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This methodology presented the unsteady three-dimensional laminar flow since Hall effects inducing the cross flow in z̃-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 Deu, Hartmann number Mu, Hall effects parameter mu, Prandtl number Pr, thermal radiation parameter δu and heat generation-absorption Qu. Hall effects reduced the transport rate in the x̃-axis but increased the transport rate in the z̃-axis. On the other hand, the Hall parameter is extravagant to transport the internal energy of the system.

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