The effects of non-uniform heat source/sink and viscous dissipation on MHD boundary layer flow of Williamson nanofluid through porous medium under convective boundary conditions are studied. Surface transport phenomena such as skin friction, heat flux and mass flux are discussed besides the three boundary layers. The striking results reported as: increase in Williamson parameter exhibiting nanofluidity and external magnetic field lead to thinning of boundary layer, besides usual method of suction and shearing action at the plate, a suggestive way of controlling the boundary layer growth. It is easy to implement to augment the strength of magnetic field by regulating the voltage in the circuit. Also, addition of nano particle to the base fluid serves as an alternative device to control the growth of boundary layer and producing low friction at the wall. The present analysis is an outcome of Runge-Kutta fourth order method with a self corrective procedure i.e. shooting method.
The present paper analyzes the MHD flow of nanofluid past a permeable stretched surface. The effect of non-linear radiative heat transfer, higher order chemical reaction and slip boundary conditions are also incorporated to the flow phenomena to enhance the heat transfer rate in the nanofluid. A suitable self-similar transformation is employed to convert PDEs into non-linear ODEs. The resulting set of differential systems is solved numerically by fourth order Runge-Kutta method with shooting technique. The impact of thermophysical quantities on the flow field is shown via graphs. The numerical results for skin friction coefficient, local Nusselt and Sherwood numbers are calculated and demonstrated via table. It is found that heat generation is favorable to enhance the rate of shear stress as well as rate of heat transfer, further absorption retards mass transfer rate significantly. Also, the thickness of species distribution increases as the order of the chemical reaction n increases.
The present study is intended to analyse the effect of heat and mass transfer on boundary layer stagnation point flow of a viscous fluid over a non-isothermal shrinking sheet subject to transverse magnetic field and variable surface temperature. The medium of flow is considered to be porous. Further, the effect of variable surface temperature and concentration are also taken care of in the present analysis. The governing partial differential equations (PDEs) are transformed into ordinary differential equations (ODEs) by suitable similarity transformations. The numerical simulation is carried out using Runge-Kutta method of fourth order with shooting technique. The physical significance of pertinent parameters of the flow phenomenon is studied with the help of graphs and tables. One striking outcome of the present analysis is that the unstable velocity profiles with inflection points are marked due to power law variation of temperature and concentration of the linearly stretchable bounding surface leaving aside the smooth fall in temperature and concentration (span wise) across the flow field. Further, it is noted that increase in magnetic field intensity, suction and thermal as well as mass buoyancy parameters enhance the skin friction concomitantly favouring the effective momentum transport.
In this study, the heat and mass transfer of the blood flow, particularly in a capillary tube having a porous lumen and permeable wall in the presence of external magnetic field are considered. The velocity, temperature and concentration of blood flow become unsteady due to the time dependence of the stretching velocity, surface temperature and surface concentration. The thermal and mass buoyancy effect on blood flow, heat transfer and mass transfer are taken into account in the presence of thermal radiation. This analysis is very much useful in the treatment of cardiovascular disorders. The equations governing the flow under some assumptions are complex in nature, but capable of presenting the realistic model of blood flow using the theory of boundary layer approximation and similarity transformation. First, the system of coupled partial differential equations (PDEs) is converted into a system of coupled ordinary differential equations (ODEs). Then the solutions are obtained by Runge-Kutta method of 4thorder with shooting technique. The effects of various parameters such as Hartman number, radiation parameter, unsteadiness parameter, permeable parameter, thermal buoyancy parameter, Prandtl number, mass buoyancy parameter, velocity slip parameter, thermal slip parameter, Schmidt number on velocity, temperature, concentration, skin friction, Nusselt number and Sherwood number are depicted through graphs. Local Sherwood number enhances because of increase in Schmidt number. Moreover, some of the important results, which are discussed in the present study and have an impact on diseases like hyperthermia, stoke and moyamoya in human body.
The natural convective flow of conducting viscous fluid between two coaxial vertical cylinders partially filled with a porous material has been studied. The flow field is subjected to externally applied magnetic field (control input) and stress jump condition at the interface of two regions. The surface of the inner cylinder is subject to the constant heat flux and outer cylinder is maintained at constant temperature. The Brinkman extended Darcy model has been applied to porous media flow. The analytical solutions of the physical model are carried out with the help of modified Bessel function and numerical solutions by Runge Kutta method associated with shooting technique. The important findings are: the permeability of the medium and interface condition play vital role for the output of the desired flow rate and consistency of flow, the squeezing of the annular gap produces a cooling effect on cylindrical surfaces, the noticeable momentum transport occurs in the region close to the interface of fluid and porous region, the adjustable magnetic field (force-act-at-a distance) and stress jump condition (act-at-the contact) are to be simulated for obtaining desired smooth flow pattern.
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