Combined effects of internal heat generation and higher order chemical reaction on the non-darcian forced convective flow of a viscous incompressible fluid with variable viscosity and thermal conductivity over a stretching surface embedded in a porous medium

Research output: Contribution to journalArticle

11 Citations (Scopus)

Abstract

In this paper, we study the combined effects of internal heat generation and higher order chemical reaction on a steady two-dimensional non-Darcian forced convective flow of a viscous incompressible fluid with variable dynamic viscosity and thermal conductivity in a fluid saturated porous medium passing over a linear stretching sheet. Using similarity transformations, the governing nonlinear-coupled partial differential equations are made dimensionless and solved numerically for similarity solutions using very robust computer algebra software Maple 8. The non-dimensional velocity, temperature and concentration distributions are presented graphically for various pertinent parameters such as relative temperature difference parameter, Darcy number, porosity parameter, reaction rate parameter and the order of the chemical reaction. The variations of Prandtl number and Schmidt number within the boundary layer are also displayed graphically when the fluid dynamic viscosity and thermal conductivity are temperature dependent. From the present numerical computations it is found that Prandtl number as well as Schmidt number must be taken as variables within the flow domain when the fluid's dynamic viscosity and thermal conductivity are variable. In the presence of internal heat generation, dynamic viscosity and thermal conductivity of the fluid are found to be higher than when it is absent. Increasing Darcy number reduces dynamic viscosity as well as thermal conductivity whereas increasing pore size reduces the Schmidt number and increases the Prandtl number within the boundary layer. For higher order reaction the rate of increase in mass transfer function is less compared to the rate of increase for the lower order reaction.

Original languageEnglish
Pages (from-to)1632-1645
Number of pages14
JournalCanadian Journal of Chemical Engineering
Volume90
Issue number6
DOIs
Publication statusPublished - Dec 2012

Fingerprint

Heat generation
Stretching
Porous materials
Chemical reactions
Thermal conductivity
Viscosity
Prandtl number
Fluids
Fluid dynamics
Boundary layers
Temperature
Algebra
Partial differential equations
Pore size
Reaction rates
Transfer functions
Mass transfer
Porosity

Keywords

  • Chemical reaction
  • Forced convection
  • Internal heat generation
  • Porous medium
  • Similar solution
  • Variable transport property

ASJC Scopus subject areas

  • Chemical Engineering(all)

Cite this

@article{c856d33368d3420bb0f5f95673f7bbed,
title = "Combined effects of internal heat generation and higher order chemical reaction on the non-darcian forced convective flow of a viscous incompressible fluid with variable viscosity and thermal conductivity over a stretching surface embedded in a porous medium",
abstract = "In this paper, we study the combined effects of internal heat generation and higher order chemical reaction on a steady two-dimensional non-Darcian forced convective flow of a viscous incompressible fluid with variable dynamic viscosity and thermal conductivity in a fluid saturated porous medium passing over a linear stretching sheet. Using similarity transformations, the governing nonlinear-coupled partial differential equations are made dimensionless and solved numerically for similarity solutions using very robust computer algebra software Maple 8. The non-dimensional velocity, temperature and concentration distributions are presented graphically for various pertinent parameters such as relative temperature difference parameter, Darcy number, porosity parameter, reaction rate parameter and the order of the chemical reaction. The variations of Prandtl number and Schmidt number within the boundary layer are also displayed graphically when the fluid dynamic viscosity and thermal conductivity are temperature dependent. From the present numerical computations it is found that Prandtl number as well as Schmidt number must be taken as variables within the flow domain when the fluid's dynamic viscosity and thermal conductivity are variable. In the presence of internal heat generation, dynamic viscosity and thermal conductivity of the fluid are found to be higher than when it is absent. Increasing Darcy number reduces dynamic viscosity as well as thermal conductivity whereas increasing pore size reduces the Schmidt number and increases the Prandtl number within the boundary layer. For higher order reaction the rate of increase in mass transfer function is less compared to the rate of increase for the lower order reaction.",
keywords = "Chemical reaction, Forced convection, Internal heat generation, Porous medium, Similar solution, Variable transport property",
author = "Rahman, {M. M.}",
year = "2012",
month = "12",
doi = "10.1002/cjce.20644",
language = "English",
volume = "90",
pages = "1632--1645",
journal = "Canadian Journal of Chemical Engineering",
issn = "0008-4034",
publisher = "Wiley-Liss Inc.",
number = "6",

}

TY - JOUR

T1 - Combined effects of internal heat generation and higher order chemical reaction on the non-darcian forced convective flow of a viscous incompressible fluid with variable viscosity and thermal conductivity over a stretching surface embedded in a porous medium

AU - Rahman, M. M.

PY - 2012/12

Y1 - 2012/12

N2 - In this paper, we study the combined effects of internal heat generation and higher order chemical reaction on a steady two-dimensional non-Darcian forced convective flow of a viscous incompressible fluid with variable dynamic viscosity and thermal conductivity in a fluid saturated porous medium passing over a linear stretching sheet. Using similarity transformations, the governing nonlinear-coupled partial differential equations are made dimensionless and solved numerically for similarity solutions using very robust computer algebra software Maple 8. The non-dimensional velocity, temperature and concentration distributions are presented graphically for various pertinent parameters such as relative temperature difference parameter, Darcy number, porosity parameter, reaction rate parameter and the order of the chemical reaction. The variations of Prandtl number and Schmidt number within the boundary layer are also displayed graphically when the fluid dynamic viscosity and thermal conductivity are temperature dependent. From the present numerical computations it is found that Prandtl number as well as Schmidt number must be taken as variables within the flow domain when the fluid's dynamic viscosity and thermal conductivity are variable. In the presence of internal heat generation, dynamic viscosity and thermal conductivity of the fluid are found to be higher than when it is absent. Increasing Darcy number reduces dynamic viscosity as well as thermal conductivity whereas increasing pore size reduces the Schmidt number and increases the Prandtl number within the boundary layer. For higher order reaction the rate of increase in mass transfer function is less compared to the rate of increase for the lower order reaction.

AB - In this paper, we study the combined effects of internal heat generation and higher order chemical reaction on a steady two-dimensional non-Darcian forced convective flow of a viscous incompressible fluid with variable dynamic viscosity and thermal conductivity in a fluid saturated porous medium passing over a linear stretching sheet. Using similarity transformations, the governing nonlinear-coupled partial differential equations are made dimensionless and solved numerically for similarity solutions using very robust computer algebra software Maple 8. The non-dimensional velocity, temperature and concentration distributions are presented graphically for various pertinent parameters such as relative temperature difference parameter, Darcy number, porosity parameter, reaction rate parameter and the order of the chemical reaction. The variations of Prandtl number and Schmidt number within the boundary layer are also displayed graphically when the fluid dynamic viscosity and thermal conductivity are temperature dependent. From the present numerical computations it is found that Prandtl number as well as Schmidt number must be taken as variables within the flow domain when the fluid's dynamic viscosity and thermal conductivity are variable. In the presence of internal heat generation, dynamic viscosity and thermal conductivity of the fluid are found to be higher than when it is absent. Increasing Darcy number reduces dynamic viscosity as well as thermal conductivity whereas increasing pore size reduces the Schmidt number and increases the Prandtl number within the boundary layer. For higher order reaction the rate of increase in mass transfer function is less compared to the rate of increase for the lower order reaction.

KW - Chemical reaction

KW - Forced convection

KW - Internal heat generation

KW - Porous medium

KW - Similar solution

KW - Variable transport property

UR - http://www.scopus.com/inward/record.url?scp=84868654233&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84868654233&partnerID=8YFLogxK

U2 - 10.1002/cjce.20644

DO - 10.1002/cjce.20644

M3 - Article

VL - 90

SP - 1632

EP - 1645

JO - Canadian Journal of Chemical Engineering

JF - Canadian Journal of Chemical Engineering

SN - 0008-4034

IS - 6

ER -