Flow and heat transfer in a rectangular converging (diverging) channel: new formulation

Document Type : Original Article

Authors

1 Department of Mathematics, Faculty of Technology and Engineering Sciences, Islamia College Peshawar, Jamrod Road, University Campus, Peshawar 25120, Khyber Pakhtunkhwa, Pakistan.

2 Electrical Department, Sarhad University of Science and Information Technology Peshawar, Khyber Pakhtunkhwa, Pakistan.

https://doi.org/10.1186/s42787-021-00126-7

Abstract

In this paper, a model problem of viscous fow and heat transfer in a rectangular
converging (diverging) channel has been investigated. The governing equations are
presented in Cartesian Coordinates and consequently they are simplifed and solved
with perturbation and numerical methods. Initially, symmetrical solutions of the
boundary value problem are found for the upper half of the channel. Later on, these
solutions are extended to the lower half and then to the whole channel. The numerical
and perturbation solutions are compared and exactly matched with each other for a
small value of the parameters involved in the problem. It is also confrmed that the
solutions for the converging/diverging channel are independent of the sign of m (the
slope). Moreover, the skin friction coefcient and heat transfer at the upper wall are
calculated and graphed against the existing parameters in diferent fgures. It is
observed that the heat transfer at walls is decreased (increased) with increasing c1
(thermal controlling parameter) for diverging (converging). It is also decreased against
Pr (Prandtle number). For c1 = 0, the temperature profles may be exactly determined
from the governing equations and the rate of heat transfer at the upper wall is
θ′
(1) = m
(1+m2)tan−1 m. It is confrmed that the skin friction coefcient behaves linearly
against Re* (modifed Reynolds number) and it is increased with increasing of Re*
(changed from negative to positive). Moreover, it is increased asymptotically against m
and converges to a constant value i.e. zero.

Keywords

Journal of the Egyptian Mathematical Society
Volume 29, Issue 1
2021
Pages 1-18

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