Abstract
This article investigates the heat transfer flow of two layers of Phan-Thien-Tanner (PTT) fluids though a cylindrical pipe. The flow is assumed to be steady, incompressible, and stable and the fluid layers do not mix with each other. The fluid flow and heat transfer equations are modeled using the linear PTT fluid model. Exact solutions for the velocity, flow rates, temperature profiles, and stress distributions are obtained. It has also been shown that one can recover the Newtonian fluid results from the obtained results by putting the non-Newtonian parameters to zero. These results match with the corresponding results for Newtonian fluids already present in the literature. Graphical analysis of the behavior of the fluid velocities, temperatures, and stresses is also presented at the end. It is also shown that maximum velocity occurs in the inner fluid layer.
| Original language | English (US) |
|---|---|
| Article number | 81 |
| Journal | Mathematics |
| Volume | 7 |
| Issue number | 1 |
| DOIs | |
| State | Published - Jan 14 2019 |
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All Science Journal Classification (ASJC) codes
- Mathematics(all)
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Exact solution for the heat transfer of two immiscible PTT fluids flowing in concentric layers through a pipe. / Siddiqui, Abdul Majeed; Zeb, Muhammad; Haroon, Tahira; Azim, Qurat ul Ain.
In: Mathematics, Vol. 7, No. 1, 81, 14.01.2019.Research output: Contribution to journal › Article
TY - JOUR
T1 - Exact solution for the heat transfer of two immiscible PTT fluids flowing in concentric layers through a pipe
AU - Siddiqui, Abdul Majeed
AU - Zeb, Muhammad
AU - Haroon, Tahira
AU - Azim, Qurat ul Ain
PY - 2019/1/14
Y1 - 2019/1/14
N2 - This article investigates the heat transfer flow of two layers of Phan-Thien-Tanner (PTT) fluids though a cylindrical pipe. The flow is assumed to be steady, incompressible, and stable and the fluid layers do not mix with each other. The fluid flow and heat transfer equations are modeled using the linear PTT fluid model. Exact solutions for the velocity, flow rates, temperature profiles, and stress distributions are obtained. It has also been shown that one can recover the Newtonian fluid results from the obtained results by putting the non-Newtonian parameters to zero. These results match with the corresponding results for Newtonian fluids already present in the literature. Graphical analysis of the behavior of the fluid velocities, temperatures, and stresses is also presented at the end. It is also shown that maximum velocity occurs in the inner fluid layer.
AB - This article investigates the heat transfer flow of two layers of Phan-Thien-Tanner (PTT) fluids though a cylindrical pipe. The flow is assumed to be steady, incompressible, and stable and the fluid layers do not mix with each other. The fluid flow and heat transfer equations are modeled using the linear PTT fluid model. Exact solutions for the velocity, flow rates, temperature profiles, and stress distributions are obtained. It has also been shown that one can recover the Newtonian fluid results from the obtained results by putting the non-Newtonian parameters to zero. These results match with the corresponding results for Newtonian fluids already present in the literature. Graphical analysis of the behavior of the fluid velocities, temperatures, and stresses is also presented at the end. It is also shown that maximum velocity occurs in the inner fluid layer.
UR - http://www.scopus.com/inward/record.url?scp=85060198671&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85060198671&partnerID=8YFLogxK
U2 - 10.3390/math7010081
DO - 10.3390/math7010081
M3 - Article
AN - SCOPUS:85060198671
VL - 7
JO - Mathematics
JF - Mathematics
SN - 2227-7390
IS - 1
M1 - 81
ER -