This paper is devoted to the analysis of the heat transfer and Navier’s slip effects in a non-Newtonian Jeffrey fluid flowing past a stretching/shrinking sheet. The nanoparticles, namely, Cu and Al_{2}O_{3} are used with a water-based fluid with Prandtl number 6.272. Velocity slip flow is assumed to occur when the characteristic size of the flow system is small or the flow pressure is very small. By using the similarity transformations, the governing nonlinear PDEs are turned into ordinary differential equations (ODE’s). Analytical results are presented and analyzed for various values of physical parameters: Prandtl number, Radiation parameter, stretching/shrinking parameter and mass transpiration for the flow and heat transfer. The considered problem is relevant to various physical applications in the field of engineering, e.g., the production of certain materials, the preparation of plastic and rubber sheets and glass blowing. It is shown that the considered nanofluid increases the thermal efficiency. The nanoparticles act as a heater by increasing the solid volume fraction and thermal radiation. Vice versa, they can act as a cooler if the strength of magnetic field is increased. The flow strength decreases by increasing the values of Deborah number.

In the recent few eras the researchers show much interest on the flow of non-Newtonian fluids. This interest is growing like a stem of a tree because of its huge technological and industrial applications in many fields such as engineering applications, exchanger of heat, extrusion of metal and polymer process, manufacturing of paper, cable coating and so on. Numerous investigations take place on the flow of a fluid through a stretching/shrinking surface. Most of them agreed that Sakiadis [^{st} work on the effect of radiation in a boundary layer flow, this work describes the radiation in the boundary layer on aerodynamic heat transfer. After this huge research was conducted on radiation. Siddheshwar et al. [

Apart from these research some of the researchers conducted an experiment on Jeffrey fluid. The magnetohydrodynamics effects and other physical mechanisms show huge significance in many Jeffrey fluid applications. Jeffrey fluid past a Narrow tube with a Magnetic field is examined in [

Inspired by the above research papers the present work is to extend the articles [_{f}

In the current work Jeffrey nanofluid flow is taken into account. This flow is a laminar steady state and it is emerging towards the x-axis near the stagnation point in the presence of _{0} is inserted at the deforming velocity of the wall _{w}(_{e}(_{∞} at the for field. The governing Navier’s stokes equations are given below:

the applied boundary conditions (see [

Sr. No. | Physical properties | Liquid phase | Copper | Alumina |
---|---|---|---|---|

1 | _{p} |
4179 | 385 | 765 |

2 | ^{3}) |
997.1 | 8933 | 3970 |

3 | 0.613 | 400 | 40 | |

4 | ^{−1}) |
0.05 | 5.97 × 10^{7} |

It is mentioned that there are two boundary conditions exist for wall temperature _{w}(_{w}(_{w} + _{w} denotes the mass flux velocity with _{w} < 0 represents suction and _{w} < 0 represents injection. For the purpose of obtaining exact solutions the fluid properties are assumed to be constant, _{1} and _{2} are associated to relaxation parameters., at lastly stretching case is represented by

The Rosseland’s formulation for the radiative heat flux can be simplified for radiation as (see [^{4} is expressed in the form of linear function of the temperature. Increasing the term ^{4} in the form of Taylor series and also some terms are ignored.

Substituting

on applying these similarity transformations to the

the constant parameters inserted in the

The BC’s transformed to

Here

The skin friction coefficient _{f} and Local Nusselt number _{x} is given by

Substituting, _{f} and _{x} are given by

Let us assume the solution of the

For limiting case Λ = 0, then

Further, we assuming the solution of temperature equation

Substituting

After some manipulation on equating

where, _{1} and _{2}, and also the Parameter _{C} will change with these parameters, the _{f} and

Therefore, the _{f} will decreases by increasing first and second order slip

Next we take particular case Λ = 1, and

Substituting this in

where

The Jeffrey nanofluid flow is considered in the current investigation, the impact of inclined MHD and second order slip is taken into account with this flow in the presence of

The effect of tangential velocity on similarity variable

The impact of skin friction coefficient _{f} on the functions Chandrasekhar’s number _{f} is increases with increasing the inclined angle _{f} is decreases with increasing the Chandrasekhar’s number _{f} will decreases by increasing the slip parameters _{1} and _{2}. The large values of

_{C} and increases with increase of Radiation parameter

_{C}. In both figures the Nusselt number

Similarly, the same investigation carried out for _{2}_{3}-water

The current article investigates the Jeffrey nanofluid flow in the presence of

Flow fluid decreases with increase of Deborah number

The skin friction coefficient _{f} will decreases by increasing the slip parameters _{1} and _{2}.

The rate of heat transfer increases by adding nanofluid.

Temperature _{1}, and _{2}.

The classical Crane [_{1} = _{2} = _{3} = 1.

The classical Pavlov [_{1} = _{2} = _{3} =

The Turkyilmazoglu [_{1} = _{2} = _{3} = 1,

The present work is help to conduct future research on nanofluid flows, and also direct integration technique is one of the easy ways to solve the energy equation, it helps to many reasearchers.

coefficients of first and second order slip, respectively

constants

_{0}

uniform magnetic field (

_{P}

specific heat at constant pressure (^{−1}^{−1})

constant

complementary error function

solution domain

mean absorption coefficient

_{1}and

_{2}

first and second order slip, respectively

Prandtl number

Chandrasekhar’s number

_{r}

radiative heat flux

_{w}

local heat flux (^{−2})

thermal radiation

_{∞}

ambient temperature (

_{w}

temperature at wall (

temperature (

_{w}(

velocity at wall

_{e}(

potential velocity

_{w}

mass flux (^{−1})

_{C}

mass transpiration

components of velocity (^{−1})

Cartesian coordinate (

electrical conductivity (^{−1})

Stefan-Boltzmann constant (^{−2}^{−4})

stretching/shrinking parameter

_{1}

_{2}

related to relaxation parameter

Deborah number (_{2})

strength parameter

similarity variable

_{nf}

kinematic viscosity of nanofluid (^{2}^{−1})

_{f}

kinematic viscosity of base fluid (^{2}^{−1})

_{nf}

density of nanofluid (^{−3})

_{f}

density of base fluid (^{−3})

thermal diffusivity of nanofluid.

_{nf}

dynamic viscosity of nanofluid (^{−1}^{−1})

_{f}

dynamic viscosity of base fluid (^{−1}^{−1})

thermal conductivity (

temperature jump

_{w}

skin friction

inclined angle

quantities at wall

quantities at freestream

fluid

snanofluid

magnetohydrodynamics

ordinary differential equation

partial differential equation