Calculation of conjugate heat transfer problem with volumetric heat generation using the Galerkin method (original) (raw)
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The Galerkin method solution of the conjugate heat transfer problems for the cross-flow conditions
A conjugate heat transfer model of fluid flow across a solid heat conducting structure has been built. Two examples are presented: a.) air-stream cooling of the solid structure and b.) flow across rods with volumetric heat generation. To construct the model, a Volume Average Technique (VAT) has been applied to the momentum and the energy transport equations for a fluid and a solid phase to develop a specific form of porous media flow equations. The model equations have been solved with the semi-analytical Galerkin method. The detailed velocity and temperature fields in the fluid flow and the solid structure have been obtained. Using the solution fields, the whole-section drag coefficient Cd and the whole-section Nusselt number Nu have been also calculated. To validate the developed solution procedure, the results have been compared to the results of the finite volume method and to the experimental data. The comparison demonstrates an excellent agreement.
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Numerical Heat Transfer, Part B: Fundamentals, 2003
A fast-running computational algorithm based on the volume averaging technique (VAT) is developed and solutions are obtained using the Galerkin method (GM). The goal is to extend applicability of the GM to the area of heat exchangers in order to provide a reliable benchmark for numerical calculations of conjugate heat transfer problems. Using the VAT, the computational algorithm is fast-running, but still able to present a detailed picture of temperature fields in air flow as well as in the solid structure of the heat sink. The calculated whole-section drag coefficient C d and Nusselt number Nu were compared with finite-volume method (FVM) results and with experimental data to verify the computational model. The comparison shows good agreement. The present results demonstrate that the selected Galerkin approach is capable to perform heat exchanger calculations where the thermal conductivity of the solid structure has to be taken into account.
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Engineering Journal, 2009
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Conjugate heat transfer (CHT) analysis has been carried out for laminar flow past flat plate and turbulent flow between parallel plates using a commercial CFD software CFXTASCFlow. Navier-Stokes equations alongwith k − ε turbulence model in the fluid and conduction equation in the solid have been solved simultaneously to obtain the flow features. The computed temperature distribution of the flow past flat plat matches very well with analytical and other numerical results. For the turbulent flow between parallel plates, nondimensional temperature distribution and Nusselt number distribution matches very well with the analytical and experimental results for different values of Reynolds number and thickness of the heat transfer plate.
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In this study, a numerical weak coupling strategy for the modeling of a conjugate heat transfer phenomenon is considered. Where the incompressible Navier-Stokes equations are solved using the Semi-Implicit Method for Pressure Linked Equations (SIMPLE) as a first step, and then the heat conduction equation for solid is solved in a second step considering the convective velocity field resulting from the first step. A finite-difference approach is used for both discretized time and spatial operators. In this paper, a two-dimensional simulation case study of a steady uniform streamwise flow around heated rectangular and triangle solids is presented. The simulation is forward in time until the steady-state regime is reached as the residuals converge and tend to zero. The spatial analysis of the temperature is obtained through the numerical resolution of the incompressible Navier-Stokes energy equation and the heat diffusion equation for the fluid and solid media, respectively. The result...
Conjugate heat transfer inside a porous channel
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Analytical and numerical analyses have been performed for fully developed forced convection in a fluid-saturated porous medium channel bounded by two parallel plates. The channel walls are assumed to be finite in thickness. Conduction heat transfer inside the channel wall is also accounted and the full problem is treated as a conjugate heat transfer problem. The flow in the porous material is described by the Darcy-Brinkman momentum equation. The outer surfaces of the solid walls are treated as isothermal. A temperature dependent volumetric heat generation is considered inside the solid wall only. Analytical expressions for velocity, temperature, and Nusselt number are obtained after simplifying and solving the governing differential equations with reasonable approximations. Subsequent results obtained by numerical calculations show an excellent agreement with the analytical results.