Abstract
Laminar flow of non-Newtonian power-law fluids with temperature dependent rheological properties as well as temperature dependent thermal fluid conductivity has been considered. Three different kinds of thermal boundary conditions have been taken into account. The basic equation of energy has been solved by means of an approximate analytical method of optimal linearization. A simple formula for calculating the pressure drop valid for all the cases considered has been derived. Some selected results are presented.
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Abbreviations
- \(Y = r/R\) :
-
dimensionless radial coordinate
- \(\theta = \left( {T - {T_i}} \right)/{T_i}\) :
-
dimensionless temperature
- \(B{i_e} = {\alpha _e}R/{\lambda _e}\) :
-
Biot number
- \(\mathop {B{i_e}}\limits^ \wedge = \frac{{2n}}{{3n + 1}}B{i_e},\mathop {B{i_e}}\limits^ \wedge = \left( {1 + {\alpha _1}} \right)\mathop {B{i_e}}\limits^ \wedge\) :
-
modified Biot numbers
- \(Br = {\left( {{\tau _w}/{K_i}} \right)^{\left( {n + 1} \right)/n}} \cdot \left( {{K_i}{R^2}} \right)/\left( {{\lambda _i}{T_i}} \right)\) :
-
Brinkman number
- \(\mathop {Br}\limits^ \wedge = \frac{{2n}}{{3n + 1}}\sqrt {Br\gamma } ,\mathop {Br}\limits^{\hat \wedge } = \mathop {Br}\limits^ \wedge /\sqrt {1 - \alpha /\gamma }\) :
-
modified Brinkman numbers
- \({\operatorname{Re} _i} = \left[ {ev_m^{2 - n}{{\left( {2R} \right)}^n}} \right]/\left[ {{8^{n - 1}}{{\left( {\frac{{3n + 1}}{{4n}}} \right)}^n}{K_i}} \right]\) :
-
modified Reynolds number
- \({\alpha _1} = \frac{{\alpha /\gamma }}{{1 - \alpha /\gamma }}\) :
-
constant specifying the dependence of thermal fluid conductivity on temperature
References
Nowak Z, Gryglaszewski P, Stacharska-Targosz J (1980) ul. Warszawska 24 Wärme-und Stoffübertragung 14: 281
Nowak Z, Gryglaszewski P, Stacharska-Targosz J (1982) Acta Mechanica 45: 205
Nowak Z, Gryglaszewski P, Stacharska-Targosz J (1983) Proc 11th PCCE Meeting 2: 189
Nowak Z, Stacharska-Targosz J (1984) Mena B, GarciaRejón A, Rangel-Nafaile C (eds) Advances in Rheology (Proc IXth Intern Congr Rheology) Universidad Nacional Autonoma de México, Vol 2, p 127
Nowak Z, Stacharska-Targosz J (1985) ZAMM 66: T252
Vujanovic B (1973) Int J Heat Mass Transfer 16: 315
Sokolov J (1957) Ukrain J Mathematics 1: 9
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© 1988 Springer-Verlag Berlin Heidelberg
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Stacharska-Targosz, J., Gryglaszewski, P. (1988). Heat transfer in laminar flow of non-Newtonian fluids. In: Giesekus, H., Hibberd, M.F. (eds) Progress and Trends in Rheology II. Steinkopff, Heidelberg. https://doi.org/10.1007/978-3-642-49337-9_43
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DOI: https://doi.org/10.1007/978-3-642-49337-9_43
Publisher Name: Steinkopff, Heidelberg
Print ISBN: 978-3-642-49339-3
Online ISBN: 978-3-642-49337-9
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