Heat-Transfer Effects on the Developing Laminar Flow Inside Vertical Tubes

1966 ◽  
Vol 88 (2) ◽  
pp. 214-222 ◽  
Author(s):  
W. T. Lawrence ◽  
J. C. Chato
Keyword(s):  
Heat Flux ◽  
Transition Process ◽  
Constant Heat Flux ◽  
Wall Heat Flux ◽  
Axial Position ◽  
Fluid Viscosity ◽  
Constant Heat ◽  
Constant Wall Temperature ◽  
Constant Wall Heat Flux ◽  
Vertical Tubes

A numerical method was developed for the calculation of entrance flows in vertical tubes for the cases of upflow or downflow and constant wall heat flux or constant wall temperature. The solutions were in excellent agreement with experimental data obtained with water flowing upward in a vertical heated tube. The results show that both the density and the viscosity have to be treated as nonlinear functions of temperature. Consequently, for the constant heat flux condition, the velocity and temperature profiles constantly change and never reach “fully developed” states. The transition to turbulent flow was also studied. The experimental measurements demonstrated that the transition process depends on the developing velocity profiles. For the constant heat flux case, transition will always occur at some axial position. For a given entrance condition, the distance to transition is fixed by the fluid flow rate and the wall heat flux. For the experimental results, a tentative transition criterion was obtained, which depends only on the velocity profile shape, fluid viscosity, and the entrance Reynolds number.

scholarly journals HEAT TRANSFER OF LAMINAR FLOW IN VERTICAL TUBES WITH CONSTANT WALL HEAT FLUX

1968 ◽  
Vol 1 (2) ◽  
pp. 120-124 ◽  
Author(s):  
NOBUO MITSUISHI ◽  
OSAMU MIYATAKE ◽  
MITSURU YANAGIDA
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Laminar Flow ◽  
Wall Heat Flux ◽  
Constant Wall Heat Flux ◽  
Vertical Tubes

Laminar Forced Convection in Transversely Corrugated Microtubes

2019 ◽  
Vol 141 (3) ◽  
Author(s):  
F. Talay Akyildiz ◽  
Dennis A. Siginer
Keyword(s):  
Heat Flux ◽  
Analytical Solution ◽  
Forced Convection ◽  
Wall Temperature ◽  
Wall Heat Flux ◽  
Bulk Temperature ◽  
Straight Tube ◽  
Computational Domain ◽  
Constant Wall Temperature ◽  
Constant Wall Heat Flux

Forced convection heat transfer in fully developed laminar flow in transversely corrugated tubes is investigated for nonuniform but constant wall heat flux as well as for constant wall temperature. Epitrochoid conformal mapping is used to map the flow domain onto the unit circle in the computational domain. The governing equations are solved in the computational domain analytically. An exact analytical solution for the temperature field is derived together with closed form expressions for bulk temperature and Nusselt number for the case of the constant heat flux at the wall. A variable coefficient Helmholtz eigenvalue problem governs the case of the constant wall temperature. A novel semi-analytical solution based on the spectral Galerkin method is introduced to solve the Helmholtz equation. The solution in both constant wall heat flux and constant wall temperature case is shown to collapse onto the well-known results for the circular straight tube for zero waviness.

Heat Convection Within an Eccentric Annulus Heated at Either Constant Wall Temperature or Constant Heat Flux

2012 ◽  
Vol 134 (8) ◽  
Author(s):  
F. M. Mahfouz
Keyword(s):  
Heat Flux ◽  
Numerical Solution ◽  
Wall Temperature ◽  
Outer Wall ◽  
Constant Heat Flux ◽  
Heat Convection ◽  
Radius Ratio ◽  
Constant Heat ◽  
Constant Wall Temperature ◽  
Eccentric Annulus

Natural heat convection within an annular annulus bounded by two horizontal vertically eccentric long cylinders has been investigated. The annulus inner wall has been heated and maintained at either constant wall temperature CWT or constant heat flux CHF while the outer wall is cooled and maintained at constant temperature. The induced buoyancy driven flow and the associated heat convection are predicted through solving numerically the full conservation equations for mass, momentum, and energy using Fourier spectral method. Beside Rayleigh and Prandtl numbers, the heat convection process in the annulus depends on the annulus radius ratio and eccentricity (normalized by the radius difference). The study considered a moderate range of Rayleigh numbers up to 105 while Prandtl number is fixed at 0.7. The radius ratio is considered up to 3.2 while the eccentricity is varied between − 0.65 and + 0.65. The study has revealed that at certain radius ratio for a given Rayleigh number and eccentricity, the heat transfer is minimum in case of CWT and the mean inner wall temperature is maximum in case of CHF. The study has also shown, in the range considered for controlling parameters, that multiple convection cells only exist in case of CWT and only for positive eccentricity. Moreover, the study has shown that the present numerical solution of the pure conduction problem is almost identical with the newly presented analytical solution which confirms the high accuracy of the numerical solution.

Natural Convection in a Vertical Slit Microchannel With Superhydrophobic Slip and Temperature Jump

2013 ◽  
Vol 136 (3) ◽  
Author(s):  
C. Y. Wang ◽  
Chiu-On Ng
Keyword(s):  
Heat Flux ◽  
Flow Rate ◽  
Wall Temperature ◽  
Temperature Jump ◽  
Slip Surface ◽  
Critical Value ◽  
Constant Heat Flux ◽  
Constant Heat ◽  
Constant Wall Temperature ◽  
Temperature Jump Coefficient

Recent developments in microscale heat exchangers have heightened the need for the understanding of fluid flow and heat transfer in a microchannel. In this study, we look into fully-developed buoyancy-driven flow in a vertical parallel-plate microchannel, which has one wall exhibiting superhydrophobic slip and temperature jump, and another wall being a normal no-slip surface. Analytical solutions are derived for free convection in the channel, where the heating is applied to either one of the two walls, and by either constant wall temperature or constant heat flux. We examine how the superhydrophobic slip and temperature jump may affect the volume flow rate and the Nusselt number under various heating conditions. There exists a critical value of the temperature jump coefficient, above which the flow rate will be larger by heating the no-slip surface than by heating the superhydrophobic surface, whether by constant wall temperature or by constant heat flux. The opposite is true when the temperature jump coefficient is below the critical value. Also, the temperature jump can have a negative effect on the flow rate when the heating is by constant temperature on the superhydrophobic side of the channel, but will have a positive effect when the heating is on the no-slip side of the channel.

Laminar fully developed flow and heat transfer of Robertson–Stiff fluids in a rectangular duct

2005 ◽  
Vol 83 (2) ◽  
pp. 165-182 ◽  
Author(s):  
M E Sayed-Ahmed ◽  
A S El-Yazal
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Wall Heat Flux ◽  
Physical Parameters ◽  
Rectangular Duct ◽  
Constant Wall Temperature ◽  
Fully Developed Flow ◽  
Flow And Heat Transfer ◽  
Power Law Fluids ◽  
Constant Wall Heat Flux

The laminar fully developed flow and heat transfer through a rectangular duct of a viscous incompressible Robertson–Stiff fluid is investigated. Robertson–Stiff fluids are time independent non-Newtonian materials possessing a yield value. The governing momentum and energy equations are solved numerically using finite-difference approximations. We consider two cases of thermal boundary conditions: H1 the "circumferentially constant wall temperature and axially constant wall heat flux" and H2 the "circumferentially and axially constant wall heat flux". The velocity, temperature, the average friction factor and Nusselt numbers for the two cases are computed for various values of the physical parameters. The present results have been compared with the known solutions for Newtonian and power-law fluids and are found to be in good agreement.PACS Nos.: 47.50.+d, 47.15.–x

Chemically Reacting Hydromagnetic Unsteady Flow of a Radiating Fluid Past a Vertical Plate with Constant Heat Flux

2012 ◽  
Vol 67 (5) ◽  
pp. 239-247 ◽  
Author(s):  
Oluwole Daniel Makinde
Keyword(s):  
Heat Flux ◽  
Vertical Plate ◽  
Nonlinear Partial Differential Equations ◽  
Constant Heat Flux ◽  
Radiation Absorption ◽  
Constant Heat ◽  
Boundary Layer Equations ◽  
Finite Difference Technique ◽  
Constant Wall Heat Flux ◽  
Chemically Reacting

The combined effects of thermal radiation absorption and magnetic field on an unsteady chemically reacting convective flow past an impulsively started vertical plate is studied in the presence of a constant wall heat flux. Boundary layer equations are derived and the resulting approximate nonlinear partial differential equations are solved numerically using a semi-discretization finite difference technique. A parametric study of all parameters involved is conducted, and a representative set of numerical results for the velocity, temperature, and concentration profiles as well as the skin-friction parameter and Sherwood number are illustrated graphically to show typical trends of the solutions. Further validation with previous works is carried out and an excellent agreement is achieved.

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