Conjugate Heat Transfer

Introduction:

Conjugate heat transfer corresponds with the combination of heat transfer in solids and heat transfer in fluids. In solids, conduction often dominates whereas, in fluids, convection usually dominates. Conjugate heat transfer is observed in many situations. For example, heat sinks are optimized to combine heat transfer by conduction in the heat sink with the convection in the surrounding fluid.

Super-cycle modle:

Super-cycling was used to perform the conjugate heat transfer simulation. The timescale associated with heat transfer in solids and fluids is different due to different specific heat and capacitance values. Solids have a higher value and as a result, takes more time to heat compared to fluids. So, if the simulation is carried out at the same time-step as that of fluid flow, the solid region temperature will change very slowly. Hence, super-cycling is used which performs a steady-state simulation of the solid region in periodic intervals.

Dimenssions:

• length of cylinder = 0.2 m
• length of outer daimeter = 0.03 m
• length of inner daimeter = 0.02 m

Geometry:

Boundary condition:

1) Inlet comdition:

• Neumann boundary condition for pressure.
• Dirichlet boundary condition for velocity. The value for velocity was calculated using
• Reynold\'s number formula:
• Re=ρ⋅V⋅Dμ\">Re=`(rho*V*D)/mu`
• Reynold\'s number = 7000 as per the problem statement
• Density = 1.225 kg⋅m-3
• Viscosity = 1.81e-5 kg⋅m/s
• Hence, the Velocity = 3.45 m/s

2) Outlet condition:

• Neumann boundary condition for inlet velocity.
• Drichlet boundary condition for outlet static pressure 101325 pa.

3) Outer side wall of cylinder:

• Stationary wall with slip boundary coundion
• Define hetflux temperature 10000 W/m^2 for heating the fluid in cylinder by convetion.

4) Cylinder thickness:

• Define stationary wall and slip boundary condtion for solid, and temperature use Neumann boundary condition because it is adiabatic.

5)Interface:

• It is has been divided interface into two Regions Forward region and backward region.
• The forwrd region is assigned to fluid it is law of wall boundary condtion.
• the backward region is assignede to solid it is slip boundary condtion and temperature is neumann boundary condition.

Itial conditions and regions:

We define two regions in conjugate heat transfer

1)fluid region

• Pressure = 101325 pa
• temperature = 300 K
• Velocity = 3.45 m/s
• Define species O2 ,N2

2) solid region

• Define stream ID = 1
• Define meterial AlUMINIUM and mass Fraction = 1

Mesh size:

We use to analysis different grid size

• 0.002 m
• 0.003 m
• 0.004 m

Results:

Grid size 0.004:

Mesh:

Temperature:

Y+:

Idreg:

1)solid region for red

2)fluid region for blue

Velocity:

Animation:

Solid Temperature Plot: 1484 k

Fluid Temperature: 1147 K

Mean temperature:

Base grid size 0.003:

Base Grid:

Idreg:

Y+:

Temperature:

Velocity :

Animation:

Mean temperature : 1523 k

Solid temperature : 1523 k

Fluid temperature: 1288 K

Base grid 0.002:

Mesh:

Idreg:

Temperature:

Velocity:

Animation:

Plot:

Temperature:

Solid mean Temperature: 1261 k

Fluid mean temperature: 1035 k

Mean temperature for all three casue:

Super cycle intervel time for all three cause:

Super cycle time:

Super cycle stage intervel=0.03 simulation time = 499

Super cycle stage intervel=0.02 simulation time = 531

Super cycle stage intervel=0.01 simulation time = 524

Temperature defferece:

Solid Temperature FluidTemperature

1) Base mesh 0.004 = 1484 k 1187 k

2) Base mesh 0.003 = 1323 k 1066 k

3) Base mesh 0.002 = 1261 k 986 k

CONCLUSION:

• For low values of supercycle time-length, the simulation time is less.
• Temperature converges after 0.2 sec for all the three cases.
• The temperature value begins to change the earliest when the time-length is lowest.
• Fine grid size gives high cell count and simulation time is high.
• The Grid size is finer then temperature will be decreases.
• Y + value is increase the mesh is coarse.
• the temperature in solid is increase than fluid region because increase grid size.