An exact solution to steady heat conduction in a two-dimensional slab on a one-dimensional fin: application to frosted heat exchangers

Analytical studies for the thermal performance of a heat exchanger dealt with frost formation phenomena too simplistically by either proposing models without robust validations or using correlations for heat transfer coefficients derived for a specific heat exchanger experimentally.

“However, analytical studies for the thermal performance of a heat exchanger [20-23] dealt with the frost formation phenomena too simplistically by either proposing models without robust validations or using correlations for heat transfer coefficients that were derived for a specific heat exchanger experimentally.”

As manifested by the data (see Xia and Jacobi, 2004), a higher decrease rate in heat transfer rate was almost always associated with a higher increase rate in pressure drop.

“Since as manifested by the data (see Xia and Jacobi, 2004), a higher decrease rate in heat transfer rate was almost always associated with a higher increase rate in pressure drop”

Xia and Jacobi [10] solved the heat conduction equation for a composite medium consisting of a two-dimensional frost layer on a one-dimensional fin.

“In order to avoid the error associated with neglecting conduction heat transfer in the frost layer along the direction of the fin length, Xia and Jacobi [10] solved the heat conduction equation for a composite medium consisting of a two-dimensional frost layer on a onedimensional fin.”

The effects of neglecting temperature variations along the frost surface can be profound.

“However, such a model neglects temperature variations along the frost surface, and the effects of such a simplification can be profound (see Xia and Jacobi [10]).”

Xia and Jacobi [10] provided a simplified, one-term analytical solution for the fin efficiency, valid over a wide range of conditions, including most frost-coated metallic fins.

“They provided a simplified, one-term analytical solution for the fin efficiency, valid over a wide range of conditions, including most frost-coated metallic fins.”

An effective heat transfer coefficient is needed in Xia and Jacobi's model, and such an approach is justified if the sensible heat ratio is constant over the surface.

“An effective heat transfer coefficient is also needed in their model, and such an approach is justified if the sensible heat ratio is constant over the surface (this restriction is discussed later in detail).”