2008
DOI: 10.1002/mma.994
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Flow of a non‐linear (density‐gradient‐dependent) viscous fluid with heat generation, viscous dissipation and radiation

Abstract: SUMMARYIn this paper, we study the flow of a compressible (density-gradient-dependent) non-linear fluid down an inclined plane, subject to radiation boundary condition. The convective heat transfer is also considered where a source term, similar to the Arrhenius type reaction, is included. The non-dimensional forms of the equations are solved numerically and the competing effects of conduction, dissipation, heat generation and radiation are discussed.

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Cited by 10 publications
(6 citation statements)
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“…A look at the governing equation (1)- (4) reveals that constitutive relations are required for T, q, f , , and r. Less obvious is the fact that in many practical problems involving competing effects, such as temperature and concentration, the body force b, which in problems dealing with natural convection oftentimes depends on the temperature and is modeled using the Boussinesq assumption (see [28]), now might have to be modeled in such a way that it is also a function of concentration (see for example, Equation (2.2) of [15]). Furthermore, in many problems involving chemical reactions, there is usually a (heat) source term, Q, in Equation (4) that also has to be constitutively modeled (see [12,18]). Ignoring these effects, along with the influence of radiation, we will now briefly discuss the three necessary constitutive relations, namely equations for T, q, and f , for closure.…”
Section: Constitutive Relationsmentioning
confidence: 99%
See 1 more Smart Citation
“…A look at the governing equation (1)- (4) reveals that constitutive relations are required for T, q, f , , and r. Less obvious is the fact that in many practical problems involving competing effects, such as temperature and concentration, the body force b, which in problems dealing with natural convection oftentimes depends on the temperature and is modeled using the Boussinesq assumption (see [28]), now might have to be modeled in such a way that it is also a function of concentration (see for example, Equation (2.2) of [15]). Furthermore, in many problems involving chemical reactions, there is usually a (heat) source term, Q, in Equation (4) that also has to be constitutively modeled (see [12,18]). Ignoring these effects, along with the influence of radiation, we will now briefly discuss the three necessary constitutive relations, namely equations for T, q, and f , for closure.…”
Section: Constitutive Relationsmentioning
confidence: 99%
“…Non-linear fluids in Couette geometries have been extensively analyzed for different purposes. Massoudi and Phuoc [12] studied the flow of a compressible (density-gradient-dependent) non-linear fluid down an inclined plane, subject to radiation boundary condition. They assumed that the heat of reaction appears as a source term in the energy equation; in a sense they did not allow for a chemical reaction to occur and thus the conservation equation for the chemical species was ignored.…”
Section: Introductionmentioning
confidence: 99%
“…in many problems involving chemical reactions, there is usually a (heat) source term, Q, in equation (2.4), which also must be constitutively modeled (see Straughan, 2004Straughan, , 2008Massoudi and Phuoc, 2008). 4 The expression Eulerian-Eulerian approach is a rather poor expression, and in fact a misleading one.…”
Section: Multi-phase (Component) Approachmentioning
confidence: 99%
“…To replace the classical theory of capillarity, which specifies a jump condition at the surface separating homogeneous fluids possessing different densities, Korteweg proposed smooth constitutive equations for the stresses that depend on density gradient 1 . Massoudi & Phuoc (2008) studied the flow of a compressible (density-gradientdependent) non-linear fluid down an inclined plane, subject to radiation boundary condition. They assumed that the heat of reaction appears as a source term in the energy equation; in a sense they did not allow for a chemical reaction to occur and thus the conservation equation for the chemical species was ignored.…”
Section: Introductionmentioning
confidence: 99%
“…In this Chapter, we provide a brief discussion of the important constitutive aspects of heat transfer in flows of complex fluids. We study the flow of a compressible (density gradient type) non-linear fluid down an inclined plane, subject to radiation boundary condition (For a full treatment of this problem, we refer the reader to Massoudi & Phuoc, 2008). The convective heat transfer is also considered where a source term, similar to the Arrhenius type reaction, is included.…”
Section: Introductionmentioning
confidence: 99%