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Control of buoyant flow and heat dissipation in a porous annular chamber using a thin baffle

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Abstract

This paper reports the numerical simulations on buoyant thermal transfer inside the finite porous cylindrical annular region with a thin circular baffle attached to inner cylinder. The main objective of this investigation is to provide a detailed impact of baffle on flow and heat transport rates due to the direct relevance of this problem to the design of heat exchangers. The side walls of annular enclosure are maintained at uniform, but different temperatures, while the top and bottom walls are insulated. The Brinkman-extended Darcy model is adopted for the momentum equations, and simulations of the governing PDEs are performed using the ADI and SLOR algorithms. The predictions from the present simulations detected that the size and position of baffle has predominant impact on buoyant flow and thermal transport characteristics. It has been detected that the thermal dissipation rates could be enhanced by positioning the baffle near the upper boundary, while increasing the baffle length leads to the reduction of thermal transport. The size and location of baffle emerges out as an important quantity in regulating the global thermal transfer through modifying the flow regimes in the annular geometry. Interestingly, the magnitude of flow circulation enhances with an increase in Rayleigh and Darcy numbers for any baffle length and position.

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Abbreviations

A:

Aspect ratio

cp :

Specific heat at constant pressure

D:

Width of the annulus (m)

Da:

Darcy number

g:

Acceleration due to gravity (m/s2)

H:

Height of the annulus (m)

h:

Dimensional location of baffle (m)

K:

Permeability of the porous medium (m2)

k:

Thermal conductivity (W/(m K))

l :

Dimensional length of baffle (m)

L:

Dimensionless location of the baffle

\(\overline{Nu}\) :

Average Nusselt number

p:

Fluid pressure (Pa)

Pr:

Prandtl number

Ra:

Thermal Rayleigh number

RaD :

Darcy-Rayleigh number \(\left( {Ra_{D} = \frac{{gK\beta_{T} (\theta_{h} - \theta_{c} )D^{2} }}{\upsilon k\alpha }} \right)\)

T:

Dimensionless temperature

t*:

Dimensional time (s)

t:

Dimensionless time

(ri, ro):

Radius of inner and outer cylinders (m)

(r, z):

Dimensional radial and axial co-ordinates (m)

(R, Z):

Dimensionless radial and axial co-ordinates

(u, w):

Dimensional velocity components in (r, z) directions (m/s)

(U, W):

Dimensionless velocity components in (R, Z) directions

α:

Thermal diffusivity (m2/s)

β:

Thermal expansion coefficient (1/K)

ε:

Dimensionless length of baffle

ζ:

Dimensionless vorticity

θ:

Dimensional temperature (K)

λ:

Radius ratio

υ:

Kinematic viscosity (m2/s)

ρ:

Fluid density (kg/m3)

ϕ:

Porosity of the porous medium

ψ:

Dimensionless stream function

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Acknowledgements

BVP expressed gratitude to the Management and to VTU, Belgaum, India. MS acknowledges the funding support by the VGST, GoK, under Grant Number KSTePS/VGST-KFIST (L1)/2017. YD was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIP) (No. NRF-2019R1A2B5B01070579).

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Authors and Affiliations

  1. Department of Mathematics, BMS Institute of Technology and Management, Bengaluru, 560064, India

    B. V. Pushpa

  2. Department of Mathematics, KNU-Center for Nonlinear Dynamics, Kyungpook National University, Daegu, 41566, Republic of Korea

    Younghae Do

  3. Faculty of Mathematics, General Requirements Department, University of Technology and Applied Sciences (CAS-Ibri), P. O. Box 14, 516, Ibri, Oman

    M. Sankar

  4. Department of Mathematics, School of Engineering, Presidency University, Bengaluru, 560064, India

    M. Sankar

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  1. B. V. Pushpa
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  2. Younghae Do
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  3. M. Sankar
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Contributions

MS formulated the problem and designed code. BVP performed numerical simulations. YD and BVP analyzed the simulations and prepared the manuscript.

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Correspondence to M. Sankar.

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Pushpa, B.V., Do, Y. & Sankar, M. Control of buoyant flow and heat dissipation in a porous annular chamber using a thin baffle. Indian J Phys 96, 1767–1781 (2022). https://doi.org/10.1007/s12648-021-02120-2

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  • DOI: https://doi.org/10.1007/s12648-021-02120-2

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