ )2 pLk₂