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The current study focused on forced convection water boundary layer flow on permeable diverging channel for variable physical properties of fluid. The formation of coupled nonlinear partial differential equations is expressed in terms of non-dimensional quantity using similarity transformation. The solution of non-dimensional differential equation obtained by numerical finite difference scheme with combination of quasi-linearization technique. It is found that the Eckert number is significant in the boundary layer region in laminar flow, and also, the effects of physical parameters are investigated numerically and shown graphically. © 2021, Springer Nature Singapore Pte Ltd.

World University root node

Mathematics

School of Advanced Sciences

Chennai Campus

Lecture Notes in Mechanical Engineering

Effect of Viscous Dissipation of Laminar Flow over a Flat Plate with Variable Properties

The purpose of this study report is to examine the unsteady force convection flow on irregular boundary over a diverging channel with effect of viscous dissipation. The fundamental equations of fluid, continuity, momentum, and energy equations are converted into dimensionless form. The resulting coupled partial differential equations are linearized by quasilinearization technique, the backward, and central difference scheme for nonuniform mesh used to solve the system of linear equations. We found that finite difference scheme for nonuniform mesh gives smoothness of solution compared to finite difference scheme for uniform mesh on irregular boundary, this is evident from Figure 2. Near the wall region, as viscous dissipation (Ec) increases from 0.2 to 0.5, the temperature profiles overshoots 20% to 112%. Also the effects of Reynolds number (Re) on heat transfer coefficient is comparatively less than skin-friction coefficient. © 2020 Wiley Periodicals LLC

Heat Transfer

Analysis of unsteady force convection flows on irregular boundary over a diverging channel

Objective: The objective of the current study is to deal with magnetohydrodynamic (MHD) nanoliquid flow over moving vertical plate with variable Prandtl numbers and viscosities. This analysis also includes the influence of thermal radiation. Quite significant variation in viscosity and Prandtl number in high-range temperature is observed. Thus, Prandtl number and viscosity are surmised to vary as an inversely proportional linear function of temperature. Problem definition: The MHD nanoliquid flow is considered along with the semi-infinite plate with the velocity Uw toward the x-direction, which is also the direction for free-stream velocity (Formula presented.). The geometrical sketch of the physical problem with the coordinate system is shown in Figure 1. The coordinate system has two coordinate axes: the (Formula presented.) -coordinate (x) and (Formula presented.) -coordinate (y). They are perpendicular to each other. The mathematical modeling of physical problem has been formulated by incorporating viscous terms into the governing equation related to thermal radiation, buoyant force, Brownian motion, thermophoresis, and magnetic parameter. Methodology: The mathematical modeling of current physical problem consists of highly nonlinear partial differential equations which have been solved numerically using quasilinearization technique along with finite difference method. The present outcome during numerical simulation is outlined in terms of velocity, temperature, and concentration profiles and they are analyzed with suitable physical reasons. Main results: The impact of various parameters on the velocity, temperature, and concentration profiles has been discussed with physical explanation. Velocity profile (Formula presented.) of the fluid enhances and concentration (Formula presented.) reduces with escalating buoyancy parameter (Formula presented.). In particular, 13% increment in velocity profile is observed as (Formula presented.) increases by 0.9 scale [(Formula presented.)], whereas 17% reduction in concentration profiles is noticed as (Formula presented.) increases by 0.5 scale [(Formula presented.)] at other fixed parameters. It is observed that magnetic parameter (Formula presented.) increases the temperature (Formula presented.) and concentration profiles (Formula presented.), whereas it works as deduction parameter for velocity profile (Formula presented.). The increasing value of thermophoresis (Formula presented.) and Lewis number (Formula presented.) works as catalyst for velocity, temperature, and concentration profiles. As thermophoresis (Formula presented.) increases from 0.5 to 2.0, temperature profile approximately increases 65% at other fixed parameters. As Lewis number (Formula presented.) increases from 0.5 to 4.0, then the temperature increases approximately 75% at other fixed parameters. © 2020 Wiley Periodicals LLC

MHD nanofluid flow with variable physical parameters via thermal radiation: A numerical study

Consideration is given to the problem of steady axisymmetric creeping flow of a micropolar fluid around the spherical drop of non-Newtonian liquid shell covered with permeable medium. The field equations of micropolar fluids are presented in terms of velocity vector and microrotation vector. External liquid permeates into the porous layer, but it is not mixed with the liquid located in the internal cavity of a capsule. The flow inside the permeable medium is described by the Brinkman equation. The stream function solution for the external flow field is derived in terms of modified Bessel's function and Gegenbauer's polynomial. The solution is determined by dilating the stream function in terms of the dimensionless parameter S for the internal flow field (Reiner-Rivlin liquid sphere). Analytical expressions for the pressure field, coupling number, microrotation component, viscosity ratio, permeability parameter, and drag force are calculated. The effect of various parameters on the drag force is presented graphically and discussed. It is observed that the drag on a micropolar fluid sphere is more than that on a permeable sphere. Different limiting cases are also considered. © 2020 by Begell House, Inc.

Journal of Porous Media

Drag on a reiner-rivlin liquid sphere embedded in a porous region placed in a micropolar fluid

The present work focus on water boundary layer flow over an exponential permeable stretching sheet in the presence of suction/injection with variable viscosity and prandtl number. The nonlinear partial differential equations governing flow and thermal fields are presented in non-dimensional form using suitable non-similar transformation. Finally non dimensional partial differential the equations are solved by the implicit finite difference method in combination with the Quasi-linearization technique. The numerical results for skin-friction and local Nusselt number are shown graphically to display effects of physical parameters. © Springer Nature Singapore Pte Ltd. 2020.

Springer Proceedings in Mathematics and Statistics

Water boundary layer flow over an exponentially permeable stretching sheet with variable viscosity and prandtl number

The objective of the current study is to investigate the forced convection laminar boundary layer flow over a flat plate in a diverging channel with variable viscosity. The physical governing equations are converted to nondimensional partial differential equations (PDEs) using similarity transformation. The coupled PDEs with boundary constrains are solved numerically using quasilinearization technique. Computational results are given in terms of flow parameter (Formula presented.), suction or injection A, and viscous dissipation parameter Ec. Stability analysis was conducted and the solutions were found to be stable for real values of (Formula presented.). We found that variable Prandtl number with quasilinearization technique method gives smoothness of solution compared to fixed Prandtl number. This is shown graphically for different fluids in Section 5. Also, the significant effect of the suction/injection parameter (Formula presented.) on velocity, temperature profiles, skin friction, and heat transfer is observed. © 2020 Wiley Periodicals LLC

Boundary layer flow and stability analysis of forced convection over a diverging channel with variable properties of fluids

The objective of this paper works is to study, a stability analysis of two dimensional boundary layer forced convection over a fixed vertical plate vary in viscosity and prandtl number with time dependent . The governing equations are transformed to non linear coupled partial differential equations with boundary conditions have been solved numerically by finite difference scheme in combination with quasi-linearization technique with suitable step size along the stream- wise direction. Results are showed different values of mass transfer parameter (A) . It was found that the solutions is stable when increases the suction/injection parameter A.

International Journal of Innovative Technology and Exploring Engineering Regular Issue

A Stability of Force Convection Boundary Layer Laminar flow in Diverging Chennal

Boundary layer flow phenomenons on a stretching sheet find numerous applications in industrial processes such as manufacture and extraction of rubber and polymer sheets. The current study focuses on two-dimensional water boundary layer flow on exponential stretching surface with a vertical plate for variable physical properties of fluid such as viscosity and Prandtl number. The Quasilinearization technique has been used on governing equations to transform nonlinear to linear equations and these equations are discretized by finite difference techniques to get numerical solutions. The effect of buoyancy parameters (λ), velocity ratio parameter (ε) and streamwise coordinator (ξ) on velocity profiles (F), temperature profiles (θ), local skin-friction coefficient (Cfx(ReLξexp(ξ))1/2) and the local Nusselt number (Nux(ReLξexp(ξ))−1/2) has been analyzed graphically based on numerical outcome. The magnitude of velocity profiles (F) increases and temperature profile decreases approximately by 4% and 16% with increases the buoyancy parameter from λ = 1 to λ = 3 at = 0.5 and ξ = 1.0. The skinfriction and heat transfer coefficient increases approximately by 22% and 27% with an increase in ξ from 0.5 to 1.0 at fixed ε = 0.5 and λ = 1.0. The variations of velocity profiles and temperature profiles have more impact with ε as compared to ξ and λ. The benchmark studies were carried out to validate the current results with previously published work and found to be in excellent agreement. © 2019 Wiley Periodicals, Inc.

Department of Mathematics

VIT Unitversity

Heat Transfer - Asian Research

Analysis of a boundary layer flow over moving an exponentially stretching surface with variable viscosity and Prandtl number

Purpose The purpose of the present study is to analyze the mixed convection water boundary layer flows over moving vertical plate with variable viscosity and Prandtl number. The non-linear partial differential equation governing the flow and thermal fields are presented in non-dimensional form by using appropriate transformation. The quasi-linearization technique in combination with implicit finite difference scheme has been adopted to solve the nonlinear-coupled partial differential equation. The numerical results are displayed graphically to illustrate the influence of various non-dimensional physical parameters on velocity and temperature. Further, the numerical results for local skin-friction coefficient and local Nusselt number are also reported. The present findings are compared with previously reported results, and these comparisons are found to be in excellent agreement.Design/methodology/approach The nonlinear partial differential equations governing the flow and thermal fields have been solved numerically using the implicit finite difference scheme in combination with the quasi-linearization technique. The numerical results are presented in terms of skin friction and heat transfer rate which are useful in determining the surface heat requirements for stabilizing the laminar boundary layer flow over a moving plate in water.Findings The effect of the ratio of free-stream velocity to the composite reference velocity is significant on the velocity profile. Near the wall region, as ratio of free stream velocity to composite reference velocity increases form 0.1 to 0.5, the velocity overshoot gets enhanced from 3 per cent to 41 per cent. The influence of buoyancy parameter and ration of free stream velocity to composite reference velocity on temperature profile is comparatively less than on velocity profiles. The increase in the skin friction coefficient is dependent on the increase in the value of ratio of free stream velocity to composite reference velocity if the buoyancy parameter λ is fixed and vice versa and increases in ΔT results in a decrease in N and Pr.Originality/value The present investigation is to deal with the solution of steady laminar water boundary layer flows over a moving plate with temperature-dependent viscosity and Prandtl number applicable for water using practical data. The fluid considered here is water, as it is one of the most common working fluids found in engineering applications.

International Journal of Numerical Methods for Heat and Fluid Flow

Analysis of mixed convection in water boundary layer flows over a moving vertical plate with variable viscosity and Prandtl number

The Scope of this paper works is to study, steady incompressible non-similar two dimensional boundary layer over a stretching surface with temperature dependent viscosity and PRANDTL number. The coupled partial differential equations with boundary conditions have been solved numerically using an implicit finite difference with combination of quasi-linearization technique with suitable step size along the stream- wise direction. The numerical results are displayed for velocity and temperature profiles with different parameter values. Further, it was found that the buoyancy parameter is more significant for water boundary flow. © 2018, Institute of Advanced Scientific Research, Inc. All rights reserved.

Physics

Journal of Advanced Research in Dynamical and Control Systems

The effects of buoyancy force of fluid flow over a water boundary layer with variable viscosity and PRANDTL number

Department of Energy and Power Electronics

School of Electrical Engineering

Vellore Campus

2017 International Conference on Trends in Electronics and Informatics (ICEI)

Design of auto-performance optimization tool for diesel engine

The present study deals with natural convection heat transfer within water (Pr = 7.2) filled inclined square cavities for hot bottom wall (case 1: isothermal heating/case 2: non-isothermal heating) and cold side walls in the presence of adiabatic top wall. The Galerkin finite element method has been used to solve the nonlinear coupled partial differential equations governing the fluid flow and thermal fields. This method is further used to solve the Poisson equation for streamfunction and heatfunction. The streamlines (ψ), isotherms (θ) and heatlines (TV) are obtained for various inclination angles (ψ = 0°, 30° and 60°) in the range of Rayleigh numbers (10 ≤Ra ≤ 10). The physical significance of heatlines have been demonstrated for a comprehensive understanding of heat energy distribution within the inclined square cavities. The flow pattern is symmetric for ψ = 0° whereas asymmetric flow pattern is observed for the ψ = 30° and 60° due to tangential and normal components of buoyancy forces. At Ra = 103, weak fluid circulation and orthogonal heatlines on isothermal surface, indicate conduction dominant heat transfer for both cases. Strong closed loop heatlines are found due to strong fluid convective circulation cells at Ra = 105. Heat transfer rates are obtained in terms of local and average Nusselt numbers. In general, the overall amount of heat transfer along the right wall increases with inclination angle and that decreases along the left wall with increase in inclination angle. The non-isothermal heating case exhibits greater heat transfer rates at the center of the bottom wall than the isothermal heating whereas average Nusselt number shows that overall heat transfer rate is larger for the isothermal heating case as compared to that of non-isothermal heating case. Copyright © 2012 by ASME.

ASME 2012 Heat Transfer Summer Conf. Collocated with the ASME 2012 Fluids Engineering Div. Summer Meeting and the ASME 2012 10th Int. Conf. on Nanochannels, Microchannels and Minichannels, HT 2012