Example1 Heat Radiation of Plate (Laminar Flow) by Forced Convection

General

Heat dissipation of a flat plate by the forced convection is solved by the steady-state analysis.
The temperature distribution and the heat flux vectors are solved.
Unless specified in the list below, the default conditions will be applied.
Obtain this session's project file. (Save the project file before open)

Analysis Space

Item

Setting

Analysis Space

Thickness in depth direction: 300mm

Model Unit

Show Results

Item	Setting
Solver	Fluid Analysis [Bernoulli] Thermal analysis [Watt]
Analysis Type	Steady-State Analysis
Laminar Flow/Turbulent Flow	Select Laminar Flow
Meshing Setup	General Mesh size: 10[mm]

Model

The material of Air (000_Air) is set to a rectangular sheet body. The boundary conditions of inlet and outlet are set on the left edge and the right edge respectively.

A heat source of thin flat plate is defined by the rectangle sheet body.

The slip wall outer boundary condition is applied to the top and bottom edges where the boundary condition is not set.

Body Attributes and Materials

Body Number/Type	Body Attribute Name	Material Name
0/Solid	air	000_Air(*)
1/Solid	hot	hot

* Available from the material DB

The material properties of the thin flat plate are set as follows.

Material Name	Tab	Properties
hot	Solid/Fluid	Solid
hot	Thermal conductivity	1x 10*5

The heat source of the thin flat plate is set on the heat source tab as follows.

Body Attribute Name	Tab	Setting
hot	Heat source	10W

Boundary Condition

Boundary Condition Name/Topology	Tab	Boundary Condition Type	Setting
Inlet/Edge	Thermal Fluid	Inlet	Forced Inflow Specify fluid velocity 0.1[m/s] Inflow Temperature : 0[deg]
Outlet/Face	Thermal Fluid	Outlet	Natural Outflow
Outer Boundary Condition	Thermal Fluid	Slip wall	–

It is said that the flow over the flat plate transitions to the turbulent flow at the Reynolds number of around 5×10^5

The Reynolds number calculated from this model form, material property, and fluid velocity is about 1986. It is small enough to analyze the laminar flow.

Viscosity μ=1.82e-5[Pa s]

Density ρ: 1.205[kg/m3]

Kinematic viscosity v=μ/ρ=1.82e-5/1.205=1.510e-5[m2/s]

Fluid velocity V=0.1[m/s]

Length of plate L=0.3[m]

Reynolds number Re = V*L/ν=0.1*0.3/1.510e-5 = 1986

Results

The temperature distribution is shown below.

The maximum temperature is 22.584 [deg].

The theoretical value of the heat transfer of the laminar flow is 24 [deg], which is close to the actual value.

Heat source Q=10 [W]

Thickness of plate W=0.3 [m]

Length of plate L=0.3 [m]

Average heat flux q=Q/(2*L*W)=55.6 [W/m2]

Viscosity μ=1.82e-5[Pa s]

Density ρ=1.205[kg/m3]

Kinematic viscosity v=μ/ρ=1.82e-5/1.205=1.510e-5[m2/s]

Thermal conductivity λ=0.0265[W/m/deg]

Specific heat Cp=1006[J/Kg/deg]

Temperature diffusivity α = λ/(ρ*Cp) = 2.19e-5 [m2/s]

Prandtl number Pr = ν/α = 0.691

Fluid velocity V = 0.1[m/s]

Laminar average heat transfer h = 0.664 λPr^1/3 ν^(-1/2) (V/L)^1/2 = 2.311 [W/m2/deg]

Temperature difference ΔT = q/h = 24.04[deg]

Below is the plotting of the temperature distribution from coordinates (250,0,-100) to coordinates (250,0,100).

The boundary layer of about 30mm is created.

The following is a vector diagram of the heat flux on the wall surface.

The heat flux on the wall surface becomes larger toward the upwind.

For reference, the results of the turbulent analysis is shown below.

Almost the same results are acquired.

(In most cases of the laminar phenomena, the turbulent analysis can be applied.)