# FINITE ELEMENT METHOD FOR HEAT TRANSFER PHENOMENON ON A CLOSED RECTANGULAR PLATE

• Collins O. Akeremale Universiti Teknologi Malaysia, Federal University Lafia
• Olusegun A Olaiju Universiti Teknologi Malaysia, Federal Polytechnics Ilaro
• Yeak Su Hoe Universiti Teknologi Malaysia
Keywords: finite element method; steady-state; squared plate; analytical method; closed rectangle

### Abstract

In the diagnosis and control of various thermal systems, the philosophy of heat fluxes, and temperatures are very crucial. Temperature as an integral property of any thermal system is understood and also, has well-developed measurement approaches. Though finite difference (FD) had been used to ascertain the distribution of temperature, however, this current article investigates the impact of finite element method (FEM) on temperature distribution in a square plate geometry to compare with finite difference approach. Most times, in industries, cold and hot fluids run through rectangular channels, even in many technical types of equipment. Hence, the distribution of temperature of the plate with different boundary conditions is studied. In this work, let’s develop a finite element method (code) for the solution of a closed squared aluminum plate in a two-dimensional (2D) mixed boundary heat transfer problem at different boundary conditions. To analyze the heat conduction problems, let’s solve the two smooth mixed boundary heat conduction problems using the finite element method and compare the temperature distribution of the plate obtained using the finite difference to that of the plate obtained using the finite element method. The temperature distribution of heat conduction in the 2D heated plate using a finite element method was used to justify the effectiveness of the heat conduction compared with the analytical and finite difference methods

### Author Biographies

Collins O. Akeremale, Universiti Teknologi Malaysia, Federal University Lafia

Department of Mathematical Sciences

Department of Mathematical Sciences

Olusegun A Olaiju, Universiti Teknologi Malaysia, Federal Polytechnics Ilaro

Department of Mathematical Sciences

Department of Mathematics and Statistics

Yeak Su Hoe, Universiti Teknologi Malaysia

Department of Mathematical Sciences

### References

Deb Nath, S. K., Peyada, N. K. (2015). Numerical Study Of The Heat Transfer Phenomenon Of A Rectangular Plate Including Void, Notch Using Finite Difference Technique. International Journal of Applied Mechanics and Engineering, 20 (4), 733–756. doi: https://doi.org/10.1515/ijame-2015-0048

Gaaloul, N., Daouas, N. (2018). An extended approach of a Kalman smoothing technique applied to a transient nonlinear two-dimensional inverse heat conduction problem. International Journal of Thermal Sciences, 134, 224–241. doi: https://doi.org/10.1016/j.ijthermalsci.2018.08.021

Beck, J. V. (1970). Nonlinear estimation applied to the nonlinear inverse heat conduction problem. International Journal of Heat and Mass Transfer, 13 (4), 703–716. doi: https://doi.org/10.1016/0017-9310(70)90044-x

Hensel, E., Hills, R. G. (1986). An Initial Value Approach to the Inverse Heat Conduction Problem. Journal of Heat Transfer, 108 (2), 248–256. doi: https://doi.org/10.1115/1.3246912

Millan, D. N. P. (2000). Resolution of a three-dimensional unsteady inverse problem by sequential method using parameter reduction and infrared thermography measurements. Numerical Heat Transfer, Part A: Applications, 37 (6), 587–611. doi: https://doi.org/10.1080/104077800274109

Lin, S.-M., Chen, C.-K., Yang, Y.-T. (2004). A modified sequential approach for solving inverse heat conduction problems. International Journal of Heat and Mass Transfer, 47 (12-13), 2669–2680. doi: https://doi.org/10.1016/j.ijheatmasstransfer.2003.11.027

Daouas, N., Radhouani, M.-S. (2004). A new approach of the kalman filter using future temperature measurements for nonlinear inverse heat conduction problems. Numerical Heat Transfer, Part B: Fundamentals, 45 (6), 565–585. doi: https://doi.org/10.1080/10407790490430598

Wang, H.-M., Chen, T.-C., Tuan, P.-C., Den, S.-G. (2005). Adaptive-Weighting Input-Estimation Approach to Nonlinear Inverse Heat-Conduction Problems. Journal of Thermophysics and Heat Transfer, 19 (2), 209–216. doi: https://doi.org/10.2514/1.8720

Daouas, N., Radhouani, M.-S. (2007). Experimental validation of an extended Kalman smoothing technique for solving nonlinear inverse heat conduction problems. Inverse Problems in Science and Engineering, 15 (7), 765–782. doi: https://doi.org/10.1080/17415970701200526

Massard, H., Orlande, H. R. B., Fudym, O. (2012). Estimation of position-dependent transient heat source with the Kalman filter. Inverse Problems in Science and Engineering, 20 (7), 1079–1099. doi: https://doi.org/10.1080/17415977.2012.712520

Wan, S., Wang, G., Chen, H., Wang, K. (2017). Application of unscented Rauch-Tung-Striebel smoother to nonlinear inverse heat conduction problems. International Journal of Thermal Sciences, 112, 408–420. doi: https://doi.org/10.1016/j.ijthermalsci.2016.11.004

Wang, G., Wan, S., Chen, H., Lv, C., Zhang, D. (2017). A double decentralized fuzzy inference method for estimating the time and space-dependent thermal boundary condition. International Journal of Heat and Mass Transfer, 109, 302–311. doi: https://doi.org/10.1016/j.ijheatmasstransfer.2017.02.001

Wang, X., Wang, G., Chen, H., Zhang, L. (2017). Real-time temperature field reconstruction of boiler drum based on fuzzy adaptive Kalman filter and order reduction. International Journal of Thermal Sciences, 113, 145–153. doi: https://doi.org/10.1016/j.ijthermalsci.2016.11.017

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