Transient Natural Convection in an Annulus with Thermal Radiation

Basant Kumar Jha,Isah Bala Yabo,Jeng-Eng Lin

doi:10.4236/am.2017.89100

Basant Kumar Jha, Isah Bala Yabo + Show 1 more

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https://doi.org/10.4236/am.2017.89100

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Abstract

The interaction of transient fully developed natural convection flow with thermal radiation inside a vertical annulus is analyzed both analytically and numerically. The Rosseland approximation is used to describe the radiative heat flux in the energy equation. The mathematical model capturing the present physical situation is highly non-linear due to the presence of radiation effect. The solution of transient model is obtained by implicit finite difference method. To check accuracy of the numerical solution, steady state solution for energy and momentum equations are derived analytically using perturbation series method. Skin-friction and Nusselt number at the outer surface of inner cylinder as well as inner surface of the outer cylinder are obtained. Selected sets of graphical results illustrating the effects of various controlling parameters involved in the problem on flow formation are discussed.

Highlights

Numerical prediction of natural convection heat transfer in horizontal annulus where the inner cylinder is hotter than outer was reported by [2]. [3] investigated natural convection of gasses in a horizontal annulus, where the inner cylinder is heated by the application of a constant heat flux and the outer cylinder is isothermally cooled. [4] conducted an investigation on natural convection in concentric and eccentric horizontal cylindrical annuli with mixed boundary conditions
The numerical solution is obtained by implicit finite difference method for transient situation
2) During transient state, the maximum value of velocity occurs at smaller radial distance from the outer surface of inner cylinder and decreases to zero asymptotically

Summary

Introduction

[14] discussed the effect of nanofluid on the natural convection heat transfer and fluid flow through an annular tube with an inner heat generating solid circular rod. [15] compiled a comprehensive theoretical study on natural convection heat transfer in nanofluid contained inside the horizontal annular space existing between two long concentric cylinder whose surface are maintained at different uniform temperatures, with primary scope to determine the main heat transfer features for various operating conditions, nanoparticle diameters, and solid-liquid combination. [20] studied numerically natural convection flow and heat transfer of Copper water nanofluid inside eccentric horizontal annulus while the inner and outer cylinder are kept at constant temperatures. [21] conducted an investigation on effect of static radial magnetic field on natural convection heat transfer in a horizontal cylindrical annulus enclosure filled with nanofluid using Boltzmann method (LBM) In [8], finite difference method in conjunction with least-squares scheme and experimental temperature data is used to predict the average heat transfer coefficient and fin efficiency on the fin of annular-fined tube. [9] carried out experimental investigation on heat transfer characteristics of Taylor-CouettePoiseuille flow in an annular channel by mounting longitudinal ribs on the rotating inner cylinder. [10] studied natural convection flow in a horizontal annulus enclosure with a transversely oscillating inner cylinder. [11] investigated transition of natural convection in an annulus between horizontal concentric cylinders theoretically by assuming two-dimensional and incompressible flow fields. [12] examined a numerical investigation on horizontal concentric annulus with open ends and conditions of either adiabatic or isothermal outer cylinder surface. [13] showed that dual steady state solutions exist above a critical Rayleigh number for free convective flows in a horizontal annulus with constant heat-flux wall. [14] discussed the effect of nanofluid on the natural convection heat transfer and fluid flow through an annular tube with an inner heat generating solid circular rod. [15] compiled a comprehensive theoretical study on natural convection heat transfer in nanofluid contained inside the horizontal annular space existing between two long concentric cylinder whose surface are maintained at different uniform temperatures, with primary scope to determine the main heat transfer features for various operating conditions, nanoparticle diameters, and solid-liquid combination. [16] conducted a numerical investigation of natural convection heat transfer in a semi-annulus enclosure filled with nanofluid using the control volume based finite element method. [17] developed and tested a discrete phase model for forced convection of nanofluids in a circular tube subjected to a uniform heat flux. [18] and [19] examined the role of magnetic field on natural convection flow of Nano-fluid using Lattice Boltzmann method. [20] studied numerically natural convection flow and heat transfer of Copper water nanofluid inside eccentric horizontal annulus while the inner and outer cylinder are kept at constant temperatures. [21] conducted an investigation on effect of static radial magnetic field on natural convection heat transfer in a horizontal cylindrical annulus enclosure filled with nanofluid using Boltzmann method (LBM)

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