Thermal Enhancement of Radiating Magneto-Nanoliquid with Nanoparticles Aggregation and Joule Heating: A Three-Dimensiona
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RESEARCH ARTICLE-PHYSICS
Thermal Enhancement of Radiating Magneto-Nanoliquid with Nanoparticles Aggregation and Joule Heating: A Three-Dimensional Flow K. Swain1 · B. Mahanthesh2 Received: 11 April 2020 / Accepted: 17 September 2020 © King Fahd University of Petroleum & Minerals 2020
Abstract This article studies the effect of nanoparticle aggregation on the 3D flow of titanium nanoliquid based on ethylene glycol (C2 H6 O2 − TiO2 ) due to an exponentially elongated surface. Thermal analysis is carried out considering linear thermal radiation, Joule heating, and mechanisms of the heat source/sink, while the aspect of the homogeneous single-order chemical reaction is included in the analysis of the solute. The variable magnetic field is also accounted. The modified Maxwell model (Maxwell–Bruggeman) is implemented to estimate the effective conductivity of the nanoliquid. The displayed equations are moderated in quantities without dimensions. The 2-point nonlinear boundary value problem (BVP) is solved by the shooting procedure. The importance of effective parameters is described through graphs. Numerical data are presented to study the friction factor, the heat transfer rate, and the mass transfer rate. It has been established that the aggregation of nanoparticles significantly improves the thermal field. Furthermore, the effect of magnetism is more in ordinary fluid than in nanofluid. Keywords Titania nanoparticles · Aggregation nanoparticles · Joule heating · Nanoliquid · Chemical reaction
List of symbols x, y, z u, v, w μn f νn f ν f ρc p n f ρc p f ρc p s k nf kf ks ρn f
B
Cartesian coordinate system (m) Velocity components along with x, y, and z directions, respectively (m/s) The viscosity of the nanofluid (kg/ms) The kinetic velocity of the nanofluid (m2 /s) Kinematic viscosity of the base fluid (m2 /s) Specific heat capacitance of the nanofluid (J/kg K) Heat capacity of foundation liquid (J/kg K) Heat capability of solid nanoparticle (J/kg K) Thermal conductivity of the nanofluid (m2 /s) Thermal conductivity of the base fluid (m2 /s) Thermal conductivity of the solid nanoparticle (m2 /s) The density of nanofluid (kg/m3 )
B. Mahanthesh [email protected]
1
Department of Mathematics, Gandhi Institute for Technology, Bhubaneswar, Odisha 752054, India
2
Department of Mathematics, CHRIST (Deemed to be University), Bengaluru, Karnataka 560029, India
ρf ρs Ec Pr Kc* Kc Q* Sc DB δ Q A A* R T Tw T∞ C φ C∞ Cw f θ Φ
The density of the base fluid (kg/m3 ) The density of solid nanoparticle (kg/m3 ) Eckert number Prandtl number The reaction rate of the solute Chemical reaction parameter Heat source/sink coefficient Schmidt number Brownian motion coefficient (m2 /s) Ratio parameter Heat source/sink parameter Temperature exponent Concentration exponent Radiation parameter Temperature K (°C) The variable temperature at the sheet Free-stream temperature K (°C) Concentration The dimensionless nanoparticle volume fraction Free-stream concentration Variable concentration at the sheet Dimensionle
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