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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.

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This paper focuses on the numerical modeling of the effect of the height of a combustion chamber on the development of a reference calorimeter whose objective is to measure the calorific value of natural gas. The impacts of temperature, velocity, and mass fraction on the exhaust gases were evaluated by varying the height of the combustion chamber. The eddy dissipation concept (EDC) approach was used to model combustion with two different chemical kinetic mechanisms: one with three steps, called the three-step mechanism defined by default in the software used, and second skeletal model, which consists of 41 steps, through the ChemKin-import file with 16 species. The main result of this study is the selection of a combustion chamber height for the reference calorimeter that produces the best performance in the combustion process, which is 70 mm, as well as the main differences in using a three-step mechanism and a skeletal model to simulate an oxy-fuel combustion reaction.

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