Analytical solutions of PDEs by unique polynomials for peristaltic flow of heated Rabinowitsch fluid through an elliptic duct
Salman Akhtar, Muhammad Hasnain Shahzad, S. Nadeem, Aziz Ullah Awan, Shahah Almutairi, Hassan Ali Ghazwani, Mohamed Mahmoud Sayed
Abstract
Abstract In this research, we have considered the convective heat transfer analysis on peristaltic flow of Rabinowitsch fluid through an elliptical cross section duct. The Pseudoplastic and Dilatant characteristics of non-Newtonian fluid flow are analyzed in detail. The Rabinowitsch fluid model shows Pseudoplastic fluid nature for $$\sigma > 0$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>σ</mml:mi> <mml:mo>></mml:mo> <mml:mn>0</mml:mn> </mml:mrow> </mml:math> and Dilatant fluid behaviour for $$\sigma < 0.$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>σ</mml:mi> <mml:mo><</mml:mo> <mml:mn>0</mml:mn> <mml:mo>.</mml:mo> </mml:mrow> </mml:math> The governing equations are transformed to dimensionless form after substituting pertinent parameters and by applying the long wavelength approximation. The non-dimensional momentum and energy equations are solved analytically to obtain the exact velocity and exact temperature solutions of the flow. A novel polynomial of order six having ten constants is introduced first time in this study to solve the energy equation exactly for Rabinowitsch fluid flow through an elliptic domain. The analytically acquired solutions are studied graphically for the effective analysis of the flow. The flow is found to diminish quickly in the surrounding conduit boundary for Dilatant fluid as compared to the Pseudoplastic fluid. The temperature depicted the opposite nature for Pseudoplastic and Dilatant fluids. The flow is examined to plot the streamlines for both Pseudoplastic and Dilatant fluids by rising the flow rate.