PPubMed20 Apr 2016Cited 34×

Radiative Squeezing Flow of Second Grade Fluid with Convective Boundary Conditions Radiative Squeezing Flow of Second Grade Fluid with Convective Boundary Conditions

T. Hayat, Sumaira Jabeen, Anum Shafiq, A. Alsaedi, Xiao-Dong Wang

Abstract

Influence of magnetohydrodynamic (MHD) flow between two parallel disks is considered. Heat transfer analysis is disclosed due to thermal radiation and convective boundary condition. Appropriate transformations are invoked to obtain the ordinary differential system. This system is solved using homotopic approach. Convergence of the obtained solution is discussed. Variations of embedded parameters into the governing problems are graphically discussed. Skin friction coefficient and Nusselt number are numerically computed and analyzed. It is noticed that temperature profile is increasing function of radiation parameter.

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The study analytically solves MHD squeezing flow of a second‑grade fluid with radiation and convective walls using homotopy analysis, revealing parameter effects on velocity, temperature, friction and heat transfer.

What’s new

i.Derived homotopy analysis method series solutions for squeezing flow of a second‑grade fluid with thermal radiation and convective boundary conditions.
ii.Performed convergence analysis and identified admissible ranges for the auxiliary parameters ℏ_f and ℏ_θ.
iii.Computed and examined skin friction coefficient and local Nusselt number for various physical parameters.
iv.Validated the analytical results by comparing with previously published data, showing excellent agreement.

How they did it

The governing continuity, momentum, and energy equations were transformed into ordinary differential equations using similarity variables. Series solutions were obtained via the homotopy analysis method with appropriate base functions and auxiliary parameters, and convergence was verified through ℏ‑curves and residual error calculations.

What they found

Series solutions converge up to six decimal places at the 8th order for momentum and 6th order for temperature.
Admissible auxiliary‑parameter ranges: -1.3 ≤ ℏ_f < -0.2 (α1=0.1) and -0.9 ≤ ℏ_θ < -0.2 (α1=0.3); convergence achieved for ℏ_f = ℏ_θ = -0.9.
Skin friction coefficient increases with larger squeezing parameter S, magnetic parameter M, fluid parameter α1, and inclination angle ψ.
Local Nusselt number rises with higher radiation parameter R, Biot numbers γ1 and γ2, and Prandtl number effects differ between upper and lower disks.

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Radiative Squeezing Flow of Second Grade Fluid with Convective Boundary Conditions Radiative Squeezing Flow of Second Grade Fluid with Convective Boundary Conditions

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