Numerical Solution for Combined Free and Forced Laminar Convection in Horizontal Rectangular Channels

1969 ◽  
Vol 91 (1) ◽  
pp. 59-66 ◽  
Author(s):  
K. C. Cheng ◽  
Guang-Jyh Hwang
Keyword(s):  
Numerical Solution ◽  
Axial Position ◽  
Uniform Wall Temperature ◽  
Thermal Boundary Conditions ◽  
Aspect Ratios ◽  
Rectangular Channels ◽  
Free And Forced Convection ◽  
Uniform Wall ◽  
Laminar Convection ◽  
Uniform Wall Heat Flux

Combined free and forced convection for steady fully developed laminar flow in horizontal rectangular channels under the thermal boundary conditions of axially uniform wall heat flux and peripherally uniform wall temperature at any axial position is approached by the method of successive overrelaxation. The convergence of the numerical solution is ascertained. Graphical results are presented for streamlines, isotherms, w/w0 versus Re Ra, f Re/(f Re)0 versus Re Ra, and Nu/Nu0 versus Re Ra for the aspect ratios γ = 0.2, 0.5, 1, 2, and 5 and Pr = 0.73. For square channels, velocity and temperature distributions for Pr = 0.73 and heat transfer results for Pr = 7.2 are also presented.

Experimental Investigation of Mixed Laminar Convection in the Entrance Region of Inclined Rectangular Channels

1986 ◽  
Vol 108 (3) ◽  
pp. 574-579 ◽  
Author(s):  
S. M. Morcos ◽  
M. M. Hilal ◽  
M. M. Kamel ◽  
M. S. Soliman
Keyword(s):  
Nusselt Number ◽  
Experimental Results ◽  
Entrance Region ◽  
Test Facility ◽  
Working Fluid ◽  
Aspect Ratios ◽  
Rectangular Channels ◽  
Axial Variation ◽  
Uniform Wall ◽  
Laminar Convection

The present experimental study considers the effect of combined forced and free laminar convection on the heat transfer in the entrance region of horizontal and inclined rectangular channels under uniform wall heat flux. The test facility includes electrically heated aluminum rectangular channels having aspect ratios AR = 2.667 and 0.375, with water as the working fluid. The experimental results included the circumferential wall temperature distribution and the axial variation of Nusselt number. Correlations of the experimental results of Nusselt number in the fully developed region were obtained in terms of Rayleigh number, Reynolds number, and inclination angle.

scholarly journals Second Law Analysis of Laminar Flow in a Circular Pipe Immersed in an Isothermal Fluid

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Vishal Anand ◽  
Krishna Nelanti
Keyword(s):  
Laminar Flow ◽  
Entropy Generation ◽  
Circular Tube ◽  
Dimensionless Temperature ◽  
Bejan Number ◽  
Uniform Wall Temperature ◽  
Thermal Boundary Conditions ◽  
Fluid Properties ◽  
Isothermal Fluid ◽  
Uniform Wall

Entropy generation and pumping power to heat transfer ratio (PPR) of a laminar flow, for a circular tube immersed in an isothermal fluid, are studied analytically in this paper. Two different fluids, namely, water and ethylene glycol, are chosen to study the influence of fluid properties on entropy generation and PPR. The expressions for dimensionless entropy generation, Bejan number and PPR are derived in a detailed way and their variations with Reynolds number, external Biot number, and the dimensionless temperature difference are illustrated. The results of the analysis are compared with those for a laminar flow in a circular tube with uniform wall temperature boundary condition. Finally, a criterion is established to determine which type of thermal boundary conditions is more suitable for a particular fluid, with respect to its influence on entropy generation.

Heat Transfer Enhancement in Laminar Slurry Pipe Flows With Power Law Thermal Conductivities

1984 ◽  
Vol 106 (3) ◽  
pp. 539-542 ◽  
Author(s):  
C. W. Sohn ◽  
M. M. Chen
Keyword(s):  
Heat Transfer ◽  
Shear Rate ◽  
Power Law ◽  
Two Phase ◽  
Uniform Wall Temperature ◽  
Uniform Wall ◽  
Laminar Pipe Flow ◽  
Theoretical Results ◽  
Uniform Wall Heat Flux ◽  
Thermal Conductivities

Generalized theoretical results for heat transfer in laminar pipe flow with power law varying thermal conductivities are presented. The study is motivated by experimental observations that above a threshold shear rate the effective thermal conductivity for disperse two-phase mixtures increases with shear rate. Using a relatively general three parameter power law model for conductivity as a function of shear rate, heat transfer results for short and long pipes as well as with developing thermal profiles were obtained for both the uniform wall heat flux and uniform wall temperature conditions. The results show that significant enhancement in heat transfer coefficient could be obtained from the microconvective effects.

Laminar Heat Transfer in Tubes Under Slip-Flow Conditions

1962 ◽  
Vol 84 (4) ◽  
pp. 363-369 ◽  
Author(s):  
E. M. Sparrow ◽  
S. H. Lin
Keyword(s):  
Heat Transfer ◽  
Wall Temperature ◽  
Slip Flow ◽  
Mean Free Path ◽  
Uniform Wall Temperature ◽  
Nusselt Numbers ◽  
Temperature Jumps ◽  
Uniform Wall ◽  
Moving Fluid ◽  
Uniform Wall Heat Flux

The effects of low-density phenomena on the fully developed heat-transfer characteristics for laminar flow in tubes has been studied analytically. Consideration is given to the slip-flow regime wherein the major rarefaction effects are manifested as velocity and temperature jumps at the tube wall. The analysis is carried out for both uniform wall temperature and uniform wall heat flux. In both cases, the slip-flow Nusselt numbers are lower than those for continuum flow and decrease with increasing mean free path. Extension of the results is made to include the effects of shear work at the wall, temperature jump modifications for a moving fluid, and thermal creep.

Combined Forced and Free Convection in the Entrance Region of an Isothermally Heated Horizontal Pipe

1982 ◽  
Vol 104 (1) ◽  
pp. 153-159 ◽  
Author(s):  
Mikio Hishida ◽  
Yasutaka Nagano ◽  
M. S. Montesclaros
Keyword(s):  
Numerical Solutions ◽  
Entrance Region ◽  
Temperature Fields ◽  
Horizontal Pipe ◽  
Uniform Wall Temperature ◽  
Nusselt Numbers ◽  
Developing Flow ◽  
Uniform Wall ◽  
Secondary Velocity ◽  
Laminar Convection

Numerical solutions are given without the aid of a large Prandtl number assumption for combined forced and free laminar convection in the entrance region of a horizontal pipe with uniform wall temperature. The steady-state solutions have been obtained from the asymptotic time solutions of the time-dependent equations of momentum and energy with the Poisson equation for pressure. Results are presented for the developing primary and secondary velocity profiles, developing temperature fields, local wall shear stress, and local and average Nusselt numbers, which reveal how the developing flow and heat transfer in the entrance region are affected by the secondary flow due to buoyancy forces.

Vorticity-Velocity Method for the Graetz Problem and the Effect of Natural Convection in a Horizontal Rectangular Channel With Uniform Wall Heat Flux

1987 ◽  
Vol 109 (3) ◽  
pp. 704-710 ◽  
Author(s):  
F. C. Chou ◽  
G. J. Hwang
Keyword(s):  
Heat Flux ◽  
Prandtl Number ◽  
Numerical Solutions ◽  
Rectangular Channel ◽  
Wall Heat Flux ◽  
Entrance Region ◽  
Grashof Number ◽  
Uniform Wall ◽  
Laminar Convection ◽  
Uniform Wall Heat Flux

Numerical solutions given by a vorticity-velocity method are presented for combined free and forced laminar convection in the thermal entrance region of a horizontal rectangular channel without the assumptions of large Prandtl number and small Grashof number. The channel wall is heated with a uniform wall heat flux. Typical developments of temperature profile, secondary flow, and axial velocity at various axial positions in the entrance region are presented. Local friction factor and Nusselt number variations are shown for Rayleigh numbers Ra = 104, 3×104, 6×104, and 105 with the Prandtl number as a parameter. The solution for the limiting case of large Prandtl number and small Grashof number obtained from the present study confirms the data of existing literature. It is observed that the large Prandtl number assumption is valid for Pr = 10 when Ra ≤ 3×104 but for a larger Prandtl number when the Rayleigh number is higher.

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