### Solusi Persamaan keseimbangan Massa Reaktor Menggunakan Metode Pemisahan Variabel

#### Abstract

Mass balance of reactor equation express the change of mass concentration of substances in and out of the closed system. This equation has inhomogeneous boundary conditions, that is the conditions at the time of its entry to the reactor and the conditions under which the substance out of the reactor. In this study, the mass concentration of substances produced after the reaction in the reactor is zero. In the inhomogeneous boundary conditions, using the method of separation of variables, there are obstacles to complete the equation. So we need to first transformation. Transformation is done with the aim to change the conditions which originally inhomogeneous boundary into a homogeneous boundary condition, so the method of separation of variables can be used to solve partial differential equations that have a homogeneous boundary conditions. The results obtained by the analysis, the faster a substance that spreads to the reactor, the less amount of mass concentration of substances that undergo a change; the greater the mass coefficient of substances that react in the reactor, the more the number of mass concentration of substances that are subject to change

#### Keywords

homogeneous boundary condition; inhomogeneous boundary condition; method of separation of variabel

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#### References

B. Barnes and G. R. Fulford, Mathematical Modelling with Case Studies A Differential Equation Using Maple and Matlab Second Edition, London: CRC Press, 2009.

W. A. Strauss, Partial Differential Equation An Introduction, Singapore: John Wiley & Sons.Inc, 1992.

J. Caldwell, Mathematical Modelling Case Studies and Projects, New York: Kluwer Academic Publishers, 2004.

W. E. Boyce and R. C. DiPrima, Elementarry Differential Equation and Boundary Value Proplem Ninth Edition, USA: John Wiley & Sons, Inc, 2009.

M. A. Pinsky, Partial Differential Equation and Boundary-Value Problem With Aplication Third Edition, Rhode Island: Waveland Press, 2003.

R. P. Agarwal and D. O'Regan, Ordinary and Partial Differential Equation With Special Function, Fourier Series and Boundary Value Problems, New York: Spinger Scince + Business Media, 2009.

DOI: https://doi.org/10.18860/ca.v4i1.3173

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