A new algorithm for internal heat generation in nanofluid flow due to a stretching sheet in a porous medium

2014 ◽  
Vol 24 (5) ◽  
pp. 1020-1043 ◽  
Author(s):  
P.K. Kameswaran ◽  
Z.G. Makukula ◽  
P. Sibanda ◽  
S.S. Motsa ◽  
P.V.S.N. Murthy
Keyword(s):  
Mass Transfer ◽  
Differential Equations ◽  
Exact Solutions ◽  
Heat And Mass Transfer ◽  
Hypergeometric Series ◽  
Stretching Sheet ◽  
Internal Heat ◽  
Internal Heat Generation ◽  
Nanofluid Flow ◽  
Content Type

Purpose – The purpose of this paper is to study heat and mass transfer in copper-water and silver-water nanofluid flow over stretching sheet placed in saturated porous medium with internal heat generation or absorption. The authors further introduce a new algorithm for solving heat transfer problems in fluid mechanics. The model used for the nanofluid incorporates the nanoparticle volume fraction parameter and a consideration of the chemical reaction effects among other features. Design/methodology/approach – The partial differential equations for heat and mass transfer in copper-water and silver-water nanofluid flow over stretching sheet were transformed into a system of nonlinear ordinary differential equations. Exact solutions for the boundary layer equations were obtained in terms of a confluent hypergeometric series. A novel spectral relaxation method (SRM) is used to obtain numerical approximations of the governing differential equations. The exact solutions are used to test the convergence and accuracy of the SRM. Findings – Results were obtained for the fluid properties as well as the skin friction, and the heat and mass transfer rates. The results are compared with limiting cases from previous studies and they show that the proposed technique is an efficient numerical algorithm with assured convergence that serves as an alternative to numerical methods for solving nonlinear boundary value problems. Originality/value – A new algorithm is used for the first time in this paper. In addition, new exact solutions for the energy and mass transport equations have been obtained in terms of a confluent hypergeometric series.

Numerical investigation of three-dimensional nanofluid flow with heat and mass transfer on a nonlinearly stretching sheet using the barycentric functions

2020 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Soraya Torkaman ◽  
Ghasem Barid Loghmani ◽  
Mohammad Heydari ◽  
Abdul-Majid Wazwaz
Keyword(s):  
Mass Transfer ◽  
Differential Equations ◽  
Heat And Mass Transfer ◽  
Stretching Sheet ◽  
Volume Fraction ◽  
Three Dimensional ◽  
Operational Matrices ◽  
Nanofluid Flow ◽  
Content Type ◽  
Nonlinearly Stretching Sheet

Purpose The purpose of this paper is to investigate a three-dimensional boundary layer flow with considering heat and mass transfer on a nonlinearly stretching sheet by using a novel operational-matrix-based method. Design/methodology/approach The partial differential equations that governing the problem are converted into the system of nonlinear ordinary differential equations (ODEs) with considering suitable similarity transformations. A direct numerical method based on the operational matrices of integration and product for the linear barycentric rational basic functions is used to solve the nonlinear system of ODEs. Findings Graphical and tabular results are provided to illustrate the effect of various parameters involved in the problem on the velocity profiles, temperature distribution, nanoparticle volume fraction, Nusselt and Sherwood number and skin friction coefficient. Comparison between the obtained results, numerical results based on the Maple's dsolve (type = numeric) command and previous existing results affirms the efficiency and accuracy of the proposed method. Originality/value The motivation of the present study is to provide an effective computational method based on the operational matrices of the barycentric cardinal functions for solving the problem of three-dimensional nanofluid flow with heat and mass transfer. The convergence analysis of the presented scheme is discussed. The benefit of the proposed method (PM) is that, without using any collocation points, the governing equations are converted to the system of algebraic equations.

Exact Solutions for a Fluid-Saturated Porous Medium with Heat and Mass Transfer

2005 ◽  
Vol 21 (1) ◽  
pp. 57-62 ◽  
Author(s):  
I-C. Liu
Keyword(s):  
Mass Transfer ◽  
Porous Medium ◽  
Differential Equations ◽  
Exact Solutions ◽  
Heat And Mass Transfer ◽  
Saturated Porous Medium ◽  
Thermal Characteristics ◽  
Internal Heat ◽  
Confluent Hypergeometric Functions ◽  
Fluid Saturated Porous Medium

AbstractAn analysis is performed to the study of the momentum, heat and mass transfer of a viscous fluid-saturated porous medium past an impermeable, non-isothermal stretching sheet with internal heat generation or absorption and chemical reaction. The governing partial differential equations are converted into ordinary differential equations by means of a similarity transformation. Exact solutions of velocity components together with the pressure distribution, which can not be found in the boundary layer theory, are obtained analytically; in addition, the temperature and concentration functions are given in terms of confluent hypergeometric functions. The velocity, temperature (concentration) profiles and thermal characteristics at the sheet for relevant parameters are plotted, tabulated and discussed.

scholarly journals Analysis of Magnetohydrodynamic (MHD) Nanofluid Flow with Heat and Mass Transfer Over a Porous Stretching Sheet

2020 ◽  
Vol 25 (4) ◽  
pp. 162-174
Author(s):  
A.S. Odesola ◽  
I.O. Abiala ◽  
F.O. Akinpelu ◽  
O.J. Fenuga
Keyword(s):  
Mass Transfer ◽  
Differential Equations ◽  
Heat And Mass Transfer ◽  
Stretching Sheet ◽  
Three Dimensional ◽  
Nanofluid Flow ◽  
Linear Ordinary Differential Equations ◽  
Flow Parameters ◽  
Galerkin Finite Element Methods ◽  
Good Agreement

AbstractThis work investigates a three-dimensional Magnetohydrodynamic (MHD) nanofluid flow with heat and mass transfer over a porous stretching sheet. Firstly, partial differential equations are transformed into coupled non-linear ordinary differential equations through a similarity variables transformation and solved by Galerkin Finite Element Methods (FEM). The effects of thermal radiation, viscous dissipation and chemical reaction on the fluid flow are considered. The behaviour and properties of pertinent flow parameters on the velocity, temperature and concentration profiles are presented and discussed graphically. The effects of the friction coefficient parameter, Nusselt and Sherhood numbers are also shown and considered using tables. The work is in good agreement in comparison with the recent work in literature.

Heat Transfer on Nanofluid Flow With Homogeneous–Heterogeneous Reactions and Internal Heat Generation

2014 ◽  
Vol 136 (12) ◽  
Author(s):  
Raj Nandkeolyar ◽  
Peri K. Kameswaran ◽  
Sachin Shaw ◽  
Precious Sibanda
Keyword(s):  
Heat Transfer ◽  
Mass Transfer ◽  
Heat And Mass Transfer ◽  
Heat Generation ◽  
Internal Heat ◽  
Internal Heat Generation ◽  
Heterogeneous Reactions ◽  
Transfer Coefficients ◽  
Transfer Characteristics ◽  
Fluid Properties

We investigated heat and mass transfer on water based nanofluid due to the combined effects of homogeneous–heterogeneous reactions, an external magnetic field and internal heat generation. The flow is generated by the movement of a linearly stretched surface, and the nanofluid contains nanoparticles of copper and gold. Exact solutions of the transformed model equations were obtained in terms of hypergeometric functions. To gain more insights regarding subtle impact of fluid and material parameters on the heat and mass transfer characteristics, and the fluid properties, the equations were further solved numerically using the matlab bvp4c solver. The similarities and differences in the behavior, including the heat and mass transfer characteristics, of the copper–water and gold–water nanofluids with respect to changes in the flow parameters were investigated. Finally, we obtained the numerical values of the skin friction and heat transfer coefficients.

g-Jitter Induced Mixed Convection Flow of Heat and Mass Transfer Past an Inclined Stretching Sheet

2014 ◽  
Vol 71 (1) ◽  
Author(s):  
Noraihan Afiqah Rawi ◽  
Abdul Rahman Mohd Kasim ◽  
Mukheta Isa ◽  
Sharidan Shafie
Keyword(s):  
Mass Transfer ◽  
Differential Equations ◽  
Mixed Convection ◽  
Heat And Mass Transfer ◽  
Stretching Sheet ◽  
Convection Flow ◽  
Convection Boundary Layer ◽  
Keller Box Method ◽  
Unsteady Mixed Convection ◽  
Layer Flow

This paper studies unsteady mixed convection boundary layer flow of heat and mass transfer past an inclined stretching sheet associated with the effect of periodical gravity modulation or g-jitter. The temperature and concentration are assumed to vary linearly with x, where x is the distance along the plate. The governing partial differential equations are transformed to a set of coupled ordinary differential equations using non-similarity transformation and solved numerically by Keller-box method. Numerical results for velocity, temperature and concentration profiles as well as skin friction, Nusselt number and Sherwood number are presented and analyzed for different values of inclination angle parameter.

scholarly journals MHD Slip Flow of Newtonian Fluid past a Stretching Sheet with Thermal Convective Boundary Condition, Radiation, and Chemical Reaction

2013 ◽  
Vol 2013 ◽  
pp. 1-12 ◽  
Author(s):  
Reda G. Abdel-Rahman
Keyword(s):  
Mass Transfer ◽  
Boundary Condition ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Heat And Mass Transfer ◽  
Chemical Reaction ◽  
Stretching Sheet ◽  
Convective Boundary Condition ◽  
Nonlinear Ordinary Differential Equations ◽  
Convective Boundary

An analysis is carried out to study the problem of heat and mass transfer flow over a moving permeable flat stretching sheet in the presence of convective boundary condition, slip, radiation, heat generation/absorption, and first-order chemical reaction. The viscosity of fluid is assumed to vary linearly with temperature. Also the diffusivity is assumed to vary linearly with concentration. The governing partial differential equations have been reduced to the coupled nonlinear ordinary differential equations by using Lie group point of transformations. The system of transformed nonlinear ordinary differential equations is solved numerically using shooting techniques with fourth-order Runge-Kutta integration scheme. Comparison between the existing literature and the present study was carried out and found to be in excellent agreement. The effects of the various interesting parameters on the flow, heat, and mass transfer are analyzed and discussed through graphs in detail. The values of the local Nusselt number, the local skin friction, and the local Sherwood number for different physical parameters are also tabulated.

scholarly journals Analysis of Magnetic and Non Magnetic Nanoparticles With Newtonian/non-newtonian Base Fluids Over a Nonlinear Stretching Sheet

2020 ◽  
Author(s):  
kanwal Jabeen ◽  
Muhamad Mushtaq ◽  
Rana MUhammad Akram
Keyword(s):  
Mass Transfer ◽  
Magnetic Nanoparticles ◽  
Heat And Mass Transfer ◽  
Sodium Alginate ◽  
Stretching Sheet ◽  
Internal Heat ◽  
Al2o3 Nanoparticles ◽  
Ohmic Dissipation ◽  
Nonlinear Stretching ◽  
The Impact

Abstract Unsteady mixed convectional boundary layer flow of Casson nanofluid having magnetic( Fe3O4) and nonmagnetic( Al2O3) nanoparticles suspension within two different types of base fluids, water(Newtonian) and Sodium Alginate(non-Newtonian), which incorporates viscous and ohmic dissipation effects over a permeable nonlinear stretching sheet with magnetic field effects. Some suitable non-dimensional similarity transformations are applied to convert the governing PDEs into a system of nonlinear coupled ODEs and then solved by differential transformation method(DTM) association with Pade-approximation. To validate the present results for limited cases, a comparison was made with previously existing literature and found to be in well agreement. The impact of radiation, internal heat sink/ source, viscous and ohmic dissipation was discussed for magnetic and non-magnetic nanofluid categories by tabular and graphical demonstrations. We have presented the tabular results of various emerging parameters to discuss the nature of skin friction, Nusselt and Sherwood numbers. It was also observed that performance of non-Newtonian(Sodium Alginate) fluid in heat and mass transfer is better than Newtonian(water) based fluid but no major difference was seen in heat and mass transfer when comparison was made with Magnetic and Non-magnetic nanoparticles

Heat and mass transfer in MHD Casson nanofluid flow past a stretching sheet with thermophoresis and Brownian motion

Heat Transfer ◽  
2020 ◽  
Vol 49 (8) ◽  
pp. 5020-5037
Author(s):  
Ankalagiri Chinna Venkata Ramudu ◽  
Kempannagari Anantha Kumar ◽  
Vangala Sugunamma ◽  
Naramgari Sandeep
Keyword(s):  
Mass Transfer ◽  
Brownian Motion ◽  
Heat And Mass Transfer ◽  
Stretching Sheet ◽  
Nanofluid Flow ◽  
Casson Nanofluid ◽  
And Brownian Motion ◽  
Flow Past
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