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Study of a Eyring–Powell Fluid in a Scraped Surface Heat Exchanger

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Abstract

Flow of a Eyring–Powell fluid in a scraped surface heat exchangers (SSHEs) is analyzed. Foodstuff behaves as non-Newtonian material so for studying non-Newtonian effects inside SSHE Eyring–Powell fluid model is considered. As every physical phenomena can be interpreted mathematically therefore in this work we mathematically studied flow inside SSHE. Steady isothermal incompressible flow of Eyring–Powell fluid about a periodic sequence of pivoted scraper blade in channel with one moving wall and other is stationary, pressure gradient is imposed in the direction transverse to the wall motion is modelled using lubrication approximation theory as the gap with the blades and device wall are narrow. The resulting nonlinear boundary value problem is solved using Adomian decomposition method. Expression for velocity profiles for different region, flow rates, stream function, forces on the wall and on the blade are found. Graphical representation for velocity profile and for different flow parameter involved is also discussed. Parabolic velocity profiles in various region of SSHE are obtained which are in line with the experimental results obtained through MRI.

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Abbreviations

\(\alpha _{1}\) :

Angle of inclination of the blade

\(\alpha ,\beta \) :

Material constants of Eyring–Powell model

\(h_{0}\) :

Position of lower end of blade

\(h_{1}\) :

Position of upper end of the blade

\(h_{p}\) :

Pivot position of the blade

M :

Moment of the forces

\(u_{1}\) :

Velocity in the first region of the SSHE

\(u_{2}\) :

Velocity in the second region of the SSHE

\(u_{3}\) :

Velocity in the third region of the SSHE

\(F_{x}\) :

Drag force on the blade

\(F_{y}\) :

Lift force on the blade

\(F_{0}\) :

Force in x-direction of lower wall of the channel

\(F_{H}\) :

Force in x-direction of upper wall of the channel

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Authors and Affiliations

  1. Department of Mathematics, COMSATS Institute of Information Technology, Kamra Road, Attock, 43600, Pakistan

    A. Imran

  2. Department of Mathematics and Statistics, Riphah International University, Sector I-14, Islamabad, Pakistan

    A. Imran & M. A. Rana

  3. Department of Mathematics, York Campus, Pennsylvania State University, York, PA, 17403, USA

    A. M. Siddiqui

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  1. A. Imran
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  2. M. A. Rana
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Correspondence to A. Imran.

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Imran, A., Rana, M.A. & Siddiqui, A.M. Study of a Eyring–Powell Fluid in a Scraped Surface Heat Exchanger. Int. J. Appl. Comput. Math 4, 18 (2018). https://doi.org/10.1007/s40819-017-0436-z

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