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ARTICLE

HEAT TRANSFER ANALYSIS FOR THE UNSTEADY UCM FLUID FLOW WITH HALL EFFECTS: THE TWO-PARAMETER LIE TRANSFORMATIONS

by

a Department of Mathematics, University of Management and Technology Lahore, Sialkot Campus, 51310, Pakistan
b Department of Mathematics, University of Engineering and Technology, Lahore, 54890, Pakistan

* Corresponding Author: email:
† Current address:Department of Mathematics, College of Science, University of Ha´il, Saudi Arabia

Frontiers in Heat and Mass Transfer 2020, 15, 1-10. https://doi.org/10.5098/hmt.15.14

Abstract

This methodology presented the unsteady three-dimensional laminar flow since Hall effects inducing the cross flow in z-axis. The boundary layer and the low magnetic Reynolds number approximations are used to simplify the system of equations derived from the constitutive laws. The upper-convected Maxwell (UCM) fluid model used for Hall effects with unsteady heat transfer, which passed through the infinite stretching sheet. This flow model has intensified with the effects of magnetohydrodynamic (MHD), thermal radiation and heat generation-absorption. Here, we selected the two-parameter Lie scaling transformations to convert the highly non-linear partial differential equations (PDEs) to the ordinary differential equations (ODEs) which are studied numerically using the MATLAB bvp4c method. The main parameters are: Deborah number D_eu, Hartmann number M_u, Hall effects parameter m_u, Prandtl number P_r, thermal radiation parameter δ_u and heat generation-absorption Q_u. Hall effects reduced the transport rate in the x-axis but increased the transport rate in the z-axis. On the other hand, the Hall parameter is extravagant to transport the internal energy of the system.

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