Natural convective heat transfer in uniformly heated vertical pipe annuli

Natural convective heat transfer in vertical concentric pipe annuli is investigated both numerically and experimentally for a fluid having a Prandtl number of 0.7. Numerical calculations for three cases of different heating conditions for pipes (heated inner pipe, heated outer pipe, both pipes heated) are made of laminar flows for different inner‐to‐outer‐pipe diameter ratios d_i/d_o from 0.2 to 0.8. For each case, the thermal entrance length x/b at the modified Grashof numbers Gr^*=10² to 5 × 10⁵ is well correlated with Grashof number Gr^* and annulus length to clearance ratio L/b. Local Nusselt numbers Nu_i and Nu_o in the thermally fully developed region have certain constant values dependent on the diameter ratio d_i/d_o, regardless of Gr^* and L/b. Average Nusselt numbers Nu_i and Nu_o in the thermal entrance region are also independent of Gr^* and L/b. © 2001 Scripta Technica, Heat Trans Asian Res, 30(8): 676–688, 2001     

Fluid flow and heat transfer of natural convection around array of vertical heated plates

Natural convective flows around an array of vertical heated plates were investigated experimentally. Main concerns were directed to the influences of plate numbers on the heat transfer characteristics of the plates. Both surfaces of the test plates were heated with constant and equal heat fluxes and their local heat transfer coefficients were measured. The results showed that the coefficients of the surfaces of the array facing outward became higher than those facing inward. The flow fields around the bottom of the plate array were visualized with smoke. The result showed that the ambient flow is directed from the sides to the center of the array and enters the parallel channel obliquely. These flows cause the above difference in the coefficients. While the difference gradually diminished in between the plates placed in the central section of the array, their coefficients asymptotically approach those of the analytical correlation that assumed a uniform velocity at the channel inlet. © 2008 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.20232     

Boundary layer instability of the natural convection flow on a uniformly heated vertical plate

Direct numerical simulation is employed to investigate the two-dimensional boundary layer instability of a natural convection flow on a uniformly heated vertical plate submerged in a homogeneous quiescent environment. A Boussinesq fluid with Prandtl numbers of Pr = 0.733 (air) and 6.7 (water), in the local Rayleigh number range 0 ? Ra_x ? 2.4 × 10¹⁰, is studied. Controlled low amplitude numerical disturbances introduced into the base flow excite unstable travelling waves, with the resulting waves tracked and analyzed as they travel up the boundary layer. The numerical simulation readily reproduced what is predicted by the parallel linear stability theory for the two dimensional mode relatively short wave spectrum, but not for some parts of the long wave spectrum. Critical Rayleigh numbers have been obtained separately for both the temperature and velocity signals using the numerical results, and shown to be in good agreement with each other provided the data is renormalized using the boundary layer scalings of Sparrow and Greg [1]. It has been shown that the disturbance behavior depends on the Prandtl and Rayleigh numbers, the excitation frequency and to a lesser extent the prescribed thermal coupling at the plate.     

Entropy generation in natural convection in a symmetrically and uniformly heated vertical channel

In this study numerical predictions of local and global entropy generation rates in natural convection in air in a vertical channel symmetrically heated at uniform heat flux are reported. Results of entropy generation analysis are obtained by solving the entropy generation equation based on the velocity and temperature data. The analyzed regime is two-dimensional, laminar and steady state. The numerical procedure expands an existing computer code on natural convection in vertical channels. Results in terms of fields and profiles of local entropy generation, for various Rayleigh number, Ra, and aspect ratio values, L/b, are given. The distributions of local values show different behaviours for the different Ra values. A correlation between global entropy generation rates, Rayleigh number and aspect ratio is proposed in the ranges 10³ ⩽ Ra ⩽ 10⁶ and 5 ⩽ L/b ⩽ 20.     

Natural convection in uniformly heated vertical annuli

A numerical study of natural convection through vertical annuli with one wall uniformly heated and the other wall adiabatic was made. In this study the boundary layer simplifications of the NavierStokes equations for developing laminar flow with constant properties were solved by means of a finite difference method. Three radius ratios (0.26, 0.5 and 0.9) were investigated. The different variables (velocity, pressure defect, temperature, etc.) were determined. An apparatus was built to check the obtained numerical results for one of the conditions employed. Agreement between the theoretical and experimental values was good.     

Combined heat and mass transfer in natural convection on a vertical flat plate

In analyzing the combined heat and mass transfer in natural convection, most of the surface conditions are either maintained at an uniform wall temperature and uniform wall concentration or subjected to an uniform heat flux and uniform mass fluc. Other conditions are seldom investigated. This study is to investigate the effects of the coupled thermal and mass diffusion on the natural convection of a vertical plate for a moist air system. The surface conditions of the plate are uniform heat flux and uniform relative humidity. A finite difference numerical method is used to solve the governing equations simultaneously. The results that the relative humidity of the surface is both larger and smaller than that of the ambient are examined in detail.     

Enhancement of natural convection heat transfer from a vertical heated plate using inclined fins

An enhancement technique is developed for natural convection heat transfer from a vertical heated plate with inclined fins, attached on the vertical heated plate to isolate a hot air flow from a cold air flow. Experiments are performed in air for inclination angles of the inclined fins in the range of 30° to 90° as measured from a horizontal plane, with a height of 25 to 50 mm, and a fin pitch of 20 to 60 mm. The convective heat transfer rate for the vertical heated plate with inclined fins at an inclination angle of 60° is found to be 19% higher than that for a vertical heated plate with vertical fins. A dimensionless equation on the natural convection heat transfer of a vertical heated plate with inclined fins is presented. © 2007 Wiley Periodicals, Inc. Heat Trans Asian Res, 36(6): 334–344, 2007; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.20168     

A numerical study of combined forced and natural convection heat transfer in a vertical cylinder bundle

Combined forced and natural convection in a bundle of vertical cylinders have been studied numerically with the aid of Riemann geometry. The cylinders heated uniformly are arranged in an equilateral triangular pattern of three bundle spacings S/D = 1.1, 1.5, and 1.9. Numerical calculations are made of the mixed convection of air (Pr = 0.7) in a subchannel of the bundle at ratios of modified Grashof number to Reynolds number Gr*/Re from 1 to 10⁵. The results show that the reverse flows appear along the center line in the subchannel with increasing Gr*/Re. Local Nusselt numbers for the thermally fully‐developed region are well correlated with Gr*/Re. © 2003 Wiley Periodicals, Inc. Heat Trans Asian Res, 32(7): 639–649, 2003; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.10118     

Combined forced and natural convection heat transfer from a horizontal cylinder embedded in a porous medium

This paper reports the results of an experimental study of heat transfer by combined forced and natural convection from a horizontal cylinder embedded in a porous medium composed of randomly packed glass spheres saturated with water. The direction of the flow of water was horizontal and normal to the longitudinal axis of the cylinder. The diameter of the cylinder, D, was 11.45mm and the equivalent diameter of the glass spheres was 3.072mm. It is shown that the condition Gr_k/Re²_D ⩽ 0.5 represents a conservative criterion for segregating heat transfer data that are predominantly governed by forced convection from those in which natural convection effects are significant. A correlation hypothesis for convection heat transfer which is based upon four assumptions, primary among which is that the flow can be (conceptually) regarded as being composed of ‘coarse’ and ‘fine’ components, is presented. This hypothesis is shown to provide a basis for successfully correlating a set of experimental heat transfer data that extends from the Darcy regime into the turbulent regime and spans the intervening Forchheimer and transition regimes. It is suggested that the correlation procedure adopted here may yield useful results if applied to other geometries such as, for example, forced convection heat transfer in ducts packed with porous media.     

Fluid flow and heat transfer of opposing mixed convection adjacent to vertical heated plates

Opposing mixed convective flows induced around heated vertical plates were investigated experimentally. The experiments have been carried out with air and test plates of 100 mm and 200 mm long. The flow fields over the heated plates were visualized and the local heat transfer coefficients of the plates were measured for a wide range of Reynolds and Rayleigh numbers; Re_L = 7 × 10²−1.5 × 10⁴, Ra = 9 × 10⁶−8 × 10⁸. The visualization experiments showed that the separation of the boundary layer appears first at the trailing edge of the plate when the non‐dimensional parameter of (Gr/Re) = 0.35, and that the separation point reaches the leading edge when (Gr_L^*/Re_L^2.5) = 1.0. The heat transfer experiments showed that the above flow separation retards the heat transfer significantly from that of pure forced convection. It was also revealed that the flows over the heated plates can be categorized into forced, natural, and combined convection using the above parameter, (Gr/Re), as (Gr/Re) < 0.2, (Gr/Re) > 3 and 0.2 < (Gr/Re) < 3, respectively. © 2005 Wiley Periodicals, Inc. Heat Trans Asian Res, 34(8): 595–607, 2005; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.20080     

A correlation for the limiting dryout steam quality in forced convection in uniformly heated vertical round tubes

The paper considers the thermal crisis which is associated with the wall liquid film dryout under the conditions of forced convection. On the assumption of heat transfer deterioration due to the break of film integrity, a dimensionless relation for these conditions is obtained which is used to derive a relation for the limiting steam quality. A comparison with 1115 experimental points for water, R-12, R-21, R-113, carbon dioxide, nitrogen, helium, parahydrogen, potassium, and sodium from 23 literature sources has shown that the mean deviation does not exceed 15%, while 91% of test data coincide within ∓ 25%.     

Steady forced convection heat transfer from a heated circular cylinder to power-law fluids

Forced convection heat transfer to incompressible power-law fluids from a heated circular cylinder in the steady cross-flow regime has been investigated numerically by solving the momentum and thermal energy equations using a finite volume method and the QUICK scheme on a non-uniform Cartesian grid. The dependence of the average Nusselt number on the Reynolds number (5 ⩽ Re ⩽ 40), power-law index (0.6 ⩽ n ⩽ 2) and Prandtl number (1 ⩽ Pr ⩽ 1000) has been studied in detail. The numerical results are used to develop simple correlations as functions of the pertinent dimensionless variables. In addition to the average Nusselt number, the effects of Re, Pr and n on the local Nusselt number distribution have also been studied to provide further physical insights. The role of the two types of thermal boundary conditions, namely, constant temperature and uniform heat flux on the surface of the cylinder has also been presented.     

CHF characteristics of R-134a flowing upward in uniformly heated vertical tube

An experimental study of the critical heat flux (CHF) using R-134a in uniformly heated vertical tube was performed and 182 CHF data points were obtained from the present work to investigate the CHF characteristics of R-134a. The investigated flow parameters in R-134a were: (1) outlet pressures of 13, 16.5, 23.9 bar, (2) mass fluxes of 285-1300 kg/m² s, (3) subcooling temperatures of 5-40 °C. The CHF tests were performed in a 17.04 mm I.D. test section with heated length of 3 m. The parametric trends of CHF show a general agreement with previous understanding in the water. To assess the suitability of the CHF test using R-134a for modeling the CHF in water, Bowring correlation and Katto correlation were used in the present investigation. It was found that the present test results coincided well with the data predicted with both correlations. It demonstrates that the R-134a can be used as the CHF modeling fluid of water for the investigated flow conditions and geometric condition.     

Characteristics of forced convection heat transfer in vertical internally finned tube

This work presents a numerical investigation of a vertical internally finned tube subjected to forced convection heat transfer. The governing equations were solved numerically using the control volume technique. Nusselt number, Nu, and friction factor multiplied by Reynolds number, fRe, are influenced greatly by the height and number of the radial fins. The velocity and temperature distributions inside the tube depend on the number and height of the radial fins. This paper suggests that for best heat transfer to be achieved there is an optimum combination of fin numbers and height.     

Natural convection slip flow in a vertical microchannel heated at uniform heat flux

Numerical solutions for steady state developing natural convection flow in air, in vertical parallel-plate microchannels are accomplished. An asymmetric heating is considered and the walls are assumed to be at uniform heat flux. A first-order model is used for slip and jump boundary conditions and an analytical solution for the fully developed flow is also given. Results are performed for air, for the heat flux ratio in the 0.0–1.0 range, for Rayleigh, Ra, and Knudsen, Kn, numbers from 10^?1 to 8 × 10³ and from 0.0 to 0.10, respectively. The maximum mass flow rate is always obtained for the highest considered Kn value, whereas the average Nusselt number, Nu, increases for lower Ra (<10) and decreases for Ra > 100. Wall temperature profiles have the lowest values for highest considered Kn value at lower Ra, whereas for the developing flow, they present opposite trends. For developing flow, velocity profiles for asymmetric and symmetric heating are completely different. In developing flow velocity profiles along the wall present the highest increases for asymmetric heating and the highest considered Kn value.