Natural Convection Along Slender Vertical Cylinders With Variable Surface Temperature

1988 ◽  
Vol 110 (1) ◽  
pp. 103-108 ◽  
Author(s):  
H. R. Lee ◽  
T. S. Chen ◽  
B. F. Armaly
Keyword(s):  
Natural Convection ◽  
Wall Temperature ◽  
Spline Interpolation ◽  
Boundary Layer Equations ◽  
Nusselt Numbers ◽  
Variable Surface ◽  
Wide Range ◽  
Prandtl Numbers ◽  
Spline Interpolation Technique ◽  
Vertical Cylinders

Natural convection in laminar boundary layers along slender vertical cylinders is analyzed for the situation in which the wall temperature Tw(x) varies arbitrarily with the axial coordinate x. The governing boundary layer equations along with the boundary conditions are first cast into a dimensionless form by a nonsimilar transformation and the resulting system of equations is then solved by a finite difference method in conjunction with the cubic spline interpolation technique. As an example, numerical results were obtained for the case of Tw(x) = T∞ + axn, a power-law wall temperature variation. They cover Prandtl numbers of 0.1, 0.7, 7, and 100 over a wide range of values of the surface curvature parameter. Representative local Nusselt number as well as velocity and temperature profiles are presented. Correlation equations for the local and average Nusselt numbers are also given.

scholarly journals A Multiple-Grid Lattice Boltzmann Method for Natural Convection under Low and High Prandtl Numbers

Fluids ◽  
2021 ◽  
Vol 6 (4) ◽  
pp. 148
Author(s):  
Seyed Amin Nabavizadeh ◽  
Himel Barua ◽  
Mohsen Eshraghi ◽  
Sergio D. Felicelli
Keyword(s):  
Natural Convection ◽  
Lattice Boltzmann Method ◽  
Lattice Boltzmann ◽  
Large Scale ◽  
Bgk Model ◽  
Flow Equations ◽  
Wide Range ◽  
Prandtl Numbers ◽  
Boltzmann Method ◽  
Benchmark Solutions

A multi-distribution lattice Boltzmann Bhatnagar–Gross–Krook (BGK) model with a multiple-grid lattice Boltzmann (MGLB) model is proposed to efficiently simulate natural convection over a wide range of Prandtl numbers. In this method, different grid sizes and time steps for heat transfer and fluid flow equations are chosen. The model is validated against natural convection in a square cavity, since extensive benchmark solutions are available for that problem. The proposed method can resolve the computational difficulty in simulating problems with very different time scales, in particular, when using extremely low or high Prandtl numbers. The technique can also enhance computational speed and stability while keeping the simplicity of the BGK method. Compared with the conventional lattice Boltzmann method, the simulation time can be reduced up to one-tenth of the time while maintaining the accuracy in an acceptable range. The proposed model can be extended to other lattice Boltzmann collision models and three-dimensional cases, making it a great candidate for large-scale simulations.

Effect of 3D Diffusion Over Vertical Thin Rectangular Geometries in Natural Convection Heat Transfer

2006 ◽  
Author(s):  
Mustafa Gursoy ◽  
Mehmet Arik ◽  
Tunc Icoz ◽  
Michael Yovanovich ◽  
Theodorian Borca-Tasciuc
Keyword(s):  
Heat Transfer ◽  
Natural Convection ◽  
Fluid Motion ◽  
Heat Removal ◽  
Air Entrainment ◽  
Published Data ◽  
Diffusion Term ◽  
Nusselt Numbers ◽  
Wide Range ◽  
Rayleigh Numbers

Natural convection over vertical plates is a very well known problem in heat transfer. There are many available correlations to predict Nusselt numbers for a wide range of Rayleigh numbers. These benchmark studies on natural convection for vertical plates were conducted on rather large surfaces leading to Rayleigh numbers in the range of 0.1 to 109. In natural convection the sole driving force of fluid motion is the change in fluid density, when the diffusive limit is small compared to convective heat transfer. However, conduction to air, as well as air entrainment from sides also contributes to the heat removal from heater surfaces. An experimental study has been carried out with small and large heaters compared to published data for 2×103<Ra<4×107. Square surfaces of 12.5 and 25.4 mm, and rectangular heaters of sizes 25.4×101.6 and 25.4×203.2 mm were tested for a range of heat inputs such that the surface temperatures are controlled between 30 °C and 80 °C. It is found that published correlations underpredict the Nusselt numbers as much as 20%. It is observed that widely known correlations underpredict the experimental values since the 3D conduction and side air drifts on heat transfer are not accounted for in these correlations. However, the cuboid model which includes the 3D diffusion term showed much better agreement with the experimental results.

Natural Convection Along Slender Vertical Cylinders With Variable Surface Heat Flux

1989 ◽  
Vol 111 (4) ◽  
pp. 1108-1111 ◽  
Author(s):  
J. J. Heckel ◽  
T. S. Chen ◽  
B. F. Armaly
Keyword(s):  
Heat Flux ◽  
Natural Convection ◽  
Surface Heat Flux ◽  
Surface Heat ◽  
Variable Surface ◽  
Vertical Cylinders

scholarly journals Natural Convection Flow from an Isothermal Sphere with Temperature Dependent Thermal Conductivity

1970 ◽  
Vol 2 (2) ◽  
pp. 53-64 ◽  
Author(s):  
Md Mamun Molla ◽  
Azad Rahman ◽  
Lineeya Tanzin Rahman
Keyword(s):  
Heat Transfer ◽  
Thermal Conductivity ◽  
Natural Convection ◽  
Convection Flow ◽  
Temperature Dependent ◽  
Boundary Layer Equations ◽  
Wide Range ◽  
Conductivity Parameter ◽  
Marine Engineering ◽  
Temperature Dependent Thermal Conductivity

Laminar free convection flow from an isothermal sphere immersed in a fluid with thermal conductivity proportional to linear function of temperature has been studied. The governing boundary layer equations are transformed into a non-dimensional form and the resulting nonlinear system of partial differential equations is reduced to local non-similarity equations, which are solved numerically by very efficient implicit finite difference method together with Keller box scheme. Numerical results are presented by velocity and temperature distribution of the fluid as well as heat transfer characteristics, namely the heat transfer rate and the skin-friction coefficients for a wide range of thermal conductivity parameter γ (= 0.0, 0.5, 1.0, 2.0, 3.0, 5.0) and the Prandtl number Pr (= 0.7, 1.0, 3.0, 5.0, 7.0).   Keywords: Natural convection, temperature dependent thermal conductivity, isothermal sphere.    doi:10.3329/jname.v2i2.1872  Journal of Naval Architecture and Marine Engineering 2(2005) 53-64

Laminar Natural Convection From Isothermal Vertical Cylinders: Revisting a Classical Subject

2013 ◽  
Vol 135 (2) ◽  
Author(s):  
Jerod C. Day ◽  
Matthew K. Zemler ◽  
Matthew J. Traum ◽  
Sandra K. S. Boetcher
Keyword(s):  
Heat Transfer ◽  
Natural Convection ◽  
Convection Heat Transfer ◽  
Vertical Cylinder ◽  
Vertical Surface ◽  
Nusselt Numbers ◽  
Recent Interest ◽  
Laminar Natural Convection ◽  
Vertical Cylinders ◽  
Classical Subject

Although an extensively studied classical subject, laminar natural convection heat transfer from the vertical surface of a cylinder has generated some recent interest in the literature. In this investigation, numerical experiments are performed to determine average Nusselt numbers for isothermal vertical cylinders (102<RaL<109,0.1<L/D<10, and Pr = 0.7) situated on an adiabatic surface in a quiescent ambient environment. Average Nusselt numbers for various cases will be presented and compared with commonly used correlations. Using Nusselt numbers for isothermal tops to approximate Nusselt numbers for heated tops will also be examined. Furthermore, the limit for which the heat transfer results for a vertical flat plate may be used as an approximation for the heat transfer from a vertical cylinder will be investigated.

scholarly journals Conjugate Effects of Heat and Mass Transfer on Natural Convection Flow Across an Isothermal Horizontal Circular Cylinder With Chemical Reaction

2007 ◽  
Vol 12 (2) ◽  
pp. 191-201 ◽  
Author(s):  
Md. A. Hye ◽  
Md. M. Molla ◽  
M. A. H. Khan
Keyword(s):  
Boundary Layer ◽  
Natural Convection ◽  
Chemical Reaction ◽  
Transfer Rate ◽  
Convection Flow ◽  
Natural Convection Flow ◽  
Species Concentration ◽  
Local Skin ◽  
Boundary Layer Equations ◽  
Wide Range

Natural convection flow across an isothermal cylinder immersed in a viscous incompressible fluid in the presence of species concentration and chemical reaction has been investigated. The governing boundary layer equations are transformed into a system of non-dimensional equations and the resulting nonlinear system of partial differential equations is reduced to a system of local non-similarity boundary layer equations, which is solved numerically by a very efficient implicit finite difference method together with the Keller-box scheme. Numerical results are presented by the velocity, temperature and species concentration profiles of the fluid as well as the local skin-friction coefficient, local heat transfer rate and local species concentration transfer rate for a wide range of chemical reaction parameter γ (γ = 0.0, 0.5, 1.0, 2.0, 4.0), buoyancy ratio parameter N (N = −1.0, −0.5, 0.0, 0.5, 1.0), Schmidt number Sc (Sc = 0.7, 10.0, 50.0, 100.0) andPrandtl number Pr (Pr = 0.7, 7.0).

scholarly journals Fem Simulation of Triple Diffusive Natural Convection Along Inclined Plate in Porous Medium: Prescribed Surface Heat, Solute and Nanoparticles Flux

2017 ◽  
Vol 22 (4) ◽  
pp. 883-900 ◽  
Author(s):  
M. Goyal ◽  
R. Goyal ◽  
R. Bhargava
Keyword(s):  
Porous Medium ◽  
Natural Convection ◽  
Volume Fraction ◽  
Fem Simulation ◽  
Lewis Number ◽  
Vertical Surface ◽  
Inclined Plate ◽  
Cross Diffusion ◽  
Boundary Layer Equations ◽  
Wide Range

Abstract In this paper, triple diffusive natural convection under Darcy flow over an inclined plate embedded in a porous medium saturated with a binary base fluid containing nanoparticles and two salts is studied. The model used for the nanofluid is the one which incorporates the effects of Brownian motion and thermophoresis. In addition, the thermal energy equations include regular diffusion and cross-diffusion terms. The vertical surface has the heat, mass and nanoparticle fluxes each prescribed as a power law function of the distance along the wall. The boundary layer equations are transformed into a set of ordinary differential equations with the help of group theory transformations. A wide range of parameter values are chosen to bring out the effect of buoyancy ratio, regular Lewis number and modified Dufour parameters of both salts and nanofluid parameters with varying angle of inclinations. The effects of parameters on the velocity, temperature, solutal and nanoparticles volume fraction profiles, as well as on the important parameters of heat and mass transfer, i.e., the reduced Nusselt, regular and nanofluid Sherwood numbers, are discussed. Such problems find application in extrusion of metals, polymers and ceramics, production of plastic films, insulation of wires and liquid packaging.

Mixed Convection Along Vertical Cylinders and Needles With Uniform Surface Heat Flux

1987 ◽  
Vol 109 (3) ◽  
pp. 711-716 ◽  
Author(s):  
S. L. Lee ◽  
T. S. Chen ◽  
B. F. Armaly
Keyword(s):  
Heat Flux ◽  
Mixed Convection ◽  
Surface Heat Flux ◽  
Spline Interpolation ◽  
Surface Heat ◽  
Smooth Transition ◽  
Nusselt Numbers ◽  
Buoyancy Parameter ◽  
Curvature Parameter ◽  
Vertical Cylinders

Mixed convection along vertical cylinders and needles with uniform surface heat flux is investigated for the entire mixed convection regime. A single modified buoyancy parameter χ and a single curvature parameter Λ are employed in the analysis such that a smooth transition from pure forced convection (χ = 1) to pure free convection (χ = 0) can be accomplished. For large values of the curvature parameter and/or Prandtl number, the governing transformed equations become stiff. Thus, a numerically stable finite-difference method is employed in the numerical solution in conjunction with the cubic spline interpolation scheme to overcome the difficulties that arise from the stiffness of the equations. Local Nusselt numbers are presented for 0.1 ≤ Pr ≤ 100 that cover 0 ≤ χ ≤ 1 (∞ ≥ Ωχ ≥ 0) and 0 ≤ Λ ≤ 50. For needles (Λ ≥ 5), the local Nusselt numbers Nuχ/(Reχ1/2 + Grχ*1/5) are found to be nearly independent of the buoyancy parameter χ. Correlation equations for the local Nusselt numbers are also presented.

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