Heat Radiation of Plate (Laminar Flow) by Forced Convectionexamples|products|Murata Software Co., Ltd.

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

2D

 

Thickness in depth direction: 300mm

Model Unit

mm

 

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

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.

 

<Theoretical Value Calculation>

 

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.)