Flow and heat transfer analysis of a maxwell-power-law fluid film with forced thermal Marangoni convective

Abstract

Abstract In the present work, the Maxwell-power-law constitutive equation, which can simultaneously describe both shear thinning and viscoelasticity, is established based on a rheological experiment with welan gum solution. The flow and heat transfer properties of a Maxwell-power-law fluid with variable thickness bounded by an unsteady stretching sheet are discussed. Based on a new constitutive relation and the Cattaneo-Christov theory of variable thermal conductivity, nonlinear governing equations are formulated. Moreover, according to the constitutive relation of the Maxwell-power-law fluid, a modified thermal Marangoni convection equation is proposed. Suitable similarity transformations are employed to obtain coupled similar ordinary differential equations that are solved by a double-parameter transformation expansion method (DPTEM). An attractive phenomenon is found that the influence of momentum relaxation time on film thickness is more evident than that of the thermal relaxation time. Moreover, strengthening the Marangoni convection results in a reduction in the film thickness.