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# Mathematical model of eyring fluid in a scraped surface heat exchanger

#### A Imran,

Department of Mathematics

#### AM Siddiqui,

##### Pennsylvania State University, York, PA 17403, USA., US
Department of Mathematics

#### M Numan,

Department of Mathematics

#### MA Rana,

##### Riphah International University, Sector I-14, Islamabad, Pakistan, PK
Department of Mathematics and Statistics

#### A Waheed

Department of Mathematics

## Abstract

In this work, a novel mathematical model for steady incompressible isothermal flow of Eyring fluid in a scraped surface heat exchanger (SSHE) was explored. Foodstuff possesses non-Newtonian features, therefore for studying these effects, Eyring fluid model has been considered. For the analysis of flow inside SSHE, lubrication approximation theory (LAT) was exploited to model the flow, and exact solution is achieved. The flow about a sequence of pivoted scraper blade in a channel, in which one wall is moving and the other is at rest was analysed, and the pressure gradient applied transversely. Expressions for important flow indicators such as velocity profile, stream functions, pressures, flow rates and the probable regions of backward flow down the blades, the drag and lift forces on the blades and walls were computed. The impact of various flow parameters was exhibited graphically. It was observed that the velocity profile in all regions of SSHE increases with enhancement in the non-Newtonian parameter γ, whereas an opposite behaviour was recorded with rising value of β.

##### Keywords: exact solution,eyring fluid,lubrication approximation theory
How to Cite: Imran, A., Siddiqui, A., Numan, M., Rana, M. and Waheed, A., 2020. Mathematical model of eyring fluid in a scraped surface heat exchanger. Journal of the National Science Foundation of Sri Lanka, 48(1), pp.3–14. DOI: http://doi.org/10.4038/jnsfsr.v48i1.8818
Published on 28 Apr 2020.
Peer Reviewed