Abstract
The similarity solutions for the governing ordinary differential equations of the boundary layer corresponding to a stretching surface have been reported. Power law velocity and temperature distribution were assumed for velocity exponent 3≥m≥−0.41176, −1.1≥m≥−3, and for temperature exponent 3≥n≥−3. Solutions have been found forn=0 and allm where heat transferred from the stretching surface to the ambient. The direction and amount of heat flow were found to be dependent on the magnitude ofn andm for the same Prandtl number. Nusselt number increases with increasingm andPr for uniform and variable surface temperature however, for uniform surface heat flux it decreases with increasingm for constantPr.
Zusammenfassung
Es werden die Ähnlichkeitslösungen für die bestimmenden gewöhnlichen Grenzschichtdifferentialgleichungen bezüglich einer verstreckten Oberfläche mitgeteilt. Für Geschwindigkeits-und Temperaturverteilungen gelten Potenzansätze mit den Exponenten 3≥m≥−0,41176 und −1,1≥m≥−3 für das Geschwindigkeitsprofil und 3≥n≥−3 für das Temperaturprofil. Fürn=0 und allem ließen sich Lösungen finden; dabei floß Wärme von der verstreckten Fläche an die Umgebung. Es zeigte sich, daß Höhe und Richtung des Wärmestroms bei gleicher Prandtl-Zahl von den Werten fürn undm abhängen. Die Nußelt-Zahl wächst mit steigendemm undPr bei gleichförmiger und veränderlicher Oberflächentemperatur; sie fällt bei gleichförmigem Wärmefluß, wennm bei konstantemPr zunimmt.
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Abbreviations
- C :
-
constant
- f :
-
dimensionless stream function
- G :
-
dimensionless temperature [=(T −T ∞)/(T w −T ∞)] for uniform and variable temperature;\(\left[ { = k\left( {T - T_\infty } \right)/xq_w \sqrt {\left( {2/\left( {1 + m} \right)} \right)} } \right]\) for uniform heat flux
- k :
-
thermal conductivity
- m :
-
velocity exponent parameter
- n :
-
temperature exponent parameter
- Nu :
-
Nusselt number [=h x/k]
- Pr :
-
Prandtl number [=ν/α]
- Re :
-
Reynolds number [=U 0 x (m+1)/ν]
- T :
-
temperature
- u :
-
velocity component inx-direction
- U 0 :
-
constant
- v :
-
velocity component iny-direction
- x :
-
coordinate in direction of surface motion
- y :
-
coordinate in direction normal to surface motion
- α :
-
thermal diffusivity
- η :
-
dimensionless similarity variable\(\left[ { = y\sqrt {\left( {\left( {m + 1} \right)/2} \right)} \sqrt {\left( {U_0 x^{m - 1} /v} \right)} } \right]\)
- ν :
-
kinematic viscosity
- w :
-
condition at the surface
- ∞:
-
condition at ambient medium
- ′:
-
differentiation with respect toη
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Ali, M.E. Heat transfer characteristics of a continuous stretching surface. Warme - Und Stoffubertragung 29, 227–234 (1994). https://doi.org/10.1007/BF01539754
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DOI: https://doi.org/10.1007/BF01539754