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1

MHD mixed convection in copper-water nanofluid filled lid-driven square cavity containing multiple adiabatic obstacles with discrete heating

Gorla R. S. R., Siddiqa S., Hasan A. A., Salah T., Rashad A. M.

International Journal of Applied Mechanics and Engineering

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2020

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Vol. 25, no. 2

57--74

EN

The objective of the present work is to investigate the influence of nanoparticles of copper within the base fluid (water) on magneto-hydrodynamic mixed-convection flow in a square cavity with internal generation. A control finite volume method and SIMPLER algorithm are used in the numerical calculations. The geometry is a lid-driven square cavity with four interior square adiabatic obstacles. A uniform heat source is located in a part of the left wall and a part of the right wall of the enclosure is maintained at cooler temperature while the remaining parts of the two walls are thermally insulated. Both the upper and bottom walls of the cavity are considered to be adiabatic. A comparison with previously published works shows a very good agreement. It is observed that the Richardson number, Ri, significantly alters the behavior of streamlines when increased from 0.1 to 100.0. Also, the heat source position parameter, D, significantly changes the pattern of isotherms and its strength shifted when D moves from 0.3 to 0.7.

2

MHD free convection-radiation interaction in a porous medium - part I: numerical investigation

Vasu B., Gorla R. S. R., Murthy P. V. S. N., Prasad V. R., Bég O. Anwar, Siddiqa S.

International Journal of Applied Mechanics and Engineering

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2020

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Vol. 25, no. 1

198--218

EN

A numerical investigation of two dimensional steady magnetohydrodynamics heat and mass transfer by laminar free convection from a radiative horizontal circular cylinder in a non-Darcy porous medium is presented by taking into account the Soret/Dufour effects. The boundary layer conservation equations, which are parabolic in nature, are normalized into non-similar form and then solved numerically with the well-tested, efficient, implicit, stable Keller–Box finite-difference scheme. We use simple central difference derivatives and averages at the mid points of net rectangles to get finite difference equations with a second order truncation error. We have conducted a grid sensitivity and time calculation of the solution execution. Numerical results are obtained for the velocity, temperature and concentration distributions, as well as the local skin friction, Nusselt number and Sherwood number for several values of the parameters. The dependency of the thermophysical properties has been discussed on the parameters and shown graphically. The Darcy number accelerates the flow due to a corresponding rise in permeability of the regime and concomitant decrease in Darcian impedance. A comparative study between the previously published and present results in a limiting sense is found in an excellent agreement.

3

An intial-value technique for self-adjoint singularly perturbed two-point boundary value problems

Padmaja P., Aparna P., Gorla R. S. R.

International Journal of Applied Mechanics and Engineering

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2020

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Vol. 25, no. 1

106--126

EN

In this paper, we present an initial value technique for solving self-adjoint singularly perturbed linearvboundary value problems. The original problem is reduced to its normal form and the reduced problem is converted to first order initial value problems. This replacement is significant from the computational point of view. The classical fourth order Runge-Kutta method is used to solve these initial value problems. This approach to solve singularly perturbed boundary-value problems is numerically very appealing. To demonstrate the applicability of this method, we have applied it on several linear examples with left-end boundary layer and rightend layer. From the numerical results, the method seems accurate and solutions to problems with extremely thin boundary layers are obtained.

4

Radiation absorption and chemical reaction effects on Rivlin-Ericksen flow past a vertical moving porous plate

Sravanthi C. S., Gorla R. S. R.

International Journal of Applied Mechanics and Engineering

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2019

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Vol. 24, no. 3

675--689

EN

An analysis has been carried out to study the combined effects of radiation absorption and chemical reaction on an incompressible, electrically conducting and radiating flow of a Rivlin-Ericksen fluid along a semi-infinite vertical permeable moving plate in the presence of a transverse applied magnetic field. It is assumed that the suction velocity, the temperature and the concentration at the wall are exponentially varying with time. The dimensionless governing equations for this investigation are solved analytically using two-term harmonic and non-harmonic functions. A comparison is made with the available results in the literature for a special case and our results are in very good agreement with the known results. A parametric study of the physical parameters is made and results are presented through graphs and tables. The results indicate that the fluid velocity and temperature could be controlled by varying the radiation absorption.

5

Homotopy simulation of non-Newtonian Spriggs fluid flow over a flat plate with oscillating motion

Ray A. K., Vasu B., Gorla R. S. R.

International Journal of Applied Mechanics and Engineering

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2019

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Vol. 24, no. 2

359--385

EN

An incompressible flow of a non-Newtonian Spriggs fluid over an unsteady oscillating plate is investigated using the Homotopy Analysis Method (HAM). An analytic solution of sine and cosine oscillations of the plate has been obtained. The similarity transformation is introduced to reduce the governing partial differentia equations into a single non-linear dimensionless partial differential equation. The effects of the power index of Spriggs fluid and convergence control parameter of HAM for the flow are studied extensively. The range of the convergence control parameter for convergence of series solution for different values of the power index of Spriggs fluid is obtained. The solution for a Spriggs fluid is noticeably different from the solution obtained for a Newtonian fluid. The influences of the shear thinning and shear thickening fluid on the velocity profile are shown graphically. The transient flow effect is higher for non-Newtonian Spriggs fluid than that of a Newtonian fluid. It is also observed that the interval to reach the steady state for the cosine case is less than the sine case. The applications of Stokes’ second problem have been widely found in the variety of fields of biomedical, medical, chemical, micro and nanotechnology.

6

Effects of heat source/sink and chemical reaction on MHD Maxwell nanofluid flow over a convectively heated exponentially stretching sheet using homotopy analysis method

Sravanthi C. S., Gorla R. S. R.

International Journal of Applied Mechanics and Engineering

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2018

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Vol. 23, no. 1

137--159

EN

The aim of this paper is to study the effects of chemical reaction and heat source/sink on a steady MHD (magnetohydrodynamic) two-dimensional mixed convective boundary layer flow of a Maxwell nanofluid over a porous exponentially stretching sheet in the presence of suction/blowing. Convective boundary conditions of temperature and nanoparticle concentration are employed in the formulation. Similarity transformations are used to convert the governing partial differential equations into non-linear ordinary differential equations. The resulting non-linear system has been solved analytically using an efficient technique, namely: the homotopy analysis method (HAM). Expressions for velocity, temperature and nanoparticle concentration fields are developed in series form. Convergence of the constructed solution is verified. A comparison is made with the available results in the literature and our results are in very good agreement with the known results. The obtained results are presented through graphs for several sets of values of the parameters and salient features of the solutions are analyzed. Numerical values of the local skin-friction, Nusselt number and nanoparticle Sherwood number are computed and analyzed.

7

Bidirectionally stretched flow of Jeffrey liquid with nanoparticles, Rosseland radiation and variable thermal conductivity

Archana M., Gireesha B. J., Rashidi M. M., Prasannakumara B. C., Gorla R. S. R.

Archives of Thermodynamics

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2018

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Vol. 39, no 4

33–-57

EN

Heat and mass transfer stretched flow of an incompressible, electrically conducting Jeffrey fluid has been studied numerically. Nanoparticles are suspended in the base fluid and it has many applications such as cooling of engines, thermal absorption systems, lubricants fuel cell, nanodrug delivery system and so on. Temperature dependent variable thermal conductivity with Rosseland approximation is taken into account and suction effect is employed in the boundary conditions. The governing partial differential equations are first transformed into set of ordinary differential equations using selected similarity transformations, which are then solved numerically using Runge-Kutta-Felhberg fourth-fifth order method along with shooting technique. The flow, heat and mass transfer characteristics with local Nusselt number for various physical parameters are presented graphically and a detailed discussion regarding the effect of flow parameters on velocity and temperature profiles are provided. It is found that, increase of variable thermal conductivity, radiation, Brownian motion and thermophoresis parameter increases the rate of heat transfer. Local Nusselt number has been computed for various parameters and it is observed that, in the presence of variable thermal conductivity and Rosseland approximation, heat transfer characteristics are higher as compared to the constant thermal conductivity and linear thermal radiation.

8

Unsteady MHD mixed convection flow of a micropolar fluid over a vertical wedge

Roy N. C., Gorla R. S. R.

International Journal of Applied Mechanics and Engineering

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2017

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Vol. 22, no. 2

363--391

EN

An analysis is presented to investigate the unsteady magnetohydrodynamic (MHD) mixed convection boundary-layer flow of a micropolar fluid over a vertical wedge in the presence of thermal radiation and heat generation or absorption. The free-stream velocity and surface temperature are assumed to be oscillating in magnitude but not in the direction of the oncoming flow velocity. The governing equations have been solved by two distinct methods, namely, the finite difference method for the entire frequency range, and the series solution for low frequency range and the asymptotic series expansion method for the high frequency range. Numerical solutions provide a good agreement with the series solutions. The amplitudes of skin friction and couple stress coefficients are found to be strongly dependent on the Richardson number and the vortex viscosity parameter. The Prandtl number, the conduction-radiation parameter, the surface temperature parameter and the pressure gradient parameter significantly affect the amplitudes of skin friction, couple stress and surface heat transfer rates. However, the amplitudes of skin friction coefficient are considerably affected by the magnetic field parameter, whereas the amplitudes of heat transfer rate are appreciably changed with the heat generation or absorption parameter. In addition, results are presented for the transient skin friction, couple stress and heat transfer rate with the variations of the Richardson number, the vortex viscosity parameter, the pressure gradient parameter and the magnetic field parameter.

9

Unsteady MHD heat transfer in Couette flow of water at 4°c in a rotating system with ramped temperature via finite element method

Reddy G. J., Raju R. S., Rao J. A., Gorla R. S. R.

International Journal of Applied Mechanics and Engineering

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2017

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Vol. 22, no. 1

145--161

EN

An unsteady magnetohydromagnetic natural convection on the Couette flow of electrically conducting water at 4°C (Pr = 11.40) in a rotating system has been considered. A Finite Element Method (FEM) was employed to find the numerical solutions of the dimensionless governing coupled boundary layer partial differential equations. The primary velocity, secondary velocity and temperature of water at 4°C as well as shear stresses and rate of heat transfer have been obtained for both ramped temperature and isothermal plates. The results are independent of the mesh (grid) size and the present numerical solutions through the Finite Element Method (FEM) are in good agreement with the existing analytical solutions by the Laplace Transform Technique (LTT). These are shown in tabular and graphical forms.

10

Numerical solutions by EFGM of MHD convective fluid flow past a vertical plate immersed in a porous medium in the presence of cross diffusion effects via biot number and convective boundary condition

Raju R. S., Reddy B. M., Rashidi M. M., Gorla R. S. R.

International Journal of Applied Mechanics and Engineering

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2017

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Vol. 22, no. 3

613--636

EN

In this investigation, the numerical results of a mixed convective MHD chemically reacting flow past a vertical plate embedded in a porous medium are presented in the presence of cross diffusion effects and convective boundary condition. Instead of the commonly used conditions of constant surface temperature or constant heat flux, a convective boundary condition is employed which makes this study unique and the results more realistic and practically useful. The momentum, energy, and concentration equations derived as coupled second-order, ordinary differential equations are solved numerically using a highly accurate and thoroughly tested element free Galerkin method (EFGM). The effects of the Soret number, Dufour number, Grashof number for heat and mass transfer, the viscous dissipation parameter, Schmidt number, chemical reaction parameter, permeability parameter and Biot number on the dimensionless velocity, temperature and concentration profiles are presented graphically. In addition, numerical results for the local skin-friction coefficient, the local Nusselt number, and the local Sherwood number are discussed through tabular forms. The discussion focuses on the physical interpretation of the results as well as their comparison with the results of previous studies.

11

A numerical study of coupled non-linear equations of thermo-viscous fluid flow in cylindrical geometry

Pothanna N., Aparna P., Gorla R. S. R.

International Journal of Applied Mechanics and Engineering

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2017

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Vol. 22, no. 4

965--979

EN

In this paper we present numerical solutions to coupled non-linear governing equations of thermo-viscous fluid flow in cylindrical geometry using MATHEMATICA software solver. The numerical results are presented in terms of velocity, temperature and pressure distribution for various values of the material parameters such as the thermo-mechanical stress coefficient, thermal conductivity coefficient, Reiner Rivlin cross viscosity coefficient and the Prandtl number in the form of tables and graphs. Also, the solutions to governing equations for slow steady motion of a fluid have been obtained numerically and compared with the existing analytical results and are found to be in excellent agreement. The results of the present study will hopefully enable a better understanding applications of the flow under consideration.

12

Thermal analysis of a fully wet porous radial fin with natural convection and radiation using the spectral collocation method

Khani F., Darvishi M. T., Gorla R. S. R., Gireesha B. J.

International Journal of Applied Mechanics and Engineering

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2016

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Vol. 21, no. 2

377--392

EN

Heat transfer with natural convection and radiation effect on a fully wet porous radial fin is considered. The radial velocity of the buoyancy driven flow at any radial location is obtained by applying Darcy’s law. The obtained non-dimensionalized ordinary differential equation involving three highly nonlinear terms is solved numerically with the spectral collocation method. In this approach, the dimensionless temperature is approximated by Chebyshev polynomials and discretized by Chebyshev-Gausse-Lobatto collocation points. A particular algorithm is used to reduce the nonlinearity of the conservation of energy equation. The present analysis characterizes the effect of ambient temperature in different ways and it provides a better picture regarding the effect of ambient temperature on the thermal performance of the fin. The profiles for temperature distributions and dimensionless base heat flow are obtained for different parameters which influence the heat transfer rate.

13

Radiation and chemical reaction effects on MHD flow along a moving vertical porous plate

Reddy G. V. R., Reddy N. B., Gorla R. S. R.

International Journal of Applied Mechanics and Engineering

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2016

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Vol. 21, no. 1

157--168

EN

This paper presents an analysis of the effects of magnetohydrodynamic force and buoyancy on convective heat and mass transfer flow past a moving vertical porous plate in the presence of thermal radiation and chemical reaction. The governing partial differential equations are reduced to a system of self-similar equations using the similarity transformations. The resultant equations are then solved numerically using the fourth order Runge-Kutta method along with the shooting technique. The results are obtained for the velocity, temperature, concentration, skin-friction, Nusselt number and Sherwood number. The effects of various parameters on flow variables are illustrated graphically, and the physical aspects of the problem are discussed.

14

Effect of electric field on dispersion of a solute in an MHD flow through a vertical channel with and without chemical reaction

Umavathi J. C., Kumar J. P., Gorla R. S. R., Gireesha B. J.

International Journal of Applied Mechanics and Engineering

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2016

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Vol. 21, no. 3

683--711

EN

The longitudinal dispersion of a solute between two parallel plates filled with two immiscible electrically conducting fluids is analyzed using Taylor’s model. The fluids in both the regions are incompressible and the transport properties are assumed to be constant. The channel walls are assumed to be electrically insulating. Separate solutions are matched at the interface using suitable matching conditions. The flow is accompanied by an irreversible first-order chemical reaction. The effects of the viscosity ratio, pressure gradient and Hartman number on the effective Taylor dispersion coefficient and volumetric flow rate for an open and short circuit are drawn in the absence and in the presence of chemical reactions. As the Hartman number increases the effective Taylor diffusion coefficient decreases for both open and short circuits. When the magnetic field remains constant, the numerical results show that for homogeneous and heterogeneous reactions, the effective Taylor diffusion coefficient decreases with an increase in the reaction rate constant for both open and short circuits.

15

Transient velocity and steady state entropy generation in a microfluidic Couette flow containing charged nano particles

Gorla R. S. R., Gireesha B. J.

International Journal of Applied Mechanics and Engineering

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2015

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Vol. 20, no. 4

787--804

EN

An analysis has been provided to determine the transient velocity and steady state entropy generation in a microfluidic Couette flow influenced by electro-kinetic effect of charged nanoparticles. The equation for calculating the Couette flow velocity profile is derived for transient flow. The solutions for momentum and energy equations are used to get the exact solution for the dimensionless velocity ratio and dimensionless entropy generation number. The effects of the dimensionless entropy generation number, Bejan number, irreversibility ratio, entropy generation due to fluid friction and due to heat transfer on dimensionless time, relative channel height, Brinkman number, dimensionless temperature ratio, nanoparticle volume fraction are analyzed.

16

Natural convection and radiation in a radial porous fin with variable thermal conductivity

Darvishi M. T., Kani F., Gorla R. S. R.

International Journal of Applied Mechanics and Engineering

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2014

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Vol. 19, no. 1

27--37

EN

In this study, the effects of radiation and convection heat transfer in a radial porous fin are considered. The geometry considered is that of a rectangular profile fin. The porous fin allows the flow to infiltrate through it and solid-fluid interaction takes place. This study is performed using Darcy’s model to formulate the heat transfer equation. The thermal conductivity is assumed to be a function of temperature. The effects of the natural convection parameter Nc , radiation parameter Nr and thermal conductivity parameter m on the dimensionless temperature distribution and heat transfer rate are discussed. The results suggest that the radiation transfers more heat than a similar model without radiation.

17

Slip effects on boundary layer flow and heat transfer along a stretching cylinder

Mukhopadhyay S., Gorla R. S. R.

International Journal of Applied Mechanics and Engineering

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2013

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Vol. 18, no. 2

447--459

EN

An axi-symmetric laminar boundary layer flow of a viscous incompressible fluid and heat transfer towards a stretching cylinder is presented. Velocity slip is considered instead of the no-slip condition at the boundary. Similarity transformations are used to convert the partial differential equations corresponding to the momentum and heat equations into non-linear ordinary differential equations. Numerical solutions of these equations are obtained by the shooting method. It is found that the velocity decreases with increasing the slip parameter. The skin friction as well as the heat transfer rate at the surface is larger for a cylinder compared to those for a flat plate.

18

Probabilistic study of bone remodeling using finite element analysis

Werner C., Gorla R. S. R.

International Journal of Applied Mechanics and Engineering

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2013

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Vol. 18, no. 3

911--921

EN

The dynamic bone remodeling process is a computationally challenging research area that struggles to understand the actual mechanisms. It has been observed that a mechanical stimulus in the bone greatly affects the remodeling process. A 3D finite element model of a femur is created and a probabilistic analysis is performed on the model. The probabilistic analysis measures the sensitivities of various parameters related to the material properties, geometric properties, and the three load cases defined as Single Leg Stance, Abduction, and Adduction. The sensitivity of each parameter is based on the calculated maximum mechanical stimulus and analyzed at various values of probabilities ranging from 0.001 to 0.999. The analysis showed that the parameters associated with the Single Leg Stance load case had the highest sensitivity with a probability of 0.99 and the angle of the force applied to the joint of the proximal femur had the overall highest sensitivity.

19

Dual solutions for boundary layer flow of moving fluid over a moving surface with power-law surface temperature

Mukhopadhyay S., Gorla R. S. R.

International Journal of Applied Mechanics and Engineering

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2013

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Vol. 18, no. 1

113--124

EN

An analysis of heat transfer for boundary layer forced convective flow past a moving flat surface parallel to a moving stream is presented. The power-law surface temperature at the boundary is prescribed. The surface temperature varying directly (or inversely) with power-law exponent is considered. The similarity solutions for the problem are obtained and the reduced ordinary differential equations are solved numerically. To support the validity of the numerical results, a comparison is made with known results from the open literature for some particular cases of the present study. When the surface and the fluid move in the opposite directions, dual solutions exist.

20

Boundary layer flow and heat transfer over a permeable shrinking cylinder with surface mass transfer

Bhattacharyya K., Gorla R. S. R.

International Journal of Applied Mechanics and Engineering

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2013

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Vol. 18, no. 4

1003--1012

EN

In the present paper, the axisymmetric boundary layer flow and heat transfer past a permeable shrinking cylinder subject to surface mass transfer is studied. The similarity transformations are adopted to convert the governing partial differential equations for the flow and heat transfer into the nonlinear self-similar ordinary differential equations and then solved by a finite difference method using the quasilinearization technique. From the current investigation, it is found that the velocity in the boundary layer region decreases with the curvature parameter and increases with suction mass transfer. Moreover, with the increase of the curvature parameter, the suction parameter and Prandtl number, the heat transfer is enhanced.