Abstract
An analytical approach based on the generalized integral transform technique is presented, for the solution of laminar forced convection within the thermal entry region of ducts with arbitrarily shaped cross-sections. The analysis is illustrated through consideration of a right triangular duct subjected to constant wall temperature boundary condition. Critical comparisons are made with results available in the literature, from direct numerical approaches. Numerical results for dimensionless average temperature and Nusselt numbers are presented for different apex angles.
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- a,b :
-
sides of right triangular duct
- A c :
-
cross-sectional area of duct
- c p :
-
specific heat of fluid
- D h =4A c /p :
-
hydraulic diameter, with P the wet perimeter
- h(z):
-
heat transfer coefficient at duct wall
- k :
-
thermal conductivity
- Pe=ρc p ūD h /k :
-
Peclet number
- T(x, y, z):
-
temperature distribution
- T o :
-
inlet temperature
- T w :
-
prescribed wall temperature
- u(x, y); U(X, Y):
-
dimensional and dimensionless velocity profile
- ū :
-
average flow velocity
- x; X :
-
dimensional and dimensionless normal coordinate (Fig. 1)
- x 1(y); X 1(Y):
-
dimensional and dimensionless position at irregular boundary (Fig. 1)
- y; Y :
-
dimensional and dimensionless normal coordinate (Fig. 1)
- z; Z :
-
dimensional and dimensionless axial coordinate
- α :
-
side of right triangular duct in X direction (dimensionless)
- β :
-
side of right triangular duct in Y direction (dimensionless)
- ρ :
-
density of fluid
- θ(X, Y, Z):
-
dimensionless temperature distribution
- θ*:
-
apex angle of triangular duct (Fig. 1)
- θ**:
-
apex angle of triangular duct (Fig. 1)
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Aparecido, J.B., Cotta, R.M. Laminar thermally developing flow inside right-angularly triangular ducts. Applied Scientific Research 49, 355–368 (1992). https://doi.org/10.1007/BF00419981
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DOI: https://doi.org/10.1007/BF00419981