Computational Methods for Entry Length Heat Transfer by Combined Laminar Convection in Vertical Tubes

1977 ◽  
Vol 191 (1) ◽  
pp. 19-29 ◽  
Author(s):  
M. W. Collins ◽  
P. H. G. Allen ◽  
O. Szpiro
Keyword(s):  
Heat Transfer ◽  
Computer Time ◽  
Vertical Tube ◽  
Numerical Techniques ◽  
Temperature Dependent ◽  
Entry Length ◽  
Temperature Distributions ◽  
Temperature Dependent Properties ◽  
Laminar Convection ◽  
Vertical Tubes

Numerical techniques for the calculation of velocity and temperature distributions in heated ducts have proved accurate but expensive in computer time and capacity. It is worth investigating to what extent simplification is possible without loss of accuracy. Entry-length heat transfer to upward laminar flow with combined convection in a vertical tube is taken as typical. Comparison is made between measured values and, first, a full numerical solution for constant thermophysical properties (viscosity and thermal diffusivity), secondly, the same solution but allowing for their individual and combined variation with temperature and, thirdly, a solution which assumes a series of truncated versions of the fully developed temperature distribution to establish corresponding velocity profiles, allowing for temperature-dependent properties.

Prediction Methods for Entry Length Heat Transfer by Combined Laminar Convection in Horizontal Tubes

1982 ◽  
Vol 196 (1) ◽  
pp. 409-415 ◽  
Author(s):  
P H G Allen ◽  
O Szpiro ◽  
M W Collins
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Laminar Flow ◽  
Prediction Methods ◽  
Entry Length ◽  
Horizontal Tubes ◽  
Temperature Distributions ◽  
Constant Rate ◽  
Full Solution ◽  
Laminar Convection

Numerical prediction methods for calculating velocity and temperature distributions in heated ducts can be made accurately but are time consuming. The paper shows possible simplifications, including the neglect of the buoyancy term, and the resultant accuracy attained. The case studied is for laminar flow, entry length heat transfer in horizontal tubes with constant rate heat flux. Comparison is made between experimental results, a full solution and an approximation based on a series of truncated versions of the fully developed temperature profile. Calculations are made both with and without variation of thermophysical properties with temperature.

Internal Laminar Heat Transfer With Gas-Property Variation

1971 ◽  
Vol 93 (4) ◽  
pp. 432-440 ◽  
Author(s):  
T. B. Swearingen ◽  
D. M. McEligot
Keyword(s):  
Heat Transfer ◽  
Numerical Solutions ◽  
Bulk Temperature ◽  
Parallel Plates ◽  
Temperature Dependent ◽  
Property Variation ◽  
Constant Wall Heat Flux ◽  
Mixed Mean ◽  
Two Dimensional Flow ◽  
Temperature Dependent Properties

The results of a numerical investigation of internal laminar heat transfer to a gas with temperature-dependent properties are reported. In this investigation the authors obtained numerical solutions to the coupled partial differential equations of continuity, energy, momentum, and integral continuity describing the two-dimensional flow of perfect gas between heated parallel plates. A sequence of numerical solutions was obtained for the case of constant wall heat flux with a fully developed velocity profile at the start of the heated section and pure forced convection. The results may be summarized by Nu=Nuconst.prop.+0.024(Q+)0.3(Gzm)0.75f·Rem=24(Twall/Tbulk) where the subscript “m” refers to properties evaluated at the local mixed-mean (or bulk) temperature.

Analysis of Updated SuperCritical Water Heat Transfer Correlations for Vertical Bare Tubes

2010 ◽  
Author(s):  
Sarah Mokry ◽  
Sahil Gupta ◽  
Amjad Farah ◽  
Krysten King ◽  
Igor Pioro
Keyword(s):  
Heat Transfer ◽  
Supercritical Water ◽  
Thermophysical Properties ◽  
Vertical Tube ◽  
Large Set ◽  
Conservative Approach ◽  
Bulk Fluid ◽  
Heat Transfer Correlations ◽  
Vertical Tubes ◽  
Bare Tube

In support of developing SuperCritical Water-cooled Reactors (SCWRs), studies are currently being conducted for heat-transfer at supercritical conditions. This paper presents an analysis of heat-transfer to SuperCritical Water (SCW) flowing in bare vertical tubes as a first step towards thermohydraulic calculations in a fuel-channel. A large set of experimental data, obtained in Russia, was analyzed. Two updated heat-transfer correlations for forced convective heat transfer in the normal heat transfer regime to SCW flowing in a bare vertical tube were developed. It is expected that the next generation of water-cooled nuclear reactors will operate at supercritical pressures (∼25 MPa) with high coolant temperatures (350–625°C). Currently, there are no experimental datasets for heat transfer from power reactor fuel bundles to the fuel coolant (water) available in open literature. Therefore, for preliminary calculations, heat-transfer correlations obtained with bare tube data can be used as a conservative approach. The analyzed experimental dataset was obtained for SCW flowing upward in a 4-m-long vertical bare tube. The data was collected at pressures of about 24 MPa for several combinations of wall and bulk-fluid temperatures that were below, at, or above the pseudocritical temperature. The values for mass flux ranged from 200–1500 kg/m2s, for heat flux up to 1250 kW/m2 and inlet temperatures from 320–350°C. The Mokry et al. correlation was developed as a Dittus-Boelter-type correlation, with thermophysical properties taken at bulk-fluid temperatures. Alternatively, the Gupta et al. correlation was developed based on the Swenson et al. approach, where the majority of thermophysical properties are taken at the wall temperature. An analysis of the two updated heat-transfer correlations is presented in this paper. Both correlations demonstrated a good fit (±25% for Heat Transfer Coefficient (HTC) values and ±15% for calculated wall temperatures) for the analyzed dataset. Thus, these correlations can be used for preliminary HTC calculations in SCWR fuel bundles as a conservative approach, for SCW heat exchangers, for future comparisons with other independent datasets and for the verification of computer codes for SCWR core thermohydraulics.

Detailed Description of the Fluidized Bed Mixing and Heat Transfer by Means of Eulerian Multi-Fluid Numerical Simulations

2020 ◽  
Author(s):  
Muhammad Ali Uzair ◽  
Francesco Fornarelli ◽  
Sergio Mario Camporeale ◽  
Marco Torresi
Keyword(s):  
Heat Transfer ◽  
Fluidized Bed ◽  
Granular Flow ◽  
Fluid Model ◽  
Gas Velocity ◽  
Uniform Temperature ◽  
Temperature Dependent ◽  
Commercial Code ◽  
Temperature Dependent Properties ◽  
Superficial Gas Velocity

Abstract The hydrodynamics and heat transfer of a binary mixture of sand and biomass in a fluidized bed have been numerically investigated. The Eulerian multi-fluid model MFM incorporating kinetic theory of granular flow was used to numerically investigate fluidized bed. A commercial code has been used together with user-defined functions to correctly predict the hydrodynamics and the heat transfer. Numerical results were validated against the experiment in terms of pressure drop across the bed and concentration of biomass at different heights of the bed. Influence of additional parameters, such as superficial gas velocity and sand sizes on hydrodynamics were investigated. Additionally, heat transfer in the fluidized bed was also studied highlighting the influence of the temperature dependent properties of air on the results. The present results reveal that better mixing is achieved for smallest sand size, also promoting more uniform temperature of biomass.

Analysis of Heat Transfer in a Cylindrical Spine Fin with Variable Thermal Properties

2018 ◽  
Vol 387 ◽  
pp. 10-22 ◽  
Author(s):  
Nkejane Fallo ◽  
Raseelo Joel Moitsheki ◽  
Oluwole Daniel Makinde
Keyword(s):  
Heat Transfer ◽  
Differential Equation ◽  
Thermal Conductivity ◽  
Numerical Solutions ◽  
Three Dimensional ◽  
Numerical Techniques ◽  
Temperature Dependent ◽  
Approximate Analytical Solutions ◽  
Differential Transform ◽  
The Heat Transfer Coefficient

In this paper we analyse the heat transfer in a cylindrical spine fin. Here, both the heat transfer coefficient and thermal conductivity are temperature dependent. The resulting 2+1 dimension partial differential equation (PDE) is rendered nonlinear and difficult to solve exactly, particularly with prescribed initial and boundary conditions. We employ the three dimensional differential transform methods (3D DTM) to contract the approximate analytical solutions. Furthermore we utilize numerical techniques to determine approximate numerical solutions. The effects of parameters, appearing in the boundary value problem (BVP), on temperature profile of the fin are studied.

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