Flow and heat transfer in a rectangular converging (diverging) channel: new formulation | ||||
| Journal of the Egyptian Mathematical Society | ||||
| Volume 29, Issue 1, 2021, Page 1-18 PDF (1.99 MB) | ||||
| Document Type: Original Article | ||||
| DOI: 10.1186/s42787-021-00126-7 | ||||
 View on SCiNiTO | ||||
| Authors | ||||
| Roohi Laila1; Azhar Ali* 2; Dil Nawaz Khan Marwat1 | ||||
| 1Department of Mathematics, Faculty of Technology and Engineering Sciences, Islamia College Peshawar, Jamrod Road, University Campus, Peshawar 25120, Khyber Pakhtunkhwa, Pakistan. | ||||
| 2Electrical Department, Sarhad University of Science and Information Technology Peshawar, Khyber Pakhtunkhwa, Pakistan. | ||||
| 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 | ||||
| Flow and heat transfer; Channel of rectangular inclined plan; Walls Introduction | ||||
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