# Temperature Estimation on Boundary of Two-Dimensional Heat Conduction Problem by a Finite Volume Method

## Authors

• ภาสกร เวสสะโกศล ภาควิชาวิศวกรรมเครื่องกล คณะวิศวกรรมศาสตร์ มหาวิทยาลัยสงขลานครินทร์
• จารุวัตร เจริญสุข ภาควิชาวิศวกรรมเครื่องกล คณะวิศวกรรมศาสตร์ สถาบันเทคโนโลยีพระจอมเกล้าเจ้าคุณทหารลาดกระบัง

## Keywords:

Inverse heat conduction problem (IHCP), Finite volume method (FVM), Cubic spline, numerical method, two-dimensional heat conduction

## Abstract

This paper proposes a finite volume method for finding the unknown temperature on boundary of two-dimensional solid under heat conduction at steady state. A system of algebraic equations for unknown temperature and heat rate at nodal points are formulated and solved by the finite volume method. The inverse heat conduction problem is carried out to determine the unknown temperature on the boundary by employing the known temperature inside the domain. The cubic-spline interpolation is used to improve the accuracy of the solution on the boundary of domain. The unit square plate of isotropic homogeneous material is the domain of the problem. The functions of temperature are specified on the all boundaries of square plate. The result of this study can be summarized that the mesh size of 16 points in both x and y coordinates gives the maximum errors 0.306 oC and 0.024 oC when using finite volume method without and with cubic-spline technique, respectively, at position y = 0.625m.

## References

Dennis, B.H., Dulikravich, G.S., and Yoshimura, S., 2004, “A finite element formulation for the determination of unknown boundary conditions for three-dimensional steady thermoelastic problems”, Journal of Heat Transfer, 126, pp.110-118.

Ozisik, M.N. and Orlande, H.R.B. (2000) Inverse heat transfer fundamentals and applications. Taylor & Francis, New York.

Alifanov, O.M., 1994, Inverse Heat Transfer Problems, Springer.

Kanjanakijkasem, W., 2015, “A finite element method for predicting of unknown boundary conditions in two-dimensional steady-state heat conduction problems”, International Journal of Heat and Mass Transfer, 88, pp.891-901.

Kanjanakijkasem, W., 2016, “Estimation of spatially varying thermal contact resistance from finite element solutions of boundary inverse heat conduction problems split along material interface”, Applied Thermal Engineering, 106, pp.731-742.

Kanjanakijkasem, W., 2014, Numerical methods, Chulalongkorn University, 1st edition, Bangkok.

2018-06-29

## How to Cite

[1]
เวสสะโกศล ภ. and เจริญสุข จ., “Temperature Estimation on Boundary of Two-Dimensional Heat Conduction Problem by a Finite Volume Method”, Eng. &amp; Technol. Horiz., vol. 35, no. 2, pp. 14–21, Jun. 2018.

## Section

Research Articles