title: On three-dimensional flow and heat transfer over a non-linearly stretching sheet: analytical and numerical solutions.
abstract: This article studies the viscous flow and heat transfer over a plane horizontal surface stretched non-linearly in two lateral directions. Appropriate wall conditions characterizing the non-linear variation in the velocity and temperature of the sheet are employed for the first time. A new set of similarity variables is introduced to reduce the boundary layer equations into self-similar forms. The velocity and temperature distributions are determined by two methods, namely (i) optimal homotopy analysis method (OHAM) and (ii) fourth-fifth-order Runge-Kutta integration based shooting technique. The analytic and numerical solutions are compared and these are found in excellent agreement. Influences of embedded parameters on momentum and thermal boundary layers are sketched and discussed.
authors.affiliation: Research Centre for Modeling and Simulation (RCMS), National University of Sciences and Technology (NUST), Islamabad, Pakistan.
authors.forename: Junaid Ahmad
authors.initials: JA
authors.lastname: Khan
authors.affiliation: School of Natural Sciences (SNS), National University of Sciences and Technology (NUST), Islamabad, Pakistan.
authors.forename: Meraj
authors.initials: M
authors.lastname: Mustafa
authors.affiliation: Department of Mathematics, Quaid-I-Azam University, Islamabad, Pakistan; Nonlinear Analysis and Applied Mathematics (NAAM) Research Group, King Abdulaziz University, Jeddah, Saudi Arabia.
authors.forename: Tasawar
authors.initials: T
authors.lastname: Hayat
authors.affiliation: Nonlinear Analysis and Applied Mathematics (NAAM) Research Group, King Abdulaziz University, Jeddah, Saudi Arabia.
authors.forename: Ahmed
authors.initials: A
authors.lastname: Alsaedi
mesh_terms: D057446:Hydrodynamics; D055595:Mechanical Phenomena; D017711:Nonlinear Dynamics; D013814:Thermal Conductivity; D014783:Viscosity