Junaid Ahmad Khan

Numerical Study of Cattaneo-Christov Heat Flux Model for Viscoelastic Flow Due to an Exponentially Stretching Surface

This work deals with the flow and heat transfer in upper-convected Maxwell fluid above an exponentially stretching surface. Cattaneo-Christov heat flux model is employed for the formulation of the energy equation. This model can predict the effects of thermal relaxation time on the boundary layer. Similarity approach is utilized to normalize the governing boundary layer equations. Local similarity solutions are achieved by shooting approach together with fourth-fifth-order Runge-Kutta integration technique and Newton’s method. Our computations reveal that fluid temperature has inverse relationship with the thermal relaxation time. Further the fluid velocity is a decreasing function of the fluid relaxation time. A comparison of Fourier’s law and the Cattaneo-Christov’s law is also presented. Present attempt even in the case of Newtonian fluid is not yet available in the literature.

Model for flow of Casson nanofluid past a non-linearly stretching sheet considering magnetic field effects

Present work deals with the magneto-hydro-dynamic flow and heat transfer of Casson nanofluid over a non-linearly stretching sheet. Non-linear temperature distribution across the sheet is considered. More physically acceptable model of passively controlled wall nanoparticle volume fraction is accounted. The arising mathematical problem is governed by interesting parameters which include Casson fluid parameter, magnetic field parameter, power-law index, Brownian motion parameter, thermophoresis parameter, Prandtl number and Schmidt number. Numerical solutions are computed through fourth-fifth-order-Runge-Kutta integration approach combined with the shooting technique. Both temperature and nanoparticle volume fraction are increasing functions of Casson fluid parameter.

Three-Dimensional Flow of Nanofluid Induced by an Exponentially Stretching Sheet: An Application to Solar Energy

This work deals with the three-dimensional flow of nanofluid over a bi-directional exponentially stretching sheet. The effects of Brownian motion and thermophoretic diffusion of nanoparticles are considered in the mathematical model. The temperature and nanoparticle volume fraction at the sheet are also distributed exponentially. Local similarity solutions are obtained by an implicit finite difference scheme known as Keller-box method. The results are compared with the existing studies in some limiting cases and found in good agreement. The results reveal the existence of interesting Sparrow-Gregg-type hills for temperature distribution corresponding to some range of parametric values.

Simulations for Maxwell fluid flow past a convectively heated exponentially stretching sheet with nanoparticles

This article addresses steady flow of Maxwell nanofluid induced by an exponentially stretching sheet subject to convective heating. The revised model of passively controlled wall nanoparticle volume fraction is taken into account. Numerical solutions of the arising non-linear boundary value problem (BVP) are obtained by using MATLAB built-in function bvp4c. Simulations are performed for various values of embedded parameters which include local Deborah number, Prandtl number, Biot number, Brownian motion parameter and thermophoresis parameter. The results are consistent with the previous studies in some limiting cases. It is found that velocity decreases and temperature increases when the local Deborah number is increased. Moreover the influence of Brownian diffusion on temperature and heat transfer rate is found to be insignificant.

On three-dimensional flow and heat transfer over a non-linearly stretching sheet: analytical and numerical solutions.

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.

Boundary Layer Flow of Nanofluid Over a Nonlinearly Stretching Sheet With Convective Boundary Condition

The steady laminar two-dimensional flow of nanofluid due to nonlinearly stretching sheet is discussed. Convective surface boundary condition is employed for a thermal boundary layer problem. The newly proposed boundary condition is considered that requires nanoparticle volume fraction at the wall to be passively rather than actively controlled. Suitable similarity transformations are introduced to non-dimensionalize the governing boundary layer equations. The velocity, temperature and nanoparticle volume fraction distributions are determined by two methods namely 1) optimal homotopy analysis method and 2) fourth-fifthorder Runge-Kutta method based shooting technique. The results obtained by two solutions are in excellent agreement. Behavior of interesting parameters on the flow fields is thoroughly presented and discussed.

Sakiadis flow of Maxwell fluid considering magnetic field and convective boundary conditions

In this paper we address the flow of Maxwell fluid due to constantly moving flat radiative surface with convective condition. The flow is under the influence of non-uniform transverse magnetic field. The velocity and temperature distributions have been evaluated numerically by shooting approach. The solution depends on various interesting parameters including local Deborah number De, magnetic field parameter M, Prandtl number Pr and Biot number Bi. We found that variation in velocity with an increase in local Deborah number De is non-monotonic. However temperature is a decreasing function of local Deborah number De.

A revised model to study the MHD nanofluid flow and heat transfer due to rotating disk: numerical solutions

Here our main interest is to present numerical simulations for magneto-nanofluid flow and heat transfer near a rotating disk. Buongiorno model, featuring the novel aspects of Brownian motion and thermophoresis, is accounted. Heat dissipation effect is preserved in the energy balance equation. We take into account more realistic wall condition which requires passive control of nanoparticle concentration at the disk. The traditional Von Karman relations have been invoked to attain self-similar differential system. Keller–Box method has been implemented to compute similarity solutions of the problem. Streamlines are prepared in both two and three dimensions for adequate flow visualization. The behavior of involved parameters on the flow fields is examined graphically. It is predicted that the torque required to maintain disk in steady rotation increases when magnetic field effects are enhanced. Fluid flow in the radial, azimuthal and vertical directions is opposed by the magnetic field strength. Thermophoresis effect enhances temperature and reduces heat flux from the disk. However, Brownian diffusion has a marginal influence on temperature distribution. Heat transfer coefficient is reduced due to the inclusion of heat dissipation terms. Present results are consistent with those of the available studies in a limiting situation.

NUMERICAL ANALYSIS OF SAKIADIS FLOW PROBLEM CONSIDERING MAXWELL NANOFLUID

This article investigates the flow of Maxwell nanofluid over a moving plate in a calm fluid. Novel aspects of Brownian motion and thermophoresis are taken into consideration. Revised model for passive control of nanoparticle volume fraction at the plate is used in this study. The formulated differential system is solved numerically by employing shooting approach together with fourth-fifth-order-Runge-Kutta integration procedure and Newton’s method. The solutions are greatly influenced with the variation of embedded parameters which include the local Deborah number De, the Brownian motion parameter Nb, the thermophoresis parameter Nt, the Prandtl number Pr and the Schmidt number Sc. We found that the variation in velocity distribution with an increase in local Deborah number De is non-monotonic. Moreover, the reduced Nusselt number has a linear and direct relationship with the local Deborah number De.

Effect of Circumferential Grooves and Tip Recess on Stall Characteristics of Transonic Axial Compressor Rotor

In the modern day gas turbine engine compressors have higher loading per stage and hence reduced stability range. Although the optimum performance is located close to stability limit but the flow instabilities arises due to the sudden change in operating conditions may lead to stall. Therefore a sufficient stall margin must be maintained to avoid such situations. The casing and tip treatments offer the stall margin improvement. In the present paper the effects of tip recess, circumferential grooves and combined model on the stall characteristics of a transonic axial flow compressor rotor (NASA rotor 37) has been investigated. The tip recess depth is equivalent to nominal clearance gap of 0.0356 cm. For the second model the six grooves were placed in casing from 20% to 80% of the blade tip chord. The depth of groove is three times of the width (0.4 cm). The separation between the grooves is half of the width. The maximum improvement in stall margin (62.45%) is achieved with circumferential grooves coupled with tip recess with some performance penalties. However the improvement with combined model is marginal as compared to only circumferential grooves model. The stall margin enhancement with tip recess model is 15.50% which is relatively lower than the other two models but with less performance penalties.