Liquids are often pumped in closed loops to transfer heat from a high temperature source to a low temperature sink. They operate at low Reynolds number when the diameter of the pipe is small, the fluid velocity is low, or when the working liquid is very viscous. Ionic liquids, though environmentally friendly, typically have viscosities much larger than water. An analytical study is made of the process for the purpose of determining what the important physical parameters of the system are that will enable the largest quantity of heat to be transferred for unit work expended. For this purpose, a loop is considered that has a pump that generates a certain pressure rise and two heat exchangers, one for heating the fluid and the other for cooling it. Laminar flow that is fully-developed hy-drodynamically and thermally is assumed. The analysis is based on constant fluid properties, and analytical expressions are obtained for the heat rate and the work input.

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