M. Mustafa

Cattaneo-Christov heat flux model for rotating flow and heat transfer of upper-convected Maxwell fluid

In this paper Cattaneo-Christov heat flux model is used to investigate the rotating flow of viscoelastic fluid bounded by a stretching surface. This model is a modified version of the classical Fourier’s law that takes into account the interesting aspect of thermal relaxation time. The boundary layer equations are first modeled and then reduced to self-similar forms via similarity approach. Both analytical and numerical solutions are obtained and found in excellent agreement. Our computations reveal that velocity is inversely proportional to the viscoelastic fluid parameter. Further fluid temperature has inverse relationship with the relaxation time for heat flux and with the Prandtl number. Present consideration even in the case of Newtonian fluid does not yet exist in the literature.

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.

Numerical and Series Solutions for Stagnation-Point Flow of Nanofluid over an Exponentially Stretching Sheet

This investigation is concerned with the stagnation-point flow of nanofluid past an exponentially stretching sheet. The presence of Brownian motion and thermophoretic effects yields a coupled nonlinear boundary-value problem (BVP). Similarity transformations are invoked to reduce the partial differential equations into ordinary ones. Local similarity solutions are obtained by homotopy analysis method (HAM), which enables us to investigate the effects of parameters at a fixed location above the sheet. The numerical solutions are also derived using the built-in solver bvp4c of the software MATLAB. The results indicate that temperature and the thermal boundary layer thickness appreciably increase when the Brownian motion and thermophoresis effects are strengthened. Moreover the nanoparticles volume fraction is found to increase when the thermophoretic effect intensifies.

Stagnation-Point Flow and Heat Transfer of a Casson Fluid towards a Stretching Sheet

This article reports the flow of a Casson fluid in the region of stagnation-point towards a stretching sheet. The characteristics of heat transfer with viscous dissipation are also analyzed. The partial differential equations representing the flow and heat transfer of the Casson fluid are reduced to ordinary differential equations through suitable transformations. The flow is therefore governed by the Casson fluid parameter β, the ratio of the free stream velocity to the velocity of the stretching sheet a=c, the Prandtl number Pr, and the Eckert number Ec. The analytic solutions in the whole spatial domain have been computed by the homotopy analysis method (HAM). The dimensionless expressions for the skin friction coefficient and the local Nusselt number have been calculated and discussed.

On peristaltic motion of pseudoplastic fluid in a curved channel with heat/mass transfer and wall properties

Peristaltic motion of shear-thinning and shear-thickening fluids through a curved channel.Elastic properties of the channel walls are considered.A regular perturbation method is used for the analytical analysis.Symmetry of the profiles in the upper and lower halves of the channel is destroyed in curved channel.Present model has importance in the blood flow through micro-circulatory system. This work addresses the combined effect of wall properties and heat/mass transfer on the peristaltic motion of pseudoplastic (shear-thinning/shear-thickening) fluid in a curved channel. The mathematical model is simplified through the assumption of long wavelength of the peristaltic wave compared to the mean half-width of the channel. Series solutions for stream function, temperature and concentration of species are derived. In contrast to the case of planar channel, the profiles are not symmetric about the central line of the curved channel. The size of the trapped bolus is different in the upper and lower halves of the curved channel. Moreover the number of circulations increase/decrease in the upper/lower half of the channel when the case of planar channel is approached.

Analytical study of Cattaneo–Christov heat flux model for a boundary layer flow of Oldroyd-B fluid*

We investigate the Cattaneo–Christov heat flux model for a two-dimensional laminar boundary layer flow of an incompressible Oldroyd-B fluid over a linearly stretching sheet. Mathematical formulation of the boundary layer problems is given. The nonlinear partial differential equations are converted into the ordinary differential equations using similarity transformations. The dimensionless velocity and temperature profiles are obtained through optimal homotopy analysis method (OHAM). The influences of the physical parameters on the velocity and the temperature are pointed out. The results show that the temperature and the thermal boundary layer thickness are smaller in the Cattaneo–Christov heat flux model than those in the Fouriers law of heat conduction.

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.

Boundary layer flow of Carreau fluid over a convectively heated stretching sheet

Two-dimensional boundary layer flow of Carreau fluid past a permeable stretching sheet is studied. Heat transfer subject to convective boundary conditions is analyzed. The relevant equations are first simplified by using boundary layer assumptions and reduced to self-similar forms by appropriate transformations. The problem is governed by various interesting parameters including power-law index (n), relaxation time ( λ 1 ), Prandtl number (Pr) and the Biot number (Bi). Series solutions are computed by homotopy analysis method (HAM). Fields are influenced appreciably with the variations of embedded parameters. Numerical values of skin friction coefficient and local Nusselt number are also tabulated.

A Comparative Study for Flow of Viscoelastic Fluids with Cattaneo-Christov Heat Flux

This article examines the impact of Cattaneo-Christov heat flux in flows of viscoelastic fluids. Flow is generated by a linear stretching sheet. Influence of thermal relaxation time in the considered heat flux is seen. Mathematical formulation is presented for the boundary layer approach. Suitable transformations lead to a nonlinear differential system. Convergent series solutions of velocity and temperature are achieved. Impacts of various influential parameters on the velocity and temperature are sketched and discussed. Numerical computations are also performed for the skin friction coefficient and heat transfer rate. Our findings reveal that the temperature profile has an inverse relationship with the thermal relaxation parameter and the Prandtl number. Further the temperature profile and thermal boundary layer thickness are lower for Cattaneo-Christov heat flux model in comparison to the classical Fourier’s law of heat conduction.

Rotating Flow of Magnetite-Water Nanofluid over a Stretching Surface Inspired by Non-Linear Thermal Radiation

Present study explores the MHD three-dimensional rotating flow and heat transfer of ferrofluid induced by a radiative surface. The base fluid is considered as water with magnetite-Fe3O4 nanoparticles. Novel concept of non-linear radiative heat flux is considered which produces a non-linear energy equation in temperature field. Conventional transformations are employed to obtain the self-similar form of the governing differential system. The arising system involves an interesting temperature ratio parameter which is an indicator of small/large temperature differences in the flow. Numerical simulations with high precision are determined by well-known shooting approach. Both uniform stretching and rotation have significant impact on the solutions. The variation in velocity components with the nanoparticle volume fraction is non-monotonic. Local Nusselt number in Fe3O4–water ferrofluid is larger in comparison to the pure fluid even at low particle concentration.