Transient conjugated heat transfer in microchannels: Integral transforms with single domain formulation

Knupp, Diego C.; Cotta, Renato M.; Naveira-Cotta, Carolina P.; Kakaç, S.

doi:10.1016/j.ijthermalsci.2014.04.017

Cited by 46 publications

(26 citation statements)

References 31 publications

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“…Second, the effect of viscous dissipation on heat transfer becomes significant for flows at microscale since the wall-to-fluid temperature difference is small [11]. There exist multiple studies conducted so far to include effects of rarefaction [15], viscous dissipation, and axial conduction [16] for microscale flows. Hadjiconstantinou and Simek [17] studied the effect of axial conduction for thermally fully developed flows in microchannels.…”

Section: Contents Lists Available At Sciencedirectmentioning

confidence: 99%

Analytical solution of thermally developing microtube heat transfer including axial conduction, viscous dissipation, and rarefaction effects

Barışık

Yazıcıoğlu

Çetin

et al. 2015

International Communications in Heat and Mass Transfer

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The solution of extended Graetz problem for micro-scale gas flows is performed by coupling of rarefaction, axial conduction and viscous dissipation at slip flow regime. The analytical coupling achieved by using Gram-Schmidt orthogonalization technique provides interrelated appearance of corresponding effects through the variation of non-dimensional numbers. The developing temperature field is determined by solving the energy equation locally together with the fully developed flow profile. Analytical solutions of local temperature distribution, and local and fully developed Nusselt number are obtained in terms of dimensionless parameters: Peclet number, Knudsen number, Brinkman number, and the parameter Kappa accounting temperature-jump. The results indicate that the Nusselt number decreases with increasing Knudsen number as a result of the increase of temperature jump at the wall. For low Peclet number values, temperature gradients and the resulting temperature jump at the pipe wall cause Knudsen number to develop higher effect on flow. Axial conduction should not be neglected for Peclet number values less than 100 for all cases without viscous dissipation, and for short pipes with viscous dissipation. The effect of viscous heating should be considered even for small Brinkman number values with large length over diameter ratios. For a fixed Kappa value, the deviation from continuum increases with increasing rarefaction, and Nusselt number values decrease with an increase in Knudsen number.

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Section: Contents Lists Available At Sciencedirectmentioning

confidence: 99%

Analytical solution of thermally developing microtube heat transfer including axial conduction, viscous dissipation, and rarefaction effects

Barışık

Yazıcıoğlu

Çetin

et al. 2015

International Communications in Heat and Mass Transfer

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“…Beside these studies, extended Graetz problem solutions involving both axial fluid and wall conduction can also be seen in the Bilir [22,23] and Bilir and Ateş [24]. And also, several works for mini and micro pipe flows in transient regime and conjugate heat transfer for different boundary conditions have been conducted extensively in the past [25][26][27][28][29][30][31].…”

Section: Introductionmentioning

confidence: 99%

Numerical investigation of the effect of second order slip flow conditions on interfacial heat transfer in micro pipes

Şen

2019

Sādhanā

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Heat transfer that occurs in micro scale devices has a very important place among the engineering applications that cooling or heating. This heat transfer mechanism in devices having dimensions at micron level is a completely different problem in the macro level analysis. Therefore, in the calculations made, the flow events and heat transfer in micron scale pipes are calculated by using more realistic expressions. For this reason, in this study heat transfer in a circular micro pipe with wall and fluid conjugation for laminar rarefied gas flow in transient regime is investigated under the second order slip boundary conditions at the interface. Patankar's control volume method is used here to solve the problem numerically. This analysis includes of axial conduction, viscous dissipation and rarefaction effects which are indispensable in micro-flow structure. From the results, it is seen that the values that are indicating heat transfer are excessively affected by wall thickness, viscous heating and gas rarefaction especially in transient regime.

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“…In problems with more significant convective effects, this solution path may lead to slower convergence rates in the eigenfunction expansions. Such difficulties have been overcome through the use of convergence acceleration schemes, such as with analytical filtering and integral balance procedures [11,21,22], or by adopting a partial integral transformation scheme, which transforms only those spatial variables in which the diffusive effects predominate, yielding a transformed partial differential system to be numerically solved [23][24][25][26][27].…”

Section: Introductionmentioning

confidence: 99%

Convective Eigenvalue Problems for Convergence Enhancement of Eigenfunction Expansions in Convection–Diffusion Problems

Cotta

Naveira-Cotta

Knupp

2017

Journal of Thermal Science and Engineering Applications

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The present work considers the application of the generalized integral transform technique (GITT) in the solution of a class of linear or nonlinear convection–diffusion problems, by fully or partially incorporating the convective effects into the chosen eigenvalue problem that forms the basis of the proposed eigenfunction expansion. The aim is to improve convergence behavior of the eigenfunction expansions, especially in the case of formulations with significant convective effects, by simultaneously accounting for the relative importance of convective and diffusive effects within the eigenfunctions themselves, in comparison against the more traditional GITT solution path, which adopts a purely diffusive eigenvalue problem, and the convective effects are fully incorporated into the problem source term. After identifying a characteristic convective operator, and through a straightforward algebraic transformation of the original convection–diffusion problem, basically by redefining the coefficients associated with the transient and diffusive terms, the characteristic convective term is merged into a generalized diffusion operator with a space-variable diffusion coefficient. The generalized diffusion problem then naturally leads to the eigenvalue problem to be chosen in proposing the eigenfunction expansion for the linear situation, as well as for the appropriate linearized version in the case of a nonlinear application. The resulting eigenvalue problem with space variable coefficients is then solved through the GITT itself, yielding the corresponding algebraic eigenvalue problem, upon selection of a simple auxiliary eigenvalue problem of known analytical solution. The GITT is also employed in the solution of the generalized diffusion problem, and the resulting transformed ordinary differential equations (ODE) system is solved either analytically, for the linear case, or numerically, for the general nonlinear formulation. The developed methodology is illustrated for linear and nonlinear applications, both in one-dimensional (1D) and multidimensional formulations, as represented by test cases based on Burgers' equation.

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Transient conjugated heat transfer in microchannels: Integral transforms with single domain formulation

Cited by 46 publications

References 31 publications

Analytical solution of thermally developing microtube heat transfer including axial conduction, viscous dissipation, and rarefaction effects

Analytical solution of thermally developing microtube heat transfer including axial conduction, viscous dissipation, and rarefaction effects

Numerical investigation of the effect of second order slip flow conditions on interfacial heat transfer in micro pipes

Convective Eigenvalue Problems for Convergence Enhancement of Eigenfunction Expansions in Convection–Diffusion Problems

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