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.

**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 L_{1}, L_{2}, etc and having thermal conductivities
k_{l}, k_{2}, 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 r_{1}, r_{2} and r_{2}
and r_{3}, thermal conductivities k_{l} and k_{2} the
convective heat transfer coefficients at the inside andoutside surfaces h_{1}
and h_{2} as shown in the figure. Assuming radial conduction under
steady state

conditions we have: Fig 1.5

R_{1}
=1/ h_{1}A_{1} =1/
2 _{1} pLh_{1}

R_{2}
=ln (r_{2}
/ r_{1} )2 pLk_{1}

R_{3}
=ln (r_{3}
/ r_{2} )2 pLk_{2}

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Mechanical : Heat and Mass Transfer : Conduction : One Dimensional Steady State Heat conduction Composite Systems |

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