Mathematical modeling of boundary layer flow over a moving thin needle with variable heat flux

J Braz. Soc. Mech. Sci. Eng.

Makinde

Saleem

2019

This article presents the combined effects of melting heat transfer and linear stratification of not only the heat energy, but also stratified concentration on the motion of an electrically conducting fluid over an object with a non-uniform thickness. Owing to the melting heat transfer and stretching of fluid layers at the free stream, the case of mixed convection is considered to be more appropriate than neither free nor forced convection. Consequently, the energy and concentration equations which model the flow and satisfy the free stream conditions are presented. Suitable thermophoresis model and Boussinesq approximation for the case T m (x) < T ∞ (x) and C m (x) < C ∞ (x) were adopted. A suitable similarity transformation is applied to reduce the governing equations to coupled ordinary differential equations. These equations along with the boundary conditions were solved numerically using Runge-Kutta technique along with shooting technique. Maximum variations in the local skin friction coefficients Re 1∕2 x C fx with thermal stratification occur at larger values of temperature-dependent viscosity parameter. Temperature distribution, local skin friction coefficients Re 1∕2 x C fx and mass transfer rate S hx Re −1∕2 x are decreasing properties of thermal stratification and thermophoresis parameter.

Section: Classical Runge-kutta Methods Along With Shooting Techniquesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Mixed convection flow of Newtonian fluids over an upper horizontal thermally stratified melting surface of a paraboloid of revolution

J Braz. Soc. Mech. Sci. Eng.

Makinde

Saleem

2019

“…Cebeci and Na [2] investigated the laminar free convection heat transfer from a needle. Ahmad et al [3] examined the boundary layer flow over a moving thin needle with variable heat flux. The boundary layer flow over a stretching surface with variable thickness was analyzed by Fang et al [4].…”

Section: Introductionmentioning

confidence: 99%

Viscous Dissipation Effects on the Motion of Casson Fluid over an Upper Horizontal Thermally Stratified Melting Surface of a Paraboloid of Revolution: Boundary Layer Analysis

Ajayi

Omowaye

Journal of Applied Mathematics

2017

The problem of a non-Newtonian fluid flow past an upper surface of an object that is neither a perfect horizontal/vertical nor inclined/cone in which dissipation of energy is associated with temperature-dependent plastic dynamic viscosity is considered. An attempt has been made to focus on the case of two-dimensional Casson fluid flow over a horizontal melting surface embedded in a thermally stratified medium. Since the viscosity of the non-Newtonian fluid tends to take energy from the motion (kinetic energy) and transform it into internal energy, the viscous dissipation term is accommodated in the energy equation. Due to the existence of internal space-dependent heat source; plastic dynamic viscosity and thermal conductivity of the non-Newtonian fluid are assumed to vary linearly with temperature. Based on the boundary layer assumptions, suitable similarity variables are applied to nondimensionalized, parameterized and reduce the governing partial differential equations into a coupled ordinary differential equations. These equations along with the boundary conditions are solved numerically using the shooting method together with the Runge-Kutta technique. The effects of pertinent parameters are established. A significant increases in Re 1/2 is guaranteed with when magnitude of is large. Re 1/2 decreases with and .

“…Cebeci and Na [3] investigated the laminar free convection heat transfer from a needle. Ahmad et al [4] examined the boundary layer flow over a moving thin needle with variable heat flux where they observed that the wall temperature was significantly influenced by both the needle size parameter and the Prandtl number. Boundary layer flow over a stretching sheet with variable thickness was studied by Fang et al [5].…”

Section: Introductionmentioning

confidence: 99%

Effects of Viscous Dissipation and Double Stratification on MHD Casson Fluid Flow over a Surface with Variable Thickness: Boundary Layer Analysis

Ajayi

Omowaye

2017

JERA

In this article, the motion of two-dimensional Casson fluid flows with temperature dependent plastic dynamic viscosity together with double (i.e. thermal and solutal) stratification in the presence of Lorentz force is investigated. The case where the viscosity of the fluid tends to take energy away from the motion (kinetic energy) and transform it into internal energy is considered. The nonlinear governing equations and their associated boundary conditions are transformed and non-dimensionalized using similarity variables which are thereafter solved numerically using the shooting method together with the Runge-Kutta technique. The effects of the magnetic field parameter, temperature dependent viscosity parameter, Casson parameter, Eckert number, velocity power index, pressure gradient parameter and wall thickness parameter on the velocity, temperature, and concentration profiles are showed graphically and discussed. Substantial increase in temperature distribution is certain with an increase in the magnitude of Eckert number. Local skin friction coefficient decreases with an increase in pressure gradient parameter.