The relational expression between the amount of heat and the temperature in convection heat transfer is as follows.
The amount of heat Q is as follows.
Substituting Q into the above equation is as follows.
■What is heat transfer coefficient?
The heat transfer coefficient defines the efficiency of heat exchange by convection.
If the heat transfer coefficient is large, heat exchange is quick, and if the heat transfer coefficient is small, heat exchange becomes difficult.
The heat transfer coefficient h is defined as follows.
＜Nusselt number＞
The Nusselt number is one of the factors that determine the heat transfer coefficient in the above equation.
The Nusselt number represents how much heat transfer capacity has increased due to convection in a static liquid, and the larger the Nusselt number, the greater the heat transfer capacity.
To explain the meaning of the Nusselt number in a different way, it is how well the fluid is mixed, and it is expressed using the Reynolds number and the Prandtl number.
The Nusselt number is 1 when there is no movement of the fluid and it is hardly mixed.
The Nusselt number is often expressed by an empirical formula using the Reynolds number and the Prandtl number, and the applicable empirical formula changes depending on the state of the fluid.
As a typical empirical formula for in-cylindrical fluid, Hausen's formula is used for laminar flow, and Colburn's formula is used for turbulent flow.
＜Reynolds number＞
The Reynolds number Re is an index that indicates the likelihood of fluid turbulence and is defined below.
This is the ratio of the flow velocity to the viscosity.
The faster the flow velocity than the viscosity, the larger the Reynolds number, which makes it easier for turbulence to occur and heat exchange to occur.
On the contrary, if the viscosity is higher, the Reynolds number becomes smaller, the laminar flow becomes undisturbed, and it becomes difficult to exchange heat.
It is generally said that in a cylindrical tube, a laminar flow occurs when the Reynolds number is 2300 or less, a turbulent flow begins when the Reynolds number is 2300 or more, and a turbulent flow occurs when the Reynolds number is 4000 or more.
By the way, at first glance, Karman vortices look like turbulent flows, but because the structure of each vortex is uniform, they are classified as laminar flows, and the Reynolds number is about 50 to 300. Turbulence is a flow with microscopic fluctuations that cannot be seen with the naked eye.
＜Prandtl number＞
The Prandtl number is the ratio of the kinematic viscosity coefficient and the thermal diffusion coefficient of the fluid, which is a value unique to the fluid and means the ratio of the thickness of the velocity boundary layer to the thermal boundary layer.
The definition is as follows.
When the thermal boundary layer is thinner (the thermal diffusivity is smaller) than the velocity boundary layer, the Prandtl number becomes larger and heat exchange becomes more active. Conversely, when the thermal boundary layer is thicker than the velocity boundary layer, the Prandtl number becomes smaller.
As it is protected by the temperature layer, heat exchange is less likely to occur.
For example, the Prandtl number is Pr = 7 for water and Pr = 0.7 for air, indicating that water is easier to exchange heat.
You think this is because water feels colder even at the same temperature of 10 degrees celsius, because water has a thinner thermal boundary layer and is more likely to exchange heat.
Now that we have explained the information needed to determine the heat transfer coefficient, let's try to solve a concrete example.
■Example of calculation method of fluid temperature considering the influence of convection
Water at 20 ° C is flowing in a cylindrical tube kept at 100 ° C as shown below. What is the temperature of the water at the end of the heating section?
＜Answer＞
If the mass m of water, the surface area S of the cylinder, and the heat transfer coefficient h can be obtained, the answer can be obtained using Eq. (1). Specific heat c is given.
■Mass of water
Because, Mass = Density * Volume
■Surface area of cylinder
■Heat transfer coefficient
To calculate the heat transfer coefficient h, it is first necessary to calculate the Reynolds number and the Prandtl number.
① Reynolds number
And since it is a value larger than 4000, we can see that this is turbulent flow.
② Prandtl number
③ Nusselt number
You have the Reynolds number and the Prandtl number, calculate the Nusselt number from here.
The formula used is Colburn's formula because the fluid is turbulent.
④ Heat transfer coefficient
Now that we have the Nusselt number, we can calculate the heat transfer coefficient.
Now you have all the values you need for equation (1). Substitute the above value in (1).
＜Simulation of temperature change by convection heat transfer by Scilab＞
Calculate the solution of the above formula with Scilab. The block diagram is as follows.
The simulation results are as follows.
It takes 10s for water with a flow velocity of 0.2m / s to pass through a 2m pipe, so the temperature after 10s is equal to the outlet temperature.
Therefore, the outlet temperature is about 60.2 ° C.
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