The boundary layer equations for plane, incompressible, and steady flow are 

$$\matrix{ {u{{\partial u} \over {\partial x}} + v{{\partial u} \over {\partial y}} = - {1 \over \varrho }{{\partial p} \over {\partial x}} + v{{{\partial ^2}u} \over {\partial {y^2}}},} \cr {0 = {{\partial p} \over {\partial y}},} \cr {{{\partial u} \over {\partial x}} + {{\partial v} \over {\partial y}} = 0.} \cr }$$

Boundary Layer Theory

Thermophysical Properties Research Literature Retrieval Guide Edited by Y. S. Touloukian, J. K. Gerritsen and N. Y. Moore Second edition, revised and expanded. Book 1: Pp. xxi + 819. Book 2: Pp.621. Book 3: Pp. ix + 1315. (New York: Plenum Press, 1967.) n.p.

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Heat and Mass Transfer

Features of double stratification on stagnation point flow of Walter's B nanoliquid driven through Riga surface are examined in the current study. Via solutal stratification, radiation and thermal effects, heat and mass phenomena are evaluated. The novelty of the proposed investigation is focused on the important effect of melting phenomenon and EMHD Lorentz force along with stratification and heat generation over the rheology of the liquid flow. The influence of Brownian and thermophoresis particle deposition is included in transport equations involved in the analysis. Transformation is incorporated by the basic laws of mass, energy and linear momentum to acquire nonlinear differential system of equations. Utilizing Optimal Homotopy Analysis Method through BVPh2.0.0, optimum value of convergence control factors is estimated. Graphical findings for the dimensionless temperature, velocity and concentration for different pertinent parameters are explained. Numerical values of physical interest like skin friction coefficient, local Sherwood number and local Nusselt number are computed and visualized graphically. The heat generation and advanced modified Hartmann number improve the speed of flow. It is also observed that weaker thermal stratification upraises the rate of heat transport, and mass transport rate lessens for stronger mass stratification. In addition, contour graphs of velocity for ratio parameter A describe the accurate perception of flow. The intensity of temperature and concentration field is low owing to double stratification, whereas the stronger radiation corresponds the significantly rise in temperature. Reliability of outcomes assured by means of probable error analysis.

A study of dual stratification on stagnation point Walters' B nanofluid flow via radiative Riga plate: a statistical approach

Hybrid nanofluids are of great importance in the field of industry due to high effective thermal conductivity which causes high rates of heat transfer. The current article investigates the impact of variable magnetic field and chemical reaction of MWCNT/Fe3O4–water hybrid nanofluid over an exponentially shrinking porous sheet with slip boundary conditions. Suitable transformations convert the governing equations into coupled nonlinear ordinary differential equations. Further, these equations are solved by the help of shooting technique. The influences of operating parameters on the flow domain as well as force coefficients and rates of heat and mass transfers are computed and shown through graphs and tables. It is found that hybridity augments the temperature and concentration profiles. Further, suction/injection parameter enriches the skin friction coefficient, but reverse trend is observed for velocity slip parameter.

Influence of MWCNT/Fe3O4 hybrid nanoparticles on an exponentially porous shrinking sheet with chemical reaction and slip boundary conditions

An exertion is executed to explicate thermophysical aspects of viscoelastic fluid flow produced by a nonlinearized stretched surface. Here, viscoelasticity is characterized by Casson fluid model and expressed rheologically in momentum equation. Flow attributes of Casson fluid are thoroughly investigated under transversal magnetized field and along with provision of suction/injection to surface. Flow medium is also considered to be porous. Convective heating is supplied to the surface to depict heat transfer change within the flow domain. Nanosized particles are hanged into the Casson fluid to understand the effectiveness of Brownian motion and thermophoretic forces on the diffusion of particles. Generative chemical reactions are also considered to measure mass transport. Initially, flow narrating differential equations for concerning a problem are attained in differential equations and later on transforming into ordinary differential coupled system via similarity approach. Variations in flow associated distributions against involved parameters are divulged through graphical structures. Wall drag, thermal and mass fluxes are also calculated. Credibility of computing results is tested with the aid of comparison with previously published data in limiting sense.

MHD Casson nanofluid flow over nonlinearly heated porous medium in presence of extending surface effect with suction/injection

Heat transport and stagnation‐point flow of magnetized nanoliquid with variable thermal conductivity, Brownian moment, and thermophoresis aspects

This article studies the effect of nanoparticle aggregation on the 3D flow of titanium nanoliquid based on ethylene glycol $$ ( {\text{C}}_{ 2} {\text{H}}_{ 6} {\text{O}}_{2} - {\text{TiO}}_{2} ) $$
 due to an exponentially elongated surface. Thermal analysis is carried out considering linear thermal radiation, Joule heating, and mechanisms of the heat source/sink, while the aspect of the homogeneous single-order chemical reaction is included in the analysis of the solute. The variable magnetic field is also accounted. The modified Maxwell model (Maxwell–Bruggeman) is implemented to estimate the effective conductivity of the nanoliquid. The displayed equations are moderated in quantities without dimensions. The 2-point nonlinear boundary value problem (BVP) is solved by the shooting procedure. The importance of effective parameters is described through graphs. Numerical data are presented to study the friction factor, the heat transfer rate, and the mass transfer rate. It has been established that the aggregation of nanoparticles significantly improves the thermal field. Furthermore, the effect of magnetism is more in ordinary fluid than in nanofluid.

Thermal Enhancement of Radiating Magneto-Nanoliquid with Nanoparticles Aggregation and Joule Heating: A Three-Dimensional Flow

The convective three dimensional electrically conducting Casson nanofluid flow over an exponentially stretching sheet embedded in a saturated porous medium and subjected to thermal as well as solutal slip in the presence of externally applied transverse magnetic field (force-at-a-distance) is studied. The heat transfer phenomenon includes the viscous dissipation, Joulian dissipation, thermal radiation, contribution of nanofluidity and temperature dependent volumetric heat source. The study of mass diffusion in the presence of chemically reactive species enriches the analysis. The numerical solutions of coupled nonlinear governing equations bring some earlier reported results as particular cases providing a testimony of validation of the present study. The important findings are reported as Casson fluid contributes to accelerate the processes of momentum diffusivity but decelerates the thermal diffusivity. The effects of respective Biot numbers in temperature and concentration distributions are significant whereas cross effects are not. Further, the existence of chemical reaction stabilizes the characteristics of rate coefficients at the surface.

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Numerical analysis of three-dimensional MHD flow of Casson nanofluid past an exponentially stretching sheet

An analysis is made to investigate the effect of inclined magnetic field on Casson nanofluid over a stretching sheet embedded in a saturated porous matrix in presence of thermal radiation, non-uniform heat source/sink. The heat equation takes care of energy loss due to viscous dissipation and Joulian dissipation. The mass transfer and heat equation become coupled due to thermophoresis and Brownian motion, two important characteristics of nanofluid flow. The convective terms of momentum, heat and mass transfer equations render the equations non-linear. This present flow model is pressure gradient driven and it is eliminated with the help of potential/ambient flow condition. Surface condition is characterised by Newtonian heating/cooling. The numerical solution by Runge-Kutta method with shooting technique results in important findings: formation of inverted boundary layer is to be regulated by adjusting the relative shearing effect of plate and free stream, increase in angle of inclination and thermal radiation ascribe to low flow rate and higher thermal diffusion, in presence of Newtonian heating at the bounding surface the temperature of the nanofluid decreases with the higher values of Casson fluidity; this may have a therapeutic application to control the temperature of blood or any biological fluid.

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Kharabela Swain

Papers

Influence of MWCNT/Fe3O4 hybrid nanoparticles on an exponentially porous shrinking sheet with chemical reaction and slip boundary conditions

Heat transport and stagnation‐point flow of magnetized nanoliquid with variable thermal conductivity, Brownian moment, and thermophoresis aspects

Thermal Enhancement of Radiating Magneto-Nanoliquid with Nanoparticles Aggregation and Joule Heating: A Three-Dimensional Flow

Numerical analysis of three-dimensional MHD flow of Casson nanofluid past an exponentially stretching sheet

Heat and mass transfer of MHD Casson nanofluid flow through a porous medium past a stretching sheet with Newtonian heating and chemical reaction