# SIMPLE METHODS OF ENGINEERING CALCULATIONS FOR SOLVING TRANSFER PROBLEMS OF MULTI – SUBSTANCES IN HORIZONTAL LAYER

## Authors

• Harijs Kalis Institute of Mathematics Latvian Academy of Sciences and University of Latvia (LV)
• Ilmārs Kangro Rēzekne Higher Educational Institution; Rezekne Academy of Technologies (LV)

## Keywords:

2-D heat transfer problem, finite – volume method, finite – difference scheme, diffusion of heat and moisture

## Abstract

We consider the simple algorithms in the modelling of the transfer problem of different substances (concentration, heat, moisture, and e. c.) in plate. The approximations of corresponding initial – boundary value problem of the system of the partial differential equations (PDE) is based on the finite volume method. This procedure allows one to reduce the 2-D transfer problem described by a PDE to initial value problem for a system of ordinary differential equations (ODE) of the first or second order. In the stationary case the exact finite – difference vector scheme is obtained.

## References

Crank, J. The mathematics of diffusion, Oxford, Clarendon Press, 1956, p. 303 – 325.

Kalis, H. Effective finite-difference scheme for solving some heat transfer problems with convection in multilayer media. International Journal of Heat and Mass Transfer 43 2000, p.4467-4474.

Kalis, H., Kangro, I. The methods of engineering calculation heat transfer process through one layer for numerical modelling. Proc. Of the Int. conf.: ‘’Integration problems of the Baltic sea region countries on their way to the European Union’’, March 2-3, 2000, Rēzekne, 2000, p.44-50.

Kalis, H., Kangro, I. Simulation of the heat transport problems with radiation in p late. In.: Proc. Of the Int. conf.: “Environment, technology, resources’’, Rezekne, June 19-21, 2001, p.273-279.

Kalis, H., Kangro, I. Simple algorithm’s for the calculation of heat transport problem in p late. In.:R. Čieg is (ed.) MATHEMATICAL MODELLING AND ANALYSIS, Vol.6 Nr.1, Vilnius, 2001, p.85-96.

Kalis, H., Kangro, I. Design procedure of distribution of temperatures in the three-layer environment. In.: Proc. Of the Int. conf.: ‘’Traditions and innovations in sustainable development of society’’, Rezekne, February 28-March 2, 2002, p.176-186.

Kalis, H., Kangro, I. Simple methods of engineering calculation for solving heat transfer problems. In.: R. Čiegis (ed.) MATHEMATICA L MODELLING AND ANA LYSIS, Vol.8 Nr.1, Vilnius, 2003, p.33-42.

Kalis, H., Kangro I. Promotion of accuracy engineering – technical calculations of heat transfer in two layer environment. In.: Proc. of the Int. conf.: ‘’Scientific Achievements for Wellbeing and Development of Society – Enabling Environment for Society Wellbeing’’, Rēzekne, March 4-5, 2004, Rēzeknes Augstskola, p.91-98.

Васильев П. П. Безопасность жизнедеятельности. М.: ЮНИТИ, 2003, с.120-129.

Семенченко Б.А. Физическая метеорология. М.: Аспект Пресс, 2002, с.156-196.

2005-06-18

## Section

IT and Mathematical Methods in Environmental Sciences

## How to Cite

[1]
H. Kalis and I. Kangro, “SIMPLE METHODS OF ENGINEERING CALCULATIONS FOR SOLVING TRANSFER PROBLEMS OF MULTI – SUBSTANCES IN HORIZONTAL LAYER”, ETR, vol. 1, pp. 40–47, Jun. 2005, doi: 10.17770/etr2005vol1.2132.