An efficient numerical method for modeling silver powder heat exchanger in dilution refrigerator

Dilution refrigerator provides continuous ultralow temperature environments as low as 10 mK. It has been widely used in a variety of important applications such as quantum computations. The silver powder heat exchanger in a dilution refrigerator plays a crucial role in realizing ultralow temperatures on the order of 10 mK by precooling the circulation of helium mixtures. To study the silver powder heat exchanger quantitatively, we have proposed an efficient numerical solution method for its thermodynamic model. This method utilizes constraint conditions cleverly to convert the initial value problem of differential equations into a boundary value problem, allowing us to solve the control equations using the existing ODE function quickly. Furthermore, we demonstrate the application of this method in the evaluation and design of silver powder heat exchanger. The research results of this paper have certain significance for the development of dilution refrigerator.