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# Paired Quasi-Linearization Analysis of Heat Transfer in Unsteady Mixed Convection Nanofluid Containing Both Nanoparticles and Gyrotactic Microorganisms Due to Impulsive Motion

[+] Author and Article Information
S. S. Motsa

Professor
School of Mathematics, Statistics and Computer Science,
University of KwaZulu-Natal,
Pietermaritzburg X01 Scottsville 3209, South Africa
e-mail: sandilemotsa@gmail.com

I. L. Animasaun

Department of Mathematical Sciences,
Federal University of Technology,
Akure P.M.B. 704, Nigeria
e-mail: anizakph2007@gmail.com;
ilanimasaun@futa.edu.ng

1Corresponding author.

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received January 30, 2016; final manuscript received June 28, 2016; published online July 27, 2016. Assoc. Editor: Andrey Kuznetsov.

J. Heat Transfer 138(11), 114503 (Jul 27, 2016) (8 pages) Paper No: HT-16-1043; doi: 10.1115/1.4034039 History: Received January 30, 2016; Revised June 28, 2016

## Abstract

This paper presents the motion of unsteady gravity-induced nanofluid flow containing gyrotactic micro-organisms along downward vertical convectively heated surface subject to passively controlled nanofluid. Considering the influence of temperature on the dynamic viscosity during convection and nature of thermal conductivity during heat conduction processes, these thermophysical properties are treated as linear functions of temperature. The governing equations are nondimensionalized by using suitable similarity transformation. The dimensionless nonlinear coupled PDEs are solved using a new pseudo-spectral technique called paired quasi-linearization method (PQLM). Convergence tests and residual error analysis are also presented to validate the accuracy, solution error, and computational convergence. The proposed PQLM yields accurate results which are obtained after a very few iterations. Minimum coefficients of $(ξ/xRex)Shx$ with Sc are obtained at final steady stage.

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## References

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## Figures

Fig. 1

Physical sketch and coordinate system

Fig. 2

Solution error norms (Ef, Eθ, Eϕ, and Ew) against iterations

Fig. 6

Effect of increasing time on f′(η,ξ)

Fig. 7

Effect of increasing time on w(η, ξ)

Fig. 8

Effect of increasing ω on f′(ξ=0.5,η)

Fig. 9

Effect of decreasing ω on f′(ξ=0.5,η)

Fig. 10

Effect of Rb on f′(ξ=0.5,η)

Fig. 11

Effect of Rb on w(ξ = 0.5, η)

Fig. 12

Effect of reduced heat transfer parameter (γ) on density of motile microorganisms when ξ = 0.5

Fig. 13

Effect of reduced heat transfer parameter (γ) on temperature profiles when ξ = 0.5

## Errata

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