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Heat transfer analysis on unsteady natural convection flow of silver nanofluid in a porous square cavity using local thermal non-equilibrium model

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Abstract

This article intends to explore the onset of free convection flow of silver nanofluid in an enclosed square cavity filled with saturated porous medium bounded by adiabatic horizontal walls and isothermal vertical walls at different temperatures using a two-temperature thermal non-equilibrium model. The flow is assumed to follow Darcy law. The governing boundary layer equations are obtained based on Boussinesq approximation and Darcy model. The governing equations for fluid flow are reduced to partial differential equations with the help of non-dimensional transformation. Peaceman–Rachford alternating direction implicit (ADI) scheme is employed to solve the transformed flow equations. The physical clarification of streamlines and isotherms for liquid and solid for pertinent flow parameters is discussed graphically. The physical parameter such as average Nusselt number for fluid and solid phase, for different parameters such as inter-phase heat transfer coefficient and modified conductivity ratio is presented through graphs as well. One of the important findings is that with smaller values of the Rayleigh number Ra the centrally arranged core vortex is formed in streamlines, while the isotherms of liquid and solid phases are stratified in vertical direction close to the vertical walls. Meanwhile, it is also perceived that the vortices expand with an increasing values of Rayleigh number along the horizontal direction.

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Abbreviations

X, Y :

Dimensionless Cartesian coordinates

x, y :

Cartesian coordinates (\(\mathrm {m}\))

V :

Darcian velocity vector

U, V :

Dimensionless Darcian velocity components

u, v :

Dimensional Darcian velocity components (\(\mathrm {ms^{-1}}\))

g :

Gravitational acceleration (\(\mathrm {ms^{-2}}\))

K :

Permeability of porous medium (\(\mathrm {m^{2}}\))

k :

Thermal conductivity (\(\mathrm {WK^{-1}m^{-1}}\))

h :

Volumetric heat transfer coefficient between solid and fluid (\(\mathrm {WK^{-1}m^{-3}}\))

T :

Temperature (\(\text {K}\))

\(T_{\text {h}}, T_{\text {c}}\) :

Temperature of the hot and cold walls (\(\text {K}\))

\(T_0\) :

Reference temperature (\(\text {K}\))

W :

Cavity length (\(\text {m}\))

t :

Time (\(\text {s}\))

Ra :

Rayleigh number

H :

Inter-phase heat transfer coefficient

\(q_r\) :

Radiation flux (\(\mathrm {Wm^{-2}}\))

\(R_D\) :

Radiation parameter

\(\bar{Nu}\) :

Average Nusselt number

\(\alpha\) :

Thermal diffusivity ratio (\(\mathrm {m^{2}s^{-1}}\))

\(\beta\) :

Coefficient of thermal expansion (\(\mathrm {K^{-1}}\))

\(\mu\) :

Dynamic viscosity (\(\mathrm {Kg m^{-1}s^{-1}}\))

\(\nu\) :

Kinematic viscosity (\(\mathrm {m^{2}s^{-1}}\))

\(\varepsilon\) :

Porosity

\(\psi\) :

Stream function

\(\tau\) :

Dimensionless time

\(\gamma\) :

Modified thermal conductivity ratio

\(\Gamma\) :

Thermal diffusivity ratio

\(\theta\) :

Dimensionless temperature

\(\rho\) :

Density of the fluid (\(\mathrm {Kg m^{-3}}\))

\(\rho c_{\text {p}}\) :

Heat capacitance

\(\rho \beta\) :

Buoyancy coefficient

\(\beta _1\) :

Relaxation parameter

c :

Cold

h :

Hot

nf:

Nanofluid

f :

Fluid

s:

Solid matrix

i, j :

Mesh points in X and Y directions

g, l :

Maximum number of mesh points in X and Y directions

n :

Time step

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Authors and Affiliations

  1. Department of Applied Mathematics, Indian Institute of Technology (Indian School of Mines), Dhanbad, 826004, India

    R Kumar & G S Seth

  2. Department of Mathematics, GITAM School of Science, GITAM University, Bengaluru, 562163, Karnataka, India

    A Bhattacharyya

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  1. R Kumar
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Correspondence to R Kumar.

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Kumar, R., Bhattacharyya, A. & Seth, G.S. Heat transfer analysis on unsteady natural convection flow of silver nanofluid in a porous square cavity using local thermal non-equilibrium model. Indian J Phys 96, 2065–2078 (2022). https://doi.org/10.1007/s12648-021-02137-7

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