The function of a compressor in a refrigerator is to compress the low-pressure, low-temperature refrigerant vapor coming from the evaporator (inside the refrigerator) and increase its pressure and temperature. This high-pressure, high-temperature refrigerant vapor is then sent to the condenser (located outside the refrigerator), where it releases heat to the surroundings and condenses back into a high-pressure liquid. This process allows the refrigerator to transfer heat from the inside of the fridge to the outside, keeping the interior cool.
If a centrifugal pump were to replace the compressor, it wouldn't be able to perform the same function effectively. A centrifugal pump is designed to move liquids and doesn't compress gases like a compressor does. Without proper compression, the refrigerant cannot undergo the necessary phase changes (vapor compression and condensation) to transfer heat effectively. As a result, the refrigerator would not be able to cool down its interior, rendering it ineffective as a refrigeration system.
If neither a compressor nor a centrifugal pump is used in the refrigerator, there would be no means of actively transferring heat from the inside to the outside. In the absence of any active cooling mechanism, the refrigerator would rely solely on passive cooling (heat exchange with the surrounding environment). However, this passive cooling is generally not sufficient to maintain low temperatures inside the fridge, and the interior would gradually warm up to ambient temperature. As a consequence, the refrigerator would no longer serve its primary purpose of preserving food and beverages, leading to spoilage and potential health risks.