On frame indifferent formulation of the Maxwell–Cattaneo model of finite-speed heat conduction

Christov, C. I.

doi:10.1016/j.mechrescom.2008.11.003

Cited by 1,025 publications

(468 citation statements)

References 21 publications

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“…The plate is assumed to have constant temperature T w and T ∞ denotes the ambient fluid temperature. Heat flux model proposed by Christov 16 is taken into consideration. Making use of the standard boundary layer approximations, the equations governing the steady incompressible flow of Maxwell fluid and heat transfer can be expressed as below:…”

Section: Mathematical Modelmentioning

confidence: 99%

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Numerical solution for Sakiadis flow of upper-convected Maxwell fluid using Cattaneo-Christov heat flux model

et al. 2016

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Present work studies the well-known Sakiadis flow of Maxwell fluid along a moving plate in a calm fluid by considering the Cattaneo-Christov heat flux model. This recently developed model has the tendency to describe the characteristics of relaxation time for heat flux. Some numerical local similarity solutions of the associated problem are computed by two approaches namely (i) the shooting method and (ii) the Keller-box method. The solution is dependent on some interesting parameters which include the viscoelastic fluid parameter β, the dimensionless thermal relaxation time γ and the Prandtl number Pr. Our simulations indicate that variation in the temperature distribution with an increase in local Deborah number γ is non-monotonic. The results for the Fourier’s heat conduction law can be obtained as special cases of the present study.

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Section: Mathematical Modelmentioning

confidence: 99%

“…Eliminating q from Eqs. (3) and (4), one obtains the following equation (see Christov 16 and Han et al 18 for details)…”

Section: Mathematical Modelmentioning

confidence: 99%

Numerical solution for Sakiadis flow of upper-convected Maxwell fluid using Cattaneo-Christov heat flux model

et al. 2016

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“…Hyperbolic type energy equation exists in presence of Cattaneo's expression. Christov (2009) improved the heat conduction analysis of Cattaneo (1948) by introducing thermal relaxation time along with Oldroyd's upper-convicted derivative, in order to attain the material invariance of the model. Cattaneo-Cheristov heat flux model is the modified Fourier's form which gives thermal relaxation time.…”

Section: Introductionmentioning

confidence: 99%

Micropolar Fluid Flow Over a Nonlinear Stretching Convectively Heated Vertical Surface in the Presence of Cattaneo-Christov Heat Flux and Viscous Dissipation

Reddy¹,

Reddy²

2017

Frontiers in Heat and Mass Transfer

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The objective of the present communication is to study the problem of micropolar fluid flow with temperature dependent thermal conductivity over a nonlinear stretching convective vertical surface in the presence of Lorentz force and viscous dissipation. Due to the nature of heat transfer in the flow past vertical surface, Cattaneo-Christov heat flux model and Joule heating effects are properly accommodated in the energy equation. The governing partial differential equations for the flow and heat transfer are converted into a set of ordinary differential equations by employing the acceptable similarity transformations. Runge-Kutta and Newton's methods are utilized to resolve the altered governing nonlinear equations. Obtained numerical results are compared with the available literature and found to be an excellent agreement. The impacts of dimensionless governing flow pertinent parameters on velocity, micropolar velocity and temperature profiles are presented graphically and analyzed in detail. Further, the variations of skin friction coefficient and local Nusselt number are displayed for the sundry flow parameters. It is found that fluid temperature profile declines for larger thermal relaxation parameter. Both temperature and thermal boundary layer thickness decreases for enhancing values of Prandtl number.

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“…This phenomenon has been examined through established Fourier law of heat conduction (1822) till Cattaneo (1948) floated an adjustment in it by incorporating thermal relaxation effects. Christov (2008) upgraded his contribution by adding Oldroyd's upper convected derivatives. His modification is termed as Cattaneo-Christov heat flux model.…”

Section: Introductionmentioning

confidence: 99%

Influence of Cattaneo-Christov Heat Flux Model on MHD Hyperbolic Tangent Fluid Over a Moving Porous Surface

Azhar¹,

Iqbal²,

Maraj³

et al. 2017

Frontiers in Heat and Mass Transfer

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On frame indifferent formulation of the Maxwell–Cattaneo model of finite-speed heat conduction

Cited by 1,025 publications

References 21 publications

Numerical solution for Sakiadis flow of upper-convected Maxwell fluid using Cattaneo-Christov heat flux model

Numerical solution for Sakiadis flow of upper-convected Maxwell fluid using Cattaneo-Christov heat flux model

Micropolar Fluid Flow Over a Nonlinear Stretching Convectively Heated Vertical Surface in the Presence of Cattaneo-Christov Heat Flux and Viscous Dissipation

Influence of Cattaneo-Christov Heat Flux Model on MHD Hyperbolic Tangent Fluid Over a Moving Porous Surface

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