Equation (1) is the fluid (water) energy balance equation, where α m f is the fluid/metal tube heat transfer coefficient, λ f is the fluid thermal conductivity, and R 1 is the tube internal radius.

Where constant parameters A, B, and C from the above set are listed in Table 1. Moreover, one should pay attention to the number of nodes or possible oscillations. RK methods require many more steps to obtain results, and the calculating time depends on accuracy or defined time step. The Gear BDF method usually requires much fewer steps than the RK45 method for almost the same calculating time. In our experience, all three types of ODE numerical methods (RKfixed, RK45, and Gear BDF) can be applied in simple models to model an adsorber with attention on their limitations. We focused on the comparison of results obtained when the set of heat and mass balance ODEs for an adsorber was solved using: (1) the Runge–Kutta fixed step size fourth-order method (RKfixed), (2) the Runge–Kutta–Fehlberg 4.5th-order method with a variable step size (RK45), and (3) the Gear Backward Differentiation Formulae numerical (Gear BDF) methods. Spatial discretization was performed with equally spaced axial nodes and the PDEs were reduced to a set of ordinary differential equations (ODEs). We developed a mathematical model of temperature and uptake changes in the adsorber/desorber comprising the set of heat and mass balance partial differential equations (PDEs), together with the initial and boundary conditions and solved it by the numerical method of lines (NMOL). An adsorption heat pump with a silica gel adsorbent and water adsorbate is discussed. The main aim of this paper was to find the correct method of calculating equations of heat and mass transfer for the adsorption process and to calculate it numerically in reasonable time and with proper accuracy.

Gear method fortran