In the study of boundary layer regions, it is in practice to dimensionalize the governing system and grouping variables together into dimensionless quantities in order to curtail the total number of variables. In similar flow phenomenon the physical parameters do not vary along the streamwise direction. However in non-similar flows the physical quantities change in the streamwise direction. In non-similar flows we are forced to non-dimensionalize the governing equations through non-similarity transformations. The forced flow of Oldroyd-B fluid is initiated as a result of stretching of a surface at an exponential rate. Flows over stretching surfaces are important because of their applications in extrusion processes. The forthright purpose of this study is to consider the non-similar aspects of forced convection from flat heated surface subjected to external viscoelastic fluid flow, described by the freely growing boundary layers enclosed by a region that involves without velocity and temperature gradients. The governing system of nonlinear partial differential equations (PDE’s) is transformed into dimensionless form by proposing new non-similar transformations. The dimensionless partial differential system is solved by using local non-similarity via bvp4c. Thermal transport analysis is conducted for distinct values of dimensionless numbers. It is revealed that heat shifting process expanded by the increase in the numerical values of Prandtl number and relaxation time. The dimensionless convective heat transfer coefficient results revealed that it is declining by expanding relaxation time constant [Formula: see text] and a boost is observed by enlarging the Pr and retardation time constant [Formula: see text]. A comparison of Nusselt number is presented.
In the current article, non-similar model is developed for mixed convective boundary layer flow over a permeable vertical surface immersed in nanofluid. The flow is initiated due to the plate stretching in vertical direction and by natural means such as buoyancy. The governing dimensional equations are converted to non-dimensional equations through characteristic dimensions. Furthermore the non-similar modeling is done by choosing ξ (X) as non-similarity variable and η(X, Y) as pseudo-similarity variable. The non-similar partial differential system (PDS) is then solved by using local non-similarity method via bvp4c. The heat and mass transfer analysis are carried out by studying local Nusselt and Sherwood numbers in tabular form for some important parameters involved in the non-similar flow. The concentration, velocity and temperature profiles are graphically represented for various dimensionless number such as Prandtl number (Pr), Brownian motion (Nb), Lewis number Le and thermophoresis (Nt). Reversed flow is observed for the velocity profile as non-similar variable is varied. Enhancement in thermal profile is witnessed for Nb, Nt and reduction in temperature is observed for Pr. Concentration is reduced for different values of Pr, Le, Nb. Finally this article intends to develop an intuitive understanding of non-similar models by emphasizing the physical arguments. The authors developed the nonsimilar transformations and tackled the dimensionless non-similar structure by employing the local non-similarity technique. To the best of authors’ observations, no such study is yet published in literature. This study may be valuable for the researchers investigating towards industrial nanofluid applications, notably in geophysical and geothermal systems, heat exchangers, solar water heaters, biomedicine, and many other fields.
In this study, an analysis is made by studying more reliable nonsimilar magneto-hydrodynamics (MHD) flow of Maxwell fluid with nanomaterials. Nonsimilar transport is produced by extending of sheet with arbitrary velocity. Maxwell structure is marked to indicate the non-Newtonian fluid behavior. The leading nondimensional partial differential system (PDEs) is transmuted to a set of the nonlinear ordinary differential system (ODEs) through local nonsimilarity technique. The developing system is solved numerically using an implemented package known as bvp4c in MATLAB. The analysis discovers several physical features of thermal and velocity profiles. Remark the flow accelerated for greater Deborah and Hartman parameters. The influence of thermophoresis number on the thermal figure is minimal. The conducts of velocity, concentration, and thermal distribution and local Nusselt number and skin friction are illustrated graphically by taking distinct parameters. The consequences disclose that the local Nusselt number is an increasing function of Prandtl number; however, it is a decaying function for Brownian motion. The rise in skin friction is observed for increasing Brownian motion and Lewis numbers.
The objective of this paper is to study the mixed convective nonsimilar flow above an exponentially stretching sheet saturated by nanofluid. The leading partial differential equations (PDEs) of the problem have been modified towards dimensionless nonlinear PDEs utilizing newly proposed nonsimilarity transformations. Furthermore, local nonsimilarity procedure up to-second truncation has been operated to change the dimensionless PDEs into ordinary differential equations (ODEs). MATLAB-based algorithm bvp4c is used to observe the consequences of the distinct parameters namely Prandlt number [Formula: see text], magnetic field [Formula: see text], Lewis number [Formula: see text], Brownian motion [Formula: see text], Eckert number [Formula: see text], thermophoresis [Formula: see text] on velocity, concentration and temperature distribution are shown in graphical portray. Additional outcomes presume the heat penetration into the fluid enhances with increase in Biot number and Brownian motion. Increasing values of [Formula: see text] and [Formula: see text] cause decrease of temperature profile.
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