Summary
This paper deals with laminar, steady heat transfer in flat gaps formed by two wide parallel plates to power law fluids with temperature dependent rheological properties. Basic equations governing the problem to be discussed here are derived including the effects of viscous dissipation but neglecting the internal heat generation. The derived equations of motion, energy and continuity (the last in integral form) have been solved numerically by means of Dufort-Frankel scheme for various thermal wall conditions (constant and variable wall temperature as well as constant and variable wall heat flux). The results of numerical computations are presented in form of graphs illustrating the changes in temperature and velocity profiles as well as in local and mean Nusselt numbers and pressure drops with increasing distance from the inlet cross section. A special attention has been paid to the effects of viscous dissipation and temperature dependent rheological fluid properties on the changes mentioned above. The present work is intended to be an extension of the classical Graetz-Nusselt problem on non-Newtonian power law fluids with temperature dependent rheological properties flowing through a narrow gap formed by two wide parallel plates.
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References
Porter, J. E.: Heat transfer at low Reynolds number (Highly viscous liquids in laminar flow) — Industrial Research Fellow Report. Trans. Instn. Chem. Engrs.49, 1 (1971).
Forrest, G., Wilkinson, W. L.: Laminar heat transfer to power law fluids in tubes with constant wall temperature. Trans. Instn. Chem. Engrs.51, 331 (1973).
Forrest, G., Wilkinson, W. L.: Laminar heat transfer to power law fluids in tubes with constant wall heat flux. Trans. Instn. Chem. Engrs.52, 10 (1974).
Popovska, F., Wilkinson, W. L.: Laminar heat transfer to Newtonian and non-Newtonian fluids in tubes. Chem. Eng. Sci.32, 1155 (1977).
Nowak, Z., Gryglaszewski, P., Stacharska-Targosz, J.: Numerical study of laminar heat transfer to power law fluids in tubes with variable wall temperature. Acta Mechanica40, 237 (1981).
Nowak, Z., Gryglaszewski, P., Stacharska-Targosz, J.: The effects of viscous dissipation on laminar heat transfer to power law fluids in tubes. Wärme- und Stoffübertragung14, 81 (1980).
Nowak, Z., Gryglaszewski, P., Stacharska-Targosz, J.: Pressure drop in non-isothermal laminar flow of power law fluids in tubes with various thermal conditions. Wärme- und Stoffübertragung14, 281 (1980).
Nowak, Z., Gryglaszewski, P., Stacharska-Targosz, J.: Laminar heat transfer to power law fluids in tubes with variable wall heat flux. Acta Mechanica41, 129 (1981).
Skelland, A. H. P.: Non-Newtonian flow and heat transfer. New York: J. Wiley 1967.
Coj, P. W.: Methods of solutions of selected heat transfer problems (in Russian). Moscow: Energia 1971.
Dang Vi-Duong: Heat transfer of low peclet number power law fluid between parallel plates with heat generation. Can. J. Chem. Engn.58, 401 (1980).
Nowak, Z., Rup, K.: Die nichtisotherme, laminare, stationäre Spaltströmung einer Newtonschen Flüssigkeit. Wärme- und Stoffübertragung13, 85 (1980).
Mizushina, T., Kuriwaki, Y.: Mem. Fac. Engn., Kyoto Univ.30, 511 (1968).
Potter, D.: Computational Physics. New York: J. Wiley 1973.
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Nowak, Z., Gryglaszewski, P. & Stacharska-Targosz, J. Laminar heat transfer to power law fluids in flat gaps with various thermal wall conditions. Acta Mechanica 44, 223–236 (1982). https://doi.org/10.1007/BF01303339
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DOI: https://doi.org/10.1007/BF01303339