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.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Explore related subjects
Discover the latest articles, news and stories from top researchers in related subjects.Abbreviations
- 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)
References
Shah, R.K. and London, A.L., Laminar flow forced convection in ducts. Adv. Heat Transfer, Suppl. 1 (1978).
Shah, R.K. and Bhatti, M.S., Laminar convective heat transfer in ducts. In: S. Kakaç, R.K. Shah and W. Aung (eds), Handbook of Single-Phase Convective Heat Transfer, Chap. 3. John Wiley (1987) pp. 3.1–3.137.
Shah, R.K., Research needs in low Reynolds number flow heat exchangers. In: S. Kakaç, R.K. Shah and A.E. Bergles (eds), Low Reynolds Number Flow Heat Exchangers. New York: Hemisphere (1983) pp. 983–1000.
Aparecido, J.B., Cotta, R.M., and Özisik, M.N., Analytical solutions to two-dimensional diffusion type problems in irregular geometries. J. of the Franklin Institute, V. 326(3) (1989) 421–434.
Aparecido, J.B. and Cotta, R.M., Fully developed laminar flow in trapezoidal ducts. Proc. of the 9th Brazilian Congress of Mechanical Engineering, IX COBEM, V.1. Florianópolis, SC, December 1987 (1900) pp. 25–28.
Aparecido, J.B. and Cotta, R.M., Laminar flow inside hexagonal ducts. Computational Mechanics 6 (1990) 93–100.
Özisik, M.N. and Murray, R.L., On the solution of linear diffusion problems with variable boundary condition parameters. ASME Paper no. 74-HT-1.
Cotta, R.M. and Özisik, M.N., Laminar forced convection in ducts with periodic variation of inlet temperature. Int. J. Heat & Mass Transfer 29 (1986) 1495–1501.
Cotta, R.M. and Özisik, M.N., Transient forced convection in laminar channel flow with stepwise variations of wall temperature. Can. J. Chem. Eng. 64 (1986) 734–742.
Cotta, R.M., Steady-state diffusion with space-dependent boundary condition parameters. Proc. of the Ist National Meeting on Thermal Sciences — ENCIT 86, Rio de Janeiro, Brazil, December 1986 (1900) pp. 163–166.
Cotta, R.M. and Özisik, M.N., Diffusion problems with general time-dependent coefficients. Braz. J. Mech. Sciences, RBCM 9 (1987) 269–291.
Cotta, R.M., On the solution of periodic multidimensional diffusion problems. Int. Comm. Heat & Mass Transfer 16 (1989) 569–579.
Aparecido, J.B. and Cotta, R.M., Thermally developing laminar flow inside rectangular ducts. Int. J. Heat & Mass Transfer 33 (1990) 341–347.
Lakshminarayanan, R. and Haji-Sheik, A., A generalized closed-form solution to laminar thermal entrance problems. In: C.L. Tien, V.P. Carey and J.K. Ferrel (eds), Proc. of the 8th International Heat Transfer Conference, San Francisco, USA, July 1986, pp. 871–876.
Aparecido, J.B., Generalized integral transform for laminar flow and heat transfer inside straight ducts of arbitrary geometry. D.Sc. Dissertation, ITA, São José dos Compos, Brazil, 1988.
IMSL Library, MATH/LIB, Houston, Texas, 1987.
Cotta, R.M., Hybrid numerical-analytical approach to nonlinear diffusion problems. Num. Heat Transfer, part B. 17 (1990) 217–226.
Cotta, R.M., Diffusion-Convection Problems and the Generalized Integral Transform Technique, Núcleo de Publicações, COPPE/UFRJ, Rio de Janeiro, 1991.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
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
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/BF00419981