Temperature Distribution in Flux Channels with Discrete Contact Boundary Conditions

ABSTRACT

An analytical approach for the thermal behavior of two-dimensional rectangular flux channels with arbitrary boundary conditions on the source plane is presented. The boundary condition along the source plane can be a combination of the first kind boundary condition (Dirichlet or prescribed temperature) and the second kind boundary condition (Neumann or prescribed heat flux). To model the boundary conditions along the source plane, the method of least squares is used. The proposed solution is in the form of Fourier series expansion and can be applied to both symmetrical and non-symmetrical channels. This method is more general than other approaches and there is no need to use equivalent heat flux distributions to model isothermal heat sources. The general approach for obtaining the multidimensional temperature profile in flux channels and the advantages of the least-square method is discussed. The proposed solution can be used to calculate the temperature at any specified point in the flux channel. Two case studies are presented. The first case study is a flux channel with five discretely specified contact temperatures along the source plane. The second case study has both of the first kind and second kind boundary conditions on the source plane. The analytical results for both systems are compared with finite element method using a commercial software package. It is shown that the proposed approach can precisely model the temperature profile over the flux channel.

Additional information

Notes on contributors

Masood Razavi

Masood (Max) Razavi received his Ph.D. degree in mechanical engineering from Memorial University of Newfoundland, St. John’s, NL, Canada, in 2016. He received different awards for excellence in graduate studies and graduated with GPA of 97/100. Currently, he is working in a design team for a multi-billion transit project in Canada. He is a registered professional engineer (P.Eng.), designated Project Management Professional (PMP), and certified for Leadership in Energy & Environmental Design (LEED) from the U.S Green Building Council.

Yuri Muzychka

Yuri Muzychka is a Professor of Mechanical Engineering at Memorial University of Newfoundland, Canada. His research focus is on the development of robust models for characterizing transport phenomena using fundamental theory. He has published over 160 papers in refereed journals and conference proceedings in these areas. He is a registered professional engineer and a member of the American Institute for Aeronautics and Astronautics (AIAA) and a Fellow of the American Society of Mechanical Engineers (ASME).

Serpil Kocabiyik

Serpil Kocabiyik is a Professor of Applied Mathematics at Memorial University of Newfoundland, Canada. She obtained her doctorate in Applied Mathematics from the University of Western Ontario in 1987. Her research is an interdisciplinary blend of classical applied mathematics, fluid mechanics, heat transfer, and computational science. Currently, she serves on the Editorial Board of the Canadian Journal of Physics.