The effect of viscous dissipation and rarefaction on rectangular microchannel convective heat transfer |
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| Authors: | J van Rij T Ameel T Harman |
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| Affiliation: | 1. Hubei Key Laboratory of Theory and Application of Advanced Materials Mechanics, Wuhan University of Technology, Wuhan 430070, China;2. Department of Mechanical Engineering, The University of Hong Kong, Pokfulam Road, Hong Kong;1. Department of Mechanical Engineering, Marvdasht Branch, Islamic Azad University, Marvdasht, Iran;2. Department of Mechanical Engineering, Najafabad Branch, Islamic Azad University, Najafabad, Iran;3. Public Authority for Applied Education and Training (PAAET), College of Technological Studies (CTS), Automotive and Marine Engineering Department, Shuwaikh 70654, Kuwait;4. School of Chemical Engineering and Technology, Xi''an Jiaotong University, Xi''an, China;5. Center for Advanced Technologies, Ferdowsi University of Mashhad, Mashhad, Iran;6. Fluid Mechanics, Thermal Engineering and Multiphase Flow Research Lab. (FUTURE), Department of Mechanical Engineering, Faculty of Engineering, King Mongkut''s University of Technology Thonburi, Bangmod, Bangkok 10140, Thailand;7. The Academy of Science, The Royal Society of Thailand, Sanam Suea Pa, Dusit, Bangkok 10300, Thailand;8. Division of Computational Mechatronics, Institute for Computational Science, Ton Duc Thang University, Ho Chi Minh City, Vietnam;9. Faculty of Electrical & Electronics Engineering, Ton Duc Thang University, Ho Chi Minh City, Vietnam;1. Divison of Computational Mathematics and Engineering, Institute for Computational Science, Ton Duc Thang University, Ho Chi Minh City, Viet Nam;2. Faculty of Civil Engineering, Ton Duc Thang University, Ho Chi Minh City, Viet Nam;3. Faculty of Transportation Engineering, University of Technology, Ho Chi Minh City, VNU-HCM, Viet Nam;4. Faculty of Mechanical Engineering, Industrial University of Ho Chi Minh City, Viet Nam |
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| Abstract: | The effect of viscous dissipation and rarefaction on rectangular microchannel convective heat transfer rates, as given by the Nusselt number, is numerically evaluated subject to constant wall heat flux (H2) and constant wall temperature (T) thermal boundary conditions. Numerical results are obtained using a continuum based, three-dimensional, compressible, unsteady computational fluid dynamics algorithm with slip velocity and temperature jump boundary conditions applied to the momentum and energy equations, respectively. For the limiting case of parallel plate channels, analytic solutions for the thermally and hydrodynamically fully developed momentum and energy equations are derived, subject to both first- and second-order slip velocity and temperature jump boundary conditions, from which analytic Nusselt number solutions are then obtained. Excellent agreement between the analytical and numerical results verifies the accuracy of the numerical algorithm, which is then employed to obtain three-dimensional rectangular channel and thermally/hydrodynamically developing Nusselt numbers. Nusselt number data are presented as functions of Knudsen number, Brinkman number, Peclet number, momentum and thermal accommodation coefficients, and aspect ratio. Rarefaction and viscous dissipation effects are shown to significantly affect the convective heat transfer rate in the slip flow regime. |
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