Analytical solutions to mixed convection MHD fluid flow induced by a nonlinearly deforming permeable surface

• Published in: Communications in nonlinear science & numerical simulation Vol. 63; pp. 373 - 379
• Main Author: Turkyilmazoglu, M.
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 01.10.2018; Elsevier Science Ltd
• Subjects: Boundary layer flow; Computational fluid dynamics; Convection; Deformation; Domain walls; Dual solutions; Exact solution; Exact solutions; Flow cytometry; Fluid flow; Fluidity; Heat generation; Heat source/sink; Heat transfer; Magnetic fields; Magnetic permeability; Magnetohydrodynamics; Mass transfer; MHD flow; Microbiology; Mixed convection; Parameter identification; Polylactic acid; Polymers; Shear stress; Stretching/shrinking surface; Temperature distribution; Viscous fluids; Wall shear stresses; MHD flow; Heat source/sink; Dual solutions; Mixed convection; Stretching/shrinking surface; Mass transfer; Heat transfer; Exact solution
• ISSN: 1007-5704; 1878-7274
• DOI: 10.1016/j.cnsns.2018.04.002

•Mixed convection flow and temperature fields are presented in closed-form solutions.•Unique exact solutions are found for the stretching walls.•Momentum and temperature layers thicknesses are reduced as per the magnetic field.•Dual exact solutions are detected for the shrinking surfaces.•Upper branch solutions are more cooled leading to higher heat transfer rate. The mixed boundary layer flow and heat of an MHD viscous fluid due to a nonlinearly deforming body subjected to a uniform magnetic field with heat generation or absorption is the focus of the current paper. Although there appears to be numerous numerical works on the subject in the literature, no analytical solution yet available in the literature for the nonlinear deforming, hence the motivation here is to search for exact analytical solutions for such an highly nonlinear flow phenomenon. It is accomplished that mixed fluid flow convection admits exact solutions in the form suitable to the boundary layer character. The parameter domain for the existence of exact solutions is identified. In the case of stretching sheet, exact solutions identified are unique. However, double solutions are present over a shrinking wall, whose critical domains are exactly formulated. The temperature field coupled with the flow field is shown to possess a simple analytic expression. Such exact solutions are rare opportunities to present exact formulas for the wall shear stress as well as for the rate of heat transfer of major practical interest. The main physical implication of the results is that both momentum and temperature layers are thinned with strong magnetic fields. Also, upper branch solutions are more cooled leading to higher heat transfer rates as compared to the lower branches.