Abstract
This research obtains a mathematical formulation to determine the heat transfer in a transient state, in a calorimeter cell, considering an adiabatic system. The development of the cell was established and the mathematical model was transiently solved, which approximated the physical phenomenon under the cell operation. A numerical method for complex geometries was used to validate performance. The results obtained in the transient heat transfer in a cylinder under boundary and initial conditions were compared using an analytical solution and numerical analysis employing the finite-element method with commercial software. The study from the temperature distribution can afford, selection between a cylindrical and spherical geometry, design criteria that are generated by changing parameters such as dimension, temperature, and working fluids to develop an adiabatic calorimeter to measure the heat capacity in fluids. We show the mathematical solution with its initial and boundary conditions as well as a comparison with a numerical solution for a cylindrical cell with a maximum error from 0.075% in the temperature value, along with a theoretical and numerical analysis for a temperature difference of 1 °C.