Convection In Ducts Research Articles

Correlations for Convection in Hydrodynamically Developing Laminar Duct Flow

Abstract A generalized correlation for combined entry convection in ducts of arbitrary cross section has been developed. The correlation is constructed for the average Nusselt number using knowledge of fully developed transport constants. The general correlation reproduces the first principle solutions for the well-established round and parallel plate duct geometries to within ±5% for both constant temperature and constant heat flux wall conditions when Pr ≥ 0.7. A survey of the literature demonstrates that the new generalized correlation performs as well or better than existing correlations, which are expressed for specific geometries and wall conditions. The new correlation is generally in good agreement with the first principle solutions of less common duct geometries so long as the duct has a convective surface equal to the wetted perimeter. The new correlation is not recommended for ducts having small aspect ratios that pinch the flow when convection is prescribed by the H2 constant heat flux wall condition.

Modeling transient fully-developed natural convection in vertical ducts – Method of eigenfunction superposition

• Explicit solutions are found for transient natural convection in ducts. • Eigenfunction superposition method is well suited for fully-developed flow. • Rise time to steady state depends on the first eigenvalue of the Helmholtz equation . This paper models the transient natural convection problem for the hydrodynamical and thermal fully-developed open vertical ducts. The powerful method of eigenfunction superposition yields analytic solutions for general duct cross sections. It is found that the induced flow rate approaches a constant in the steady state, but the transient depends on the Prandtl number (Pr). The rise time to reach 95% of steady state is 3 / ( Pr λ 1 ) if Pr < 1, and is 3/λ 1 if Pr > 1, where λ 1 is the lowest eigenvalue of the Helmholtz equation. The theory is then applied to the circular, semi-circular, rectangular and equilateral triangular ducts. For low Pr at small times, the transient induced velocity is larger in the velocity boundary layer near the walls but the maximum velocity is near the corners of the duct.

Correlations for the Graetz problem in convection – Part 2: For ducts of arbitrary cross-section

A general correlation is proposed for the laminar Graetz problem associated with convection in ducts of arbitrary cross-section. The correlation assumes knowledge of fully developed transport constants, specifically the product of fully developed friction factor and Reynolds number, and the fully developed value of Nusselt number, whose values are particular to the duct geometry and wall condition. The new correlation is suitable for ducts having a convective surface equal to the wetted perimeter, and for ducts having a wall condition of either constant temperature or constant heat flux. For the majority of solutions to the Graetz problem found in the literature for various duct geometries, the new correlation is generally found to be within ±5% of first principle calculations.

ENHANCEMENT OF RATE OF HEAT TRANSFER USING VORTEX GENERATORS IN AIR HEATER

There are many applications in engineering industry that require heat addition or removal and a wide variety of heat exchange devices are used for different applications. Performance of improving coefficient of heat trsnsfer and pressure drop reducing becomes essential in all applications. Most of thermal devices like high temperature gas turbines , heat exchangers, electronic equipment, convective heat transfer plays an major role in most of the engineering applications. There are many methods to enhance rate of heat transfer. Delta wing vortex generators or promoters of turbulence are often used to calculate the flow field and they can give a worth full effect on the performance of thermal device. Many researchers have been studied extensively the applications of heat transfer which involves internal flow and mixed convection in ducts and non-circular ducts such as, rectangular, square, triangular. To attain higher coefficient of heat transfer, it is necessary that the surface of heat transfer flow is to be made turbulent. However, energy for producing such turbulence has to come from the blower or fan and the maximum turbulence leads to excessive power requirement to make the air flow through the duct. Therefore maximum turbulence must be produced in the region which is very near to surface of heat transfer i.e. in the laminar sub-layer only Excessive friction losses can be avoided by making flow should be not unduly disturbed and it is done by making the height of the roughness element to be small as compared with the dimensions of duct. The roughness element height (e) and pitch (P) are the most important parameters to characterize the roughness shape and arrangement. All these parameters namely , angle of attack (β), relative roughness pitch (P/e), relative roughness height (e/D) are usually specified as dimensionless parameters.

H2 Forced Convection for Slip Flow in an Equilateral Triangular Duct

The slip flow and temperature jump boundary conditions are derived for H2 constant flux forced convection in ducts. An exact solution is found for the fully developed equilateral triangular duct. Closed-form formulas for the temperature distribution and the Nusselt number are presented. The exact H2 Nusselt number for the no-slip case is 308/163.

Heat Transfer in a Short Parallel-Plate Channel in the Transition Regime

Heat transfer in a parallel-plate channel with uniform wall heat flux and refrigerated by water is investigated experimentally for the laminar and transition hydrodynamic regimes. The dimensions of the channel were chosen such that entry effects are relevant for a significant part of the channel length. The influence of the following parameters has been studied: inlet Reynolds number, inlet temperature and wall heat flux. Experimental results are compared with predictions based on different empirical correlations for convection in ducts. This analysis shows that the correlation of Gnielinski provides a good agreement with the experimental results for Reynolds numbers between 5,000 and 10,000 at 20°C and under relatively low heat fluxes. Experiments performed at relatively low heat fluxes show that, in the entry region previous to the laminar-turbulent transition, the behavior of the flow is well described by the combined hydrodynamic and thermal entry solution obtained by Hwang and Fan (Finite Difference Analysis of Forced-Convection Heat Transfer in Inlet Region of a Flat Rectangular Duct, Appl. Sci. Res., vol. 13, pp. 401–422, 1964). The hydrodynamic and thermal entry effects for the experimental conditions in the present work are relevant for most of the test section. The location of the transition point is affected in the first instance by the local bulk Reynolds. On the other hand, the wall heat flux affects the fluid properties, i.e., the fluid viscosity, and therefore, it also affects the transition. It was found that for the transition regime, an increase of the wall heat flux produces lower values of the convection coefficient than the values predicted by the correlation of Gnielinski. This behavior, which seems to be associated to the variation of the fluid properties, is opposite to the increase of the convection coefficient observed for heating in the laminar and turbulent regimes for water and oils. The case of an inlet Reynolds number of 5,000 was studied in detail, and the influence of heat flux on the Nusselt number is addressed.

Numerical study of the radiation effect on the flowing of mixed convection along a vertical channel

AbstractRadiation effect and mixed convection flow are solved numerically in two‐dimensional vertical channel. The main objective is to study the effect of radiation on the flow using radiation models available in Fluent software. The study is done for a Richardson number (Ri = 2.5). Our results when the radiation is ignored are compared with those of the article: Mixed convection in ducts with asymmetric wall heat fluxes [W. Aung and G. Worku, J. Heat Transfer 109, 947 (1987)]. (© 2008 WILEY‐VCH Verlag GmbH &amp; Co. KGaA, Weinheim)

A computer-aided parametric analysis of mixed convection in ducts

This study develops a novel technique of computer-aided parametric analysis (CAPA) to formulate simple correlations for thermal flow characteristics in a complex convective flow system. To demonstrate the validity of the technique, fully developed mixed convection in uniformly heated horizontal ducts of square and circular cross-sections are employed as illustrative examples. The effects of secondary flow generated by the thermal buoyancy force are included. The CAPA technique employs characteristic quantities, constant factors and multi-term relationships to convert the governing equations into a set of algebraic equations. Relatively, this technique generates more extensive results than the conventional order-of-magnitude and scaling analyses. With the aid of limited data from numerical results (or measurements), formulas for evaluating the cross-sectional averages of axial velocity and temperature, the strength of secondary vortices, friction factors and the heat transfer rates at various Pr and ReRa can be derived. Comparisons of the present results and the direct numerical solutions manifest quite satisfactory performance of the CAPA technique. Merits of the CAPA technique are: (1) less effort required in the developing procedure, (2) clear parameter-dependence of the thermal flow characteristics, and (3) convenience in using the resultant correlations of algebraic form.

Invariance relations for laminar forced convection in ducts with slowly varying cross-section

Laminar flow forced convective heat transfer in ducts with slowly varying cross-section is analysed. The analysis is based on a simplifying assumption concerning the velocity field, called the similarity assumption. It is assumed that the axial velocity profile is locally fully developed, irrespective of the variation of the cross-sectional area with axial position. It is shown that in the axisymmetric case (circular tube with varying diameter) for boundary conditions of the first kind the diameter variation has no influence at all on the heat transferred. As in the case of a tube with constant diameter, the degree of temperature equilibration depends only on the Fourier number Fo= πaL Q that is on the ratio of length of the tube, L, to flow rate Q. In the case of a plane channel, however, variations of the channel height 2 H have a pronounced influence on the transfer coefficient. It is shown that the degree of equilibration depends only on the effective Fourier number Fo eff = aB Q ·∫ 0 L dz H(z) . The heat transfer is enhanced by a narrow design of the duct. These results hold for any shape of the axial velocity distribution over the duct cross-section, provided the above-mentioned similarity assumption is justified. By analogy, all foregoing results are also applicable to the convective–diffusive mass transfer in flow through ducts with slowly varying cross-section. The range of validity of the similarity assumption is discussed in a hydrodynamic section. It can be shown that for creeping flow of a Newtonian liquid in an infinite cone or wedge this assumption is a very good approximation to the exact solution of Stokes' equations for cone or wedge angles up to 30°. Apart from Newtonian creeping flow, the assumption might well be applicable in the duct flow of a power-law fluid and in pure elongational flow as encountered in stretching filaments or sheets of liquid, where the axial velocity is constant over the cross-section.

A validated model of naturally ventilated PV cladding

A simplified method has been derived for use in the estimation of the flow rate in naturally ventilated PV cladding for buildings. The method is based on a one-dimensional ‘loop analysis’ in which the buoyancy forces are balanced by the pressure drops due to friction. Wind effects at the entrance and exit are also taken into account. The procedure yields the mass flow rate and temperature rise directly by the solution of a simple cubic equation and therefore is straightforward and simple enough to be put on a spreadsheet. This methodology allows the designer to explore various potential PV configurations at little expense and hence to focus on those designs which warrant further detailed analysis, perhaps coupled to a full building simulation package. In this paper, the fundamental theory behind the loop analysis is described. The hypothesis tested is that the form and values for the friction factors and internal heat transfer coefficients for the buoyancy driven case are the same as those for forced convection in ducts. Next, the experimental rig is discussed with which the first validation exercises are carried out for the no-wind case, using an emulation of the simple single stack PV cladding arrangement. The two key parameters are identified using the measurement error weighted least squares linear regression. Overall excellent agreement between the modelled and measured mass flow rates is seen; the hypothesis is therefore valid. A general model is then derived to describe the thermal behaviour of building-integrated PV with natural ventilation cooling for use in a wide variety of design and validation exercises.

On the choice of the reference temperature for fully-developed mixed convection in a vertical channel

The effect of the choice of the reference fluid temperature on the solutions of fully-developed mixed-convection problems in a plane vertical channel is studied. First, the boundary conditions of either uniform wall temperatures or a uniform temperature at a wall and a uniform heat flux on the opposite wall are considered. It is shown that, in these cases, the choice of the reference temperature affects both the velocity profiles and the axial change of the difference between the pressure and the hydrostatic pressure. A general method to choose the reference fluid temperature for the fully developed mixed convection in ducts is proposed. Finally, an analytical solution for the boundary condition of uniform wall heat fluxes is obtained by choosing the mean fluid temperature in each cross section as the local reference temperature.

2.5.1 SINGLE-PHASE CONVECTIVE HEAT TRANSFER: Forced convection in ducts

2.5.1 SINGLE-PHASE CONVECTIVE HEAT TRANSFER: Forced convection in ducts

Forced convection in ducts with a boundary condition of the third kind

'Song, M., and Viskanta, R., Convection Flow and Heat Transfer Between a Fluid Layer and an Anisotropic Porous Layer within a Rectangular Enclosure, Heat Transfer in Enclosures, American Society of Mechanical Engineers, HTD-Vol. 177, 1991, pp. 1-12. Arquis, E., Caltagirone, J. P., and Langlais, C., Convection in Cavities Partially Filled with Permeable Porous Materials, Proceedings of the 8th International Heat Transfer Conference, Vol. 5 (San Francisco, CA), 1986, pp. 2653-2658. Beckermann, C., Ramadhyani, S., and Viskanta, R., Convection Flow and Heat Transfer Between a Fluid Layer and a Porous Layer Inside a Rectangular Enclosure, Journal of Heat Transfer, Vol. 109, May 1987, pp. 363-370. Tong, T. W., and Subramanian, E., Convection in Rectangular Enclosures Partially Filled with a Porous Medium, International Journal of Heat and Fluid Flow, Vol. 7, March 1986, pp. 310. Sathe, S. B., Tong, T. W., and Faruque, M. A., Experimental Study of Natural Convection in a Partially Porous Enclosure, Journal of Thermophysics and Heat Transfer, Vol. 1, 1987, pp. 260-267. Ozoe, H., Sayama, H., and Churchill, S. W., Convection in an Inclined Square Cavity, International Journal of Heat and Mass Transfer, Vol. 17, 1974, pp. 401-406. Prasad, V., Lauriat, G., and Kladias, N., Non-Darcy Natural Convection in a Vertical Porous Cavity, Heat and Mass Transfer in Porous Media, Elsevier, New York, 1992, pp. 293-314.

On the eigenvalues basic to the analytical solution of convective heat transfer with axial diffusion effects

AbstractThe integral transform method is employed in the analytical solution of the non‐classical eigenvalue problem that appears in connection with the analysis of forced convection in ducts, including the effect of fluid heat diffusion in the axial direction. The related eigenfunctions are expanded in terms of eigenfunctions from a simpler auxiliary eigenvalue problem, and the original eigenvalues are determined from the associated matrix eigensystem analysis. Convergence rates of the proposed solutions are illustrated and reference results established for different values of the governing parameters.

Transient heat and mass transfer in laminar flow forced convection in ducts

The modelling of heat and mass regenerators often assumes the heat and mass transfer coefficients to be uniform and constant with time and position within the flow passages of the regenerator. This paper presents a study to examine the validity of this assumption. Experimental breakthrough curves of a single-blow test facility with a desiccant regenerator matrix are examined using a separation technique. The response curves are input to a model which computes the temporal and spatial distributions of the air-side heat and mass transfer coefficients. It is found that the variation of the Nusselt and Sherwood numbers is small for the slower mass transfer waves which determines the performance of regenerative dehumidifiers. The separation technique proves to be a powerful procedure for analysing experimental breakthrough curves.

Conjugated laminar forced convection in ducts with periodic variation of inlet temperature

Conjugated laminar forced convection with parabolic velocity is studied for flow inside both parallel-plate and circular ducts subjected to a periodically varying inlet temperature. The analysis of this classs of problems lead to a Sturm-Liouville type complex eigenvalue problem for which no known solution is available. In this work, a new methodology is presented for a direct solution of such complex eigenvalue problems in the complex domain using the shooting method along with the Runge-Kutta method. The methodology is applicable for solving both laminar and turbulent flow problems; here we consider only the laminar flow with a parabolic velocity profile. The results clearly show that the slug-flow assumption overestimates the phase lag and the Nusselt number. Some benchmark results are also presented for the eigenquantities in tabular form.

Unsteady Laminar Forced Convection in Ducts With Periodic Variation of Inlet Temperature

A theoretical and experimental study of laminar forced convection in the thermal entrance region of a rectangular duct, subjected to a sinusoidally varying inlet temperature, is presented. A general boundary condition of the fifth kind that accounts for both external convection and wall thermal capacitance effects is considered, and an analytical solution is obtained through extending the generalized integral transform technique. The variations of amplitudes and phase lags of centerline and bulk temperatures are determined as functions of modified Biot number, fluid-to-wall thermal capacitance ratio, and dimensionless inlet frequency. An apparatus has been designed, built, and used for the experimental study to provide validation of the mathematical modeling employed. Good agreement is obtained when the nonuniform sinusoidally varying inlet temperature profile obtained by experiments is incorporated into the theoretical model.

Effect of Wall Conduction on Combined Free and Forced Laminar Convection in Horizontal Tubes

Combined free and forced laminar convection in ducts is encountered in a wide variety of engineering applications, including heat exchangers designed for viscous fluids in chemical processes, solar collectors, food industries, and biomedical engineering. In many engineering applications, the boundary conditions for thermal convection in ducts cannot be considered uniform either for wall temperature or heat flux. In the thermally fully developed flow, the effect of peripheral wall conduction may be introduced by the nonuniform peripheral wall heat flux in noncircular ducts and also introduced simultaneously by the secondary flow in rectangular channels, or by the secondary flow alone in circular tubes. This paper investigates the effect of peripheral wall conduction on combined free and forced laminar convection in hydrodynamically and thermally fully developed flow in horizontal circular tubes with uniform heat input axially. A finite-difference power-law scheme is employed to solve the problem.

Mixed Convection in Ducts With Asymmetric Wall Heat Fluxes

Results are presented of a numerical study dealing with combined free and forced laminar convection in a parallel plate vertical channel with asymmetric wall heating at uniform heat fluxes (UHF). The forced flow at the inlet is assumed to be spatially uniform and directed vertically upward. Quantitative information is provided pertaining to the effects of buoyancy and asymmetric heating on the hydrodynamic and thermal parameters. For values of Gr/Re up to 500 no flow reversal is predicted, in contrast to the case of uniform wall temperatures (UWT) recently reported. Other fundamental differences between UHF and UWT also are indicated.

Transient conjugated forced convection in ducts with periodically varying inlet temperature

Transient forced convection for slug flow inside parallel-plate channels and circular ducts including conjugation to the walls is solved analytically and exactly for periodic variation of the inlet temperature. The periodic solution to the problem involved eigenfunctions and eigenvalues of a complex eigenvalue problem. The complex eigenvalue problem is solved by modifying the recently advanced Count Method, and benchmark results are presented for the eigenvalues in tabular form. The amplitude and phase lag of oscillations with respect to the conditions at the inlet are determined for the wall temperature, fluid bulk temperature and heat flux. The results for the cases of both parallel-plate channels and circular ducts are presented in the graphical form as a function of the axial position for different values of the parameters signifying the rate of energy storage in the walls. The effects of walls on damping the amplitude and altering the phase of temperature and heat flux oscillations along the duct are investigated.