A regenerative heat exchanger (see Section 8.2) has a matrix...

A regenerative heat exchanger (see Section 8.2) has a matrix in the form of parallel plates of plastic $6 \mathrm{~mm}$ thick, at a spacing of $b \mathrm{~mm}$. If the convective heat transfer coefficient for the fluid flow is ap- proximately $4 k / b$, where $k$ is the gas con- ductivity, estimate the overall heat transfer coefficient for heat transfer from the fluid into the plates. Tabulate your results for $b=$ $1,2, \ldots, 10 \mathrm{~mm}$. Take $k=0.15 \mathrm{~W} / \mathrm{m} \mathrm{K}$ for the plastic and $0.10 \mathrm{~W} / \mathrm{m} \mathrm{K}$ for the fluid.

A regenerative heat exchanger (see Section 8.2) has a matrix in the form of parallel plates of plastic $6 \mathrm{~mm}$ thick, at a
spacing of $b \mathrm{~mm}$. If the convective heat
transfer coefficient for the fluid flow is ap-
proximately $4 k / b$, where $k$ is the gas con-
ductivity, estimate the overall heat transfer
coefficient for heat transfer from the fluid
into the plates. Tabulate your results for $b=$
$1,2, \ldots, 10 \mathrm{~mm}$. Take $k=0.15 \mathrm{~W} / \mathrm{m} \mathrm{K}$ for
the plastic and $0.10 \mathrm{~W} / \mathrm{m} \mathrm{K}$ for the fluid.

Key Concepts

Thermal Conduction Through Solids

Thermal conduction involves the transfer of heat through a solid medium, governed by the material's thermal conductivity and the physical thickness of the medium. The conduction resistance, which is inversely proportional to the conductivity and directly proportional to the thickness, plays a key role in systems where heat must pass through a barrier or matrix before reaching another phase or component.

Thermal Resistance Network

In composite heat transfer systems, thermal resistance network modeling is used to simplify complex heat transfer processes by representing them as a series or parallel arrangement of individual resistances. This approach allows for the calculation of an overall heat transfer coefficient by summing the individual resistances (such as those due to convection and conduction) and then taking the reciprocal to determine the system’s overall performance.

Overall Heat Transfer Coefficient

This coefficient represents the net ability of a system to transfer heat between fluids and solids. It is determined by combining the resistances from different heat transfer processes, such as convection and conduction. The overall coefficient is essentially the inverse of the total thermal resistance of the system, meaning that lower resistance results in a higher coefficient and thus more effective heat transfer.

Convective Heat Transfer Coefficient

This coefficient quantifies the efficiency of heat transfer between a moving fluid and a surface. It captures factors such as the fluid's thermal properties, velocity, and the characteristic geometry of the system. Its value is crucial in determining the resistance to heat transfer at the fluid-solid interface, often being influenced by geometric parameters like spacing or plate dimensions.

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