Heat transfer is a discipline of thermal engineering that concerns the generation, use, conversion, and exchange of thermal energy and heat between physical systems. Heat transfer is classified into various mechanisms, such as conduction, convection, and radiation. Understanding these mechanisms is crucial for solving real-world engineering problems, ranging from designing efficient thermal management systems in electronics to optimizing large-scale industrial processes.
Conduction is the transfer of heat through a medium due to a temperature gradient, without any movement of the medium itself. This process is described by Fourier's law. A common example is the heat conduction through the walls of a house.
Convection involves the transfer of heat by the physical movement of a fluid (liquid or gas). It can be natural (due to buoyancy forces) or forced (by external means like a fan or pump). Heating water in a pot on a stove is a classic example of convection.
Radiation is the transfer of heat through electromagnetic waves without requiring a medium. It can occur in a vacuum. The heat from the sun reaching the earth and the warmth felt from a campfire are examples of radiation.
Thermofluid problems involve the combined study of fluid mechanics and thermodynamics. Key problem types include:
$$ \rho \left( \frac{\partial \mathbf{u}}{\partial t} + \mathbf{u} \cdot \nabla \mathbf{u} \right) = -\nabla p + \nabla \cdot \left( \mu \left( \nabla \mathbf{u} + \nabla \mathbf{u}^T \right) \right) + \mathbf{f} $$
$$ \rho c_p \left( \frac{\partial T}{\partial t} + \mathbf{u} \cdot \nabla T \right) = \nabla \cdot \left( k \nabla T \right) + q_{\text{rad}} + Q $$
$$ \frac{\partial \rho}{\partial t} + \nabla \cdot \left( \rho \mathbf{u} \right) = 0 $$
$$ p = \rho R T $$
All the tutorial cases in OpenFOAM located in /opt/openfoam10/tutorials/heatTransfer directory are listed and shortly explained below.
└── heatTransfer
├── buoyantFoam
│ ├── BernardCells # Simulates Rayleigh-Bénard convection cells due to thermal gradients.
│ ├── buoyantCavity # Models natural convection in a differentially heated cavity.
│ ├── circuitBoardCooling # Simulates cooling of a circuit board by natural convection and radiation.
│ ├── comfortHotRoom # Evaluates thermal comfort in a room with various heating conditions.
│ ├── externalCoupledCavity # Models natural convection in a cavity with external flow interaction.
│ ├── hotRadiationRoom # Simulates radiative heat transfer within a hot room.
│ ├── hotRadiationRoomFvDOM # Similar to hotRadiationRoom but uses FvDOM for radiation modeling.
│ ├── hotRoom # Models a hot room with natural convection, excluding radiation.
│ ├── hotRoomBoussinesq # Uses the Boussinesq approximation for natural convection in a hot room.
│ ├── hotRoomBoussinesqSteady # Steady-state simulation of natural convection in a hot room using Boussinesq approximation.
│ └── iglooWithFridges # Models thermal management in an igloo containing heat-generating fridges.
└── chtMultiRegionFoam
├── coolingCylinder2D # Simulates 2D cooling of a cylindrical object, introducing conjugate heat transfer.
├── coolingSphere # Expands on coolingCylinder2D to spherical geometry for isotropic cooling.
├── heatedDuct # Models heat transfer in a duct with a heated section.
├── heatExchanger # Simulates a basic heat exchanger focusing on thermal energy exchange.
├── reverseBurner # Models a reverse-flow burner, with combustion and heat transfer.
└── shellAndTubeHeatExchanger # Simulates a shell and tube heat exchanger, detailing fluid flow and heat transfer.
Ordering the tutorials from the simplest to the most complex can be subjective, depending on the criteria used (e.g., physics involved, geometry complexity, number of phases or regions). However, here's an attempt to list them based on the overall complexity, considering factors like the physical models used, the geometry, and the multiphysics interactions involved:
This list attempts to rank the tutorials based on their complexity, but it's important to note that the actual difficulty can vary depending on your familiarity with the specific physics involved, OpenFOAM, and CFD in general. Some tutorials, especially those involving conjugate heat transfer (CHT) with chtMultiRegionFoam, might rank higher in complexity due to the need to manage multiple regions (solid and fluid) and their interactions.
Below is a comparison of the buoyantFoam and chtMultiRegionFoam solvers in OpenFOAM:
| Item | buoyantFoam | chtMultiRegionFoam |
|---|---|---|
| Primary Use | Simulating buoyancy-driven flow | Conjugate Heat Transfer (CHT) across multiple regions |
| Flow Type | Fluid flow with heat transfer | Fluid and solid heat transfer |
| Regions Handled | Single region | Multiple regions |
| Equations Solved | Navier-Stokes equations, Energy equation | Navier-Stokes equations, Energy equation in both fluid and solid domains |
| Heat Transfer Mechanisms | Conduction, Convection | Conduction, Convection (radiation can be modeled with additional libraries) |
| Phase Change | Typically not modeled | Can be modeled, especially relevant for solid regions |
| Application Examples | Natural convection in enclosures, Atmospheric flows | Heat exchangers, Electronic cooling, Building thermal management |
| Boundary Conditions | Fluid-specific, including pressure, temperature, and velocity | Separate boundary conditions for fluid and solid interfaces |
| Solver Type | Steady-state or transient | Transient with steady-state capabilities |
| Radiation Modeling | Possible with additional modeling | Possible, often coupled with specific radiation models for accurate energy transfer in solids |
This table provides a high-level comparison between buoyantFoam and chtMultiRegionFoam,
highlighting their distinct capabilities and typical applications.
buoyantFoam is focused on fluid dynamics influenced by temperature differences,
whereas chtMultiRegionFoam is tailored for detailed thermal analysis involving both fluids and solids,
making it versatile for a wide range of engineering problems.