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I am a bit stuck trying to find out how heat is transferred through an evaporator in a refrigerator. I was using Newton's law of cooling before I realized there are more complexities in the equation as the refrigerant is in a mixture of saturated liquid and saturated gas in the evaporator.

Newton's Law of cooling (heat transfer from a solid surface to a fluid):

QL=UL*AL*LMTD

where

QL= heat transfer

UL= overal heat transfer coefficient

AL= external surface area of the evaporator

LMTD= log mean temp different over the evaporator tube. i.e. The average temperature difference between the solid surface and the fluid (air in this case) across the evaporator inlet and outlet.

My Question

Is Newton's Law of cooling applied to refrigerator evaporators and/or condensers with this equation, for a simplified calculation? Or would the results be so far from correct that calculations must always take into consideration the boiling and condensing of the refrigerant?