Unsteady Boundary Layer Flow and Heat Transfer Due to a Stretching Sheet by Quasilinearization Technique

In this paper, the problem of unsteady laminar boundary-layer flow and heat transfer of a viscous income-pressible fluid over stretching sheet is studied numerically. The unsteadiness in the flow and temperature is caused by the time-dependent stretching velocity and surface temperature. A similarity transformation is used to reduce the governing boundary-layer equations to couple higher order non-linear ordinary differential equations. These equations are numerically solved using quasi-linearization technique. The effect of the governing parameters unsteadiness parameter and Prandtl number on velocity and temperature profile is discussed. Besides the numerical results for the local skin friction coefficient and local Nusselt number are presented. The computed results are compared with previously reported work.

Nonlinear radiative heat transfer in magnetohydrodynamic(MHD)stagnation point flow of nanofluid past a stretching sheet with convective boundary condition

Two-dimensional boundary layer flow of nanofluid fluid past a stretching sheet is examined.The paper reveals the effect of non-linear radiative heat transfer on magnetohydrodynamic(MHD)stagnation point flow past a stretching sheet with convective heating.Condition of zero normal flux of nanoparticles at the wall for the stretched flow is considered.The nanoparticle fractions on the boundary are considered to be passively controlled.The solution for the velocity,temperature and nanoparticle concentration depends on parameters viz.Prandtl number Pr,velocity ratio parameter A,magnetic parameter M,Lewis number Le,Brownian motion Nb,and the thermophoresis parameter Nt.Moreover,the problem is governed by temperature ratio parameter Nr¼Tf T1
and radiation parameter Rd.Similarity transformation is used to reduce the governing non-linear boundary-value problems into coupled higher order non-linear ordinary differential equation.These equations were numerically solved using the function bvp4c from the matlab software for different values of governing parameters.Numerical results are obtained for velocity,temperature and concentration,as well as the skin friction coefficient and local Nusselt number.The results indicate that the skin friction coefficient Cf increases as the values of magnetic parameter M increase and decreases as the values of velocity ratio parameter A increase.The local Nusselt number-θ0(0)decreases as the values of thermophoresis parameter Nt and radiation parameter Nr increase and it increases as the values of both Biot number Bi and Prandtl number Pr increase.Furthermore,radiation has a positive effect on temperature and concentration profiles.

Finite element solution of nonlinear convective flow of Oldroyd-B fluid with Cattaneo-Christov heat flux model over nonlinear stretching sheet with heat generation or absorption

In this study,a two-dimensional boundary layer flow of steady incompressible nonlinear convective flow of Oldroyd-B fluid over a nonlinearly stretching sheet with Cattaneo-Christov heat flux model and heat generation or absorption is examined.The governing equations of the boundary layer flow which are highly nonlinear partial differential equations are converted to the ordinary differential equations using similarity transformations and then the Galerkin finite element method(GFEM)is used to solve the proposed problem.The effect of local Deborah numbers 0,and ft.local buoyancy parameter z,Prandtl number Pr,Deborah number y,and heat generation/absorption parameter<5 on the temperature and the velocity as well as heat transfer rate and shear stress are discussed both in graphical and tabular forms.The result shows the enlargement in the local buoyancy parameter A will improve the velocity field and the heat transfer rate of the boundary layer flow.Moreover,our present work evinced both local skin friction coefficient and heat transfer rate step up if we add the values of non-linear stretching sheet parameter and local heat generation/absorption parameter has quite the opposite effect.The numerically computed values of local skin friction coefficient and local Nusselt number are validated with available literature and evinced excellent agreement.

Magnetohydrodynamic(MHD)boundary layer stagnation point flow and heat transfer of a nanofluid past a stretching sheet with melting

The paper examines the melting heat transfer in magnetohydrodynamic(MHD)stagnation point flow of a nanofluid past a stretching sheet.Boundary layer theory is employed to simplify the system of partial differential equations of motion,energy and concentration to three coupled non-linear ordinary differential equations.The non-linear ordinary differential equations and their boundary conditions are changed into dimensionless form by using suitable similarity variables before numerically solved using fourth order Runge-Kutta-Fehlberg method along with shooting technique.The effect of pertinent parameters on different flow fields are determined and discussed in detail through several plots and tables.The numerical results are obtained for velocity,temperature and concentration profiles.It is found that the skin friction coefficient and Sherwood number decrease with an increase in B and M parameters.However,the local Nusselt number-θ′(0)increases with an increase in B and Nt.Then,the results are compared and found to be in good agreement with the previously published results in limiting cases of the problem.

Analysis of flow of visco-elastic nanofluid with third order slips flow condition,CattaneoChristov heat and mass diffusion model

This communication reports,the flow of viscoelastic nanofluid with third order slip flow condition,Cattaneo-Christov heat and mass diffusion model.The joined non-linear ordinary differential equations(ODEs)were acquired from the partial differential equations,which are resulting from conservation of momentum,energy and species.By means of similarity transformations these ODEs were alerted into dimensionless form and solved numerically by means of bvp4c solver.The effects of different parameters on velocity,temperature,and concentration profiles were examined and discussed in depth by means of graphs and tables.The outcomes indicate that the velocity profile along both x and y directions augment with higher values of viscoelastic parameter.The results also confirm that an increment in the values of ratio parameter tends to grow up the velocity profile alongside y-direction.However,the velocity profile along x-direction slows down with increment in the value of third order slip parameter.Also,the results illustrate that diminution in temperature is observed for higher Sc in the region of boundary layer.Besides,both temperature and concentration can be improved via higher Biot number.The upshots also portrayed that the local skin friction coefficient augmented within mounting values of viscoelastic fluid parameter.Furthermore,for finer values of Biot number both local Nusselt number and the local Sherwood number are enlarged.In addition,the most favorable agreement is observed among the results of the present study and those of the earlier studies.

MHD BOUNDARY-LAYER FLOW AND HEAT TRANSFER OVER PERMEABLE PLATE WITH CONVECTIVE SURFACE BOUNDARY CONDITION

A numerical analysis has been carried out to investigate the problem of magnetohydrodynamic(MHD)boundary-layer flow and heat transfer of a viscous incompressible fluid over a fixed plate.Convective surface boundary condition is taken into account for thermal boundary condition.A problem formulation is developed in the presence of thermal radiation,magnetic field and heat source/sink parameters.A similarity transformation is used to reduce the governing boundary-layer equations to couple higher-order nonlinear ordinary differential equations.These equations are numerically solved using Keller–Box method.The effect of the governing parameters such as radiation,Prandtl number,Hartman number,heat source/sink parameter on velocity and temperature profile is discussed and shown by plotting graphs.It is found that the temperature is an increasing function of convective parameter A,radiation and heat source parameters.Besides,the numerical results for the local skin friction coefficient and local Nusselt number are computed and presented in tabular form.Finally a comparison with a previously published results on a special case of the problem has done and shows excellent agreement.

The effect of induced magnetic field and convective boundary condition on MHD stagnation point flow and heat transfer of upper-convected Maxwell fluid in the presence of nanoparticle past a stretching sheet

The present study examines the effect of induced magnetic field and convectiveboundary condition on magnetohydrodynamic(MHD)stagnation point flow and heat transfer dueto upper-convected Maxwell fluid over a stretching sheet in the presence of nanoparticles.Boundary layer theory is used to simplify the equation of motion,induced magnetic field,energyand concentration which results in four coupled non-linear ordinary differential equations.Thestudy takes into account the effect of Brownian motion and thermophoresis parameters.Thegoverning equations and their associated boundary conditions are initially cast into dimensionlessfonm by similarity variables.The resulting system of equations is then solved numerically usingfourth order Runge-Kutta-Fehlberg method along with shooting technique.The solution for thegoverning equations depends on parameters such as,magnetic,velocity ratio parameter B,Biotnumber Bi,Prandtl number Pr,Lewis number Le,Brownian motion Nb,reciprocal of magnetic Prandtl number A,the thermophoresis parameter Nt,and Maxwell parameter β.The numerical results are obtained for velocity,temperature,induced magnetic field andconcentration profiles as well as skin friction coefficient,the local Nusselt number andSherwood number.The results indicate that the skin friction coefficient,the local Nusseltnumber and Sherwood number decrease with an increase in B and M parameters.Moreover,local Sherwood number-φ'(O)decreases with an increase in convective parameter Bi,but the local Nusselt number-φ'(0)increases with an increase in Bi.The results are displayed both ingraphical and tabular form to illustrate the effect of the governing parameters on thedimensionless velocity,induced magnetic field,temperature and concentration.The numericalresults are compared and found to be in good agreement with the previously published resultson special cases of the problem.