Impact of Inclined Magnetic Field and Activation Energy on Stagnation Point Flow of Nano-fluid Over a Stretching Surface

Impact of Inclined Magnetic Field and Activation Energy (Part 2)

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Impact of Inclined Magnetic Field and Activation Energy on Stagnation Point Flow of Nano-fluid Over a Stretching Surface

Impact of Inclined Magnetic Field and Activation Energy (Part 1)

Nusselt number

It is a dimensionless quantity that associates heat transfer rate in the fluid, i.e, the convection to conduction heat transfer. Mathematically, it is expressed as

(1)   \begin{equation*} Nu_x=\frac{h_x L}{k_f}\end{equation*}

In convection heat transfer, we have, h_x =\frac{Q_w}{(T_s-T_{infty})}. Whereas, by conduction we have,
Q_w = −k_f ∇T .

Generally, we can write

(2)   \begin{equation*}Nu_x=\frac{h_x L}{k_f}= CRe^m_x Pr^n\end{equation*}

Skin friction efficient

The force that happens due to interaction between fluid and solid’s surface when fluid is passing from it that leads to slow down the fluid’s velocity is termed the skin friction coefficient.

Mathematically

(3)   \begin{equation*}C_f= \frac{\tau_w}{\frac{1}{2} \rho U^2_w}\end{equation*}

and

(4)   \begin{equation*}\tau_w=\mu ( \frac{\partial u}{\partial y} )_{y=0}\end{equation*}

where τw is shear stress over the surface of a sheet, \rho represents the density of the fluid and U_w denotes the velocity of the fluid.

Sherwood number

The ratio of total mass transfer to diffusive mass transfer. Mathematically,

(5)   \begin{equation*}S h_L= \frac{h_m∆C}{D∆C/L}= \frac{h_mL}{D}\end{equation*}

where h_m stands for mass transfer coefficient, L for characteristic length and D for mass diffusitivity.

Magnetohydrodynamics (MHD)

The word magnetohydrodynamics is composed of three words such as Magneto- due to magnetic field, hydro- due to liquid and dynamics specifying the motion of the body. MHD fluids include salt water, liquid metals or electrolytes and plasma.

Stagnation Point

The point at which a fluid’s velocity becomes zero. Stagnation happens when a fluid collides with a non-rotating item or when an impediment moves through a fluid. The velocity components are 0 and their gradients are positive at a stagnation point. Furthermore, the pressure is at its ultimate peak at that instant.

Boundary layer flow

Ludwig Prandtl (1874-1953), a German physicist, introduced an idea of a boundary layer in fluid motion over a surface in 1904. A layer of reduced velocity in the fluid is called the boundary layer. It is exactly close to the solid surface which is just following the fluid. The flow is vigorous in the boundary layer for aerodynamic drag and lift of the flying objects. A boundary layer may be laminar and turbulent if the flow takes place in layer such that each layer slides pass the adjacent layers, then this layer is identified as laminar boundary layer, although the turbulent boundary layer is in which there is an intense agitation.

Continuity equation

Continuity equation in fluid dynamics states that within a system the rate of flow at which the mass enters and leaves the system is equal, plus the accumulation of mass surrounded by system. Following is the differential representation of continuity equation.

(6)   \begin{equation*}\frac{\partial \rho}{\partial t}+\nabla .(\rho v) = 0\end{equation*}

where density is presented by ρ, v represented velocity field, t presents time. The steady flow position is given by:

(7)   \begin{equation*}\nabla .(\rho v) = 0\end{equation*}

When the density is constant and flow is incompressible then we have

(8)   \begin{equation*}\nabla .v = 0\end{equation*}

Navier-Stokes equation/Momentum equation

In physical terms, the Navier-Stokes equation states that the temporal rate of change of momentum and the total of forces in a given direction are equal. These forces comprises of surface and body forces. Gravity or weight is contained in a body forces wheraeas pressure and viscous forces represents surface forces.

The Navier-stokes equation in vector form is :

(9)   \begin{equation*}\rho \frac{DV}{Dt}=-\nabla p+h+\mu \nabla^2 V\end{equation*}

Where µ represents dynamic viscosity, body force is h and ρ represents density.

(10)   \begin{equation*}\nabla =\frac{\partial^2}{\partial x^2}+\frac{\partial^2}{\partial y^2}+\frac{\partial^2}{\partial x^2}\end{equation*}

represents 3-dimensional Laplacian operator. For viscous incompressible flow Navier- Stokes equation combine with continuity equation describe an entire mathematical sketch.

Energy equation

The energy equation represents significance of thermodynamics first law and states that the change producing in energy, transfer of heat and the work done via a sys- tem are in stability. For thermal conductivity considered to be constant and in the presence of viscous dissipation term, the energy equation in vector form is given by

(11)   \begin{equation*}\rho C_p \frac{DV}{Dt}=k\nabla^2T + \phi, \end{equation*}

where \phi is viscous dissipation, k represents thermal conductivity, Cp denotes specific heat and T represents temperature.

Also visit Impact of Inclined Magnetic Field and Activation Energy (Part 1)

Impact of Inclined Magnetic Field and Activation Energy (Part 3)

Impact of Inclined Magnetic Field and Activation Energy (Part 1)

Impact of Inclined Magnetic Field and Activation Energy on Stagnation Point Flow of Nano-fluid Over a Stretching Surface

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