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Heat transport of hybrid nanomaterial in an annulus with quadratic Boussinesq approximation

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Abstract

The convective heat transfer of hybrid nanoliquids within a concentric annulus has wide engineering applications such as chemical industries, solar collectors, gas turbines, heat exchangers, nuclear reactors, and electronic component cooling due to their high heat transport rate. Hence, in this study, the characteristics of the heat transport mechanism in an annulus filled with the Ag-MgO/H2O hybrid nanoliquid under the influence of quadratic thermal radiation and quadratic convection are analyzed. The non-uniform heat source/sink and induced magnetic field mechanisms are used to govern the basic equations concerning the transport of the composite nanoliquid. The dependency of the Nusselt number on the effective parameters (thermal radiation, nonlinear convection, and temperature-dependent heat source/sink parameter) is examined through sensitivity analyses based on the response surface methodology (RSM) and the face-centered central composite design (CCD). The heat transport of the composite nanoliquid for the space-related heat source/sink is observed to be higher than that for the temperature-related heat source/sink. The mechanisms of quadratic convection and quadratic thermal radiation are favorable for the momentum of the nanoliquid. The heat transport rate is more sensitive towards quadratic thermal radiation.

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Abbreviations

a, b :

radii of the inner and outer cylinders, m

H :

non-dimensional induced magnetic field along the z-direction

u′ :

velocity of the fluid along the axial direction, m/s

J θ :

induced current density along the θ-direction

\(H_{{z^\prime }}^\prime ,\) :

induced magnetic field in the z′-direction

\(H_0^\prime ,\) :

constant magnetic strength, T

g :

acceleration due to gravity, m·s−2

u :

non-dimensional velocity along the axial direction

Ha :

Hartman number

r′, θ′,z′ :

cylindrical coordinates

r :

axis in the cylindrical coordinates

c p :

specific heat, J·kg−1·K−1

k :

thermal conductivity, W·m−1·K−1

N u1 :

Nusselt number of the inner cylinder

Nu λ :

Nusselt number of the outer cylinder

T :

temperature, K

T′ f :

ambient temperature, K

U :

characteristic velocity of the fluid, m/s

P :

pressure, Pa

R t :

thermal radiation parameter

A* :

space-related heat source/sink parameter

\(T_w^\prime ,\) :

temperature at the outer surface of the inner cylinder, K

B* :

temperature-related heat source/sink parameter.

α :

nonlinear convection parameter

η :

magnetic diffusivity

β :

thermal expansion coefficient, K−1

ϕ :

total volume concentration of Ag and MgO

λ :

radius ratio

μ :

dynamic viscosity, kg·m·s−1

ρ :

density, kg·m−3

ν :

kinematic viscosity, m2·s−1

τ 1 :

skin friction coefficient at the inner cylinder

τ λ :

skin friction coefficient at the outer cylinder

θ w :

temperature ratio parameter.

hnl:

hybrid nanoliquid

bl:

base liquid

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Acknowledgements

The authors are grateful to the Management, CHRIST (Deemed to be University), Bangalore, India for supporting our research work. The authors are also grateful to the editors and reviewers for their most valuable comments.

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  1. Department of Mathematics, CHRIST (Deemed to be University), Bangalore, 560029, Karnataka, India

    K. Thriveni & B. Mahanthesh

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  1. K. Thriveni
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  2. B. Mahanthesh
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Correspondence to B. Mahanthesh.

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Thriveni, K., Mahanthesh, B. Heat transport of hybrid nanomaterial in an annulus with quadratic Boussinesq approximation. Appl. Math. Mech.-Engl. Ed. 42, 885–900 (2021). https://doi.org/10.1007/s10483-021-2739-6

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  • DOI: https://doi.org/10.1007/s10483-021-2739-6

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