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Influence of thermal radiation on unsteady magnetohydrodynamic (MHD) free convection flow of Jeffrey fluid over a vertical plate with ramped wall temperature is studied. The Laplace transform technique is used to obtain the analytical solutions. Expressions for skin friction and Nusselt number are also obtained. Results of velocity and temperature distributions are shown graphically for embedded parameters such as Jeffrey fluid parameter

Investigation of non-Newtonian fluids has become very popular in this research area due to their wide range in industrial and technologies applications such as the plastic manufacture, performance of lubricants, food processing, or movement of biological fluids. Various models have been suggested to predict and describe the rheological behavior of non-Newtonian fluids. The Jeffrey fluid model is one of the subfamily of non-Newtonian fluids which has been given much attention in the present problem. This fluid is a relatively simple viscoelastic non-Newtonian fluid model that exhibits both relaxation and retardation effects [

Hayat and Mustafa [

Besides that, Jeffrey fluid also has been studied in peristalsis known as major mechanism of fluid transport especially in biological system, for example, urine transport from kidney to bladder through ureter, movement of chime in the gastrointestinal tract, the movement of spermatozoa in the ducts efferent of the male reproductive tract, ovum in the female fallopian tube, the locomotion of some worms, and transport of lymph in the lymphatic vessels [

Moreover, the influence of heat transfer on MHD oscillatory flow of Jeffrey fluid in a channel has been investigated by Kavita et al. [

On the other hand, the steady boundary layer flow of a Jeffrey fluid over a shrinking sheet is highlighted by Nadeem et al. [

Diverse contributions dealing with boundary layer flow over stretching sheet in various situations are well documented in Dalir et al. [

In view of the above analysis, so far no study has been made to examine the effect of ramped wall temperature in a Jeffrey fluid flow. Thus, our main focus is to discuss the influence of thermal radiation on unsteady MHD free convection flow of Jeffrey fluid over a vertical plate with ramped wall temperature. The Laplace transform technique is applied in this study in order to find the analytical solutions for velocity and temperature profiles. Expressions of skin friction and Nusselt number are also given. Graphical results are provided and discussed for embedded parameters.

The unsteady incompressible flow is described by the following governing equations:

In the above equations

Consider the effect of thermal radiation on unsteady free convection flow of Jeffrey fluid near the vertical plate situated in the

Schematic diagram for the flow of Jeffrey fluid past a vertical plate.

Under the above assumption and applying the usual Boussinesq approximation, the momentum and energy equations for unsteady free convection flow of Jeffrey fluid past an infinite vertical plate are given by

Applying the Laplace transform to (

Equation (

Meanwhile, the solution of (

The analytical solution of temperature and velocity distribution for the case of ramped wall temperature are shown in (

The expression of Nusselt number,

In this section, we discuss our present results and provide exact solutions for two special cases by taking suitable parameters equal to zero.

By making Hartmann number

Comparison of velocity

Interestingly, by putting

Comparison of velocity

Numerical computation of analytical expressions (

Velocity profile for different values of

Velocity profile for different values of

Velocity profile for different values of

Velocity profile for different values of

Velocity profile for different values of

Velocity profile for different values of

Temperature profile for different values of

Temperature profile for different values of

Temperature profile for different values of

The influence of Jeffrey fluid parameter

Further, the effect of radiation parameter

The effect of Hartmann number

Figure

This study presents a theoretical investigation of thermal radiation in unsteady MHD free convection flow of Jeffrey fluid with ramped wall temperature. The dimensionless governing equations are solved by using the Laplace transform method. Graphical results for velocity and temperature are obtained to understand the physical behavior for several embedded parameters. The results show that increasing

The authors of this paper do not have any conflict of interests regarding its publication.