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Heat transfer of viscous fluid in a vertical channel sandwiched between nanofluid porous zones

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Abstract

Mixed convection in vertical parallel channels is analyzed with the viscous fluid sandwiched between nanofluids within porous material filled in a vertical channel. The concept of single-phase transport of nanofluids is employed to define the nanofluid flow and heat transfer and the Darcy approach is incorporated to describe the circulation within the porous material. Formulated ordinary differential equations which are non-linear and coupled along with the corresponding boundary and interface conditions are solved by the regular perturbation method. The main objective is to investigate the effects of the Grashof and Brinkman numbers, solid volume fraction, porous parameter on the velocity and temperature fields. Results are shown in the graphical and tabular form. The physical characteristics governing the flow such as skin friction and rate of heat transfer are also investigated considering five different materials of nanoparticles.

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Abbreviations

Br :

Brinkman number \(\left( {Br = \frac{{\mu_{{\text{f}}}^{3} }}{{\rho_{{\text{f}}}^{2} h^{2} \left( {T_{{{\text{w1}}}} - T_{\rm w2} } \right)k_{{\text{f}}} }}} \right)\)

G :

Acceleration due to gravity

Gr :

Grashof number \(\left( {Gr = \frac{{g\beta_{{\text{f}}} \left( {T_{{{\text{w1}}}} - T_{{{\text{w2}}}} } \right)\;h^{3} }}{{\upsilon_{{\text{f}}}^{2} }}} \right)\)

h :

Channel width

k :

Thermal conductivity

P :

Non-dimensional pressure \(\left( {P = - \frac{{\rho_{{\text{f}}} h^{3} }}{{\mu_{{\text{f}}}^{2} }} \;\frac{\partial p}{{\partial x}}} \right)\)

T :

Temperature

u :

Dimensional velocity

y :

Space coordinate

β :

Thermal expansion coefficient

θ :

Dimensionless temperature

μ :

Dynamic viscosity

ν :

Kinematic viscosity

ρ :

Density

σ :

Porous parameter \(\left( {\sigma = {h \mathord{\left/ {\vphantom {h {\sqrt \kappa }}} \right. \kern-\nulldelimiterspace} {\sqrt \kappa }}} \right)\)

τ :

Skin friction

ϕ :

Volume fraction of the solid nanoparticles

nf :

Nanofluid

f :

Base fluid

s :

Solid nanoparticles

i :

Quantities for the fluids in region-I, region-II and region-III

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Acknowledgements

This work of Mikhail A. Sheremet was supported by the Regional Scientific and Educational Mathematical Centre of Tomsk State University.

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Authors and Affiliations

  1. Department of Mathematics, Gulbarga University, Kalaburgi, Karnataka, 585106, India

    Jawali C. Umavathi

  2. Regional Scientific and Educational Mathematical Centre, Tomsk State University, Tomsk, Russia, 634050

    Mikhail A. Sheremet

Authors
  1. Jawali C. Umavathi
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Correspondence to Mikhail A. Sheremet.

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Umavathi, J.C., Sheremet, M.A. Heat transfer of viscous fluid in a vertical channel sandwiched between nanofluid porous zones. J Therm Anal Calorim 144, 1389–1399 (2021). https://doi.org/10.1007/s10973-020-09664-1

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