Research of the problems of heat conduction in fluids

In the fluid of the pipeline, the phenomena of heat convection, heat conduction, and radiation heat transfer occur between the pipeline and the outside world as well as between the pipeline and the inside. In the calculation of the relevant temperature and heat, we need to know the heat transfer coefficient, pipeline characteristic length, flow velocity, and other data to get the results. Based on previous research results, this paper will use Ansys software to explore the change law of heat transfer effect with various parameters. We can find that in the simulation, as the flow rate increases, the heating effect will become worse and worse.


Introduction
Heat conduction in pipelines has always been a major issue in heat transfer research.In the process of heat transfer, heat is exchanged and transferred mainly through heat conduction, heat convection and heat radiation.In the process of heat transfer, Fourier's law, Newton's cooling formula, and the flow equation are satisfied.This paper mainly studies the forced convection in the pipeline, but also introduces concepts such as the boundary layer for supplementary explanation.The specific heat transfer effect in the flow process should be determined according to various parameters.Through data simulation, this paper reveals some laws of heat transfer of liquid through pipelines, which have guiding significance for heating and cooling liquids.

Basic concepts Heat conduction:
Heat conduction rate Equation -Fourier's Law: For the element of thickness dx, the heat transferred into the face at x, and the heat conducted out of the face at x+dx, are given, per unit area, by: 1D problem (x variation only) -no partial derivatives.in steady state (no time derivatives).At a steady state, there can be no energy accumulation in the element, implying that  It can be obtained from the Newtonian cooling formula q 2 = k w (T wi − T wo ) t w (8) According to the law of energy conservation, ignoring the loss, we can get the following formula q = (T i − T 0 ) In the actual heat transfer process, the specific temperature distribution will be related to the specific thermal conductivity, thermal diffusion coefficient and convective heat transfer coefficient.
Firstly, the concept of Bi number is introduced: It reflects the relative magnitude of convective heat transfer capacity and heat conduction capacity.For example, Bi<<1.and meaning means that λ is very large, and the heat transfer effect in the thin plate is good, so the temperature tends to be consistent.Because the heat transfer is not good outside, the temperature varies greatly with the spatial distribution.When Bi number >>1, the external temperature tends to be the same, while the internal temperature changes greatly [1].
The main research direction of this paper is convective heat transfer, and it also focuses on introducing related concepts.Pr: represents the dimensionless combination number of interaction between energy and momentum transport processes in the fluid, reflecting the relationship between energy transport and momentum transport processes.
In forced convection, the formula is summarized in the following general form: External flow (boundary layer): Fluid properties evaluated at average: When it's laminar flow(Re<5*10 5 ) The local value of Nu at x can be expressed as Nu x = 0.0332Re x In general, the velocity is zero at the contact boundary, and the closer you get to the center of the fluid, the closer you get to the velocity.
At the larger Prandtl number, the convective transport due to the vortex shedding process dominates over the diffusive transport.As the Prandtl number decreases, diffusive effects become important.Moreover, the thermal boundary layer increases with decrements of the Prandtl number, which results in a reduction in the local and mean non-dimensional heat transfer coefficients [2].
Temperature is the maximum contact surface, the closer to the center of the fluid, the closer to its own flow rate.
For the total heat conduction:Q = hAΔT For natural convection heat transfer, the empirical formula is as follows: Gr number represents the relative magnitude of buoyancy force and viscous force, reflecting the strength of natural convection.

Derivation of theoretical formula
First we imagine a model of a hollow tube with an internal heat source placed inside.
We divide it along the length of the pipe into an infinite number of tiny segments, each of which is dx.Let the wall thickness of the pipe be δ.Because it's a thin wall, we can just write the wall volume: Let the wall temperature be tw.The initial wall temperature is t0.Liquid temperature is tf.The initial temperature of the liquid is t1.
According to Newton's cooling formula: In unit length, the rising temperature of the tube wall: So if I integrate this over length, I get: C1 and C2 are the specific heat capacity of tube wall and liquid respectively.Thus we can calculate the specific heat capacities of different regions of the wall and liquid at stability [3][4].

Software simulation
According to the empirical formula and practical experiment, we can get some general rules of heat transfer with a change of parameters.Ansys software is used here to simulate and change the parameters in order to find its rules and have a more accurate and comprehensive understanding of its changing rules.
Firstly, we simulated the forced convection heat transfer in the pipe: the model established was a pipe with a length of 200mm, an outer diameter of 30mm and an inner diameter of 24mm.The wall of the tube is used as the heating source.Some parameters are now changed, and a cloud map is created to show the results.This model is built in Solidworks The water flow rate is set at 0.01m/s, the wall material is copper, the inlet temperature is 300K, and the initial wall temperature is 300K.
When the energy source provided is 5000000W/m 3 : Figures 2 and 3are the X-Z direction cloud and the X-Y direction scatter plot, respectively.Make X-Y map according to x-z cross section cloud map (Figure 4): It can be found that the law: because the pipe wall is heated as a heat source, the average temperature of the fluid near the outlet will be higher than that at the entrance, and the heat source temperature will be transferred to the pipe wall and the fluid, which conforms to the law of energy conservation.We can find that the heating process of the fluid is an outside-in process.It is supposed that the boundary layer and the thermal conductivity inside the fluid do not tend to infinity.In addition, we know from the cloud image that the temperature of the pipe wall at the inlet is lower than that at the outlet, indicating that the energy generated by the heat source at the inlet is first transferred to the pipe wall.Since the starting temperature of the fluid is very low and the temperature difference is large, a large amount of heat is applied to the fluid temperature at the inlet.Then, as the fluid warms up, the temperature difference decreases, so more heat is allocated to the wall.As can also be seen in the X-Y chart, the temperature changes become more and more gentle, which is caused by the smaller temperature difference.
When the velocity of the fluid is greatly increased to 1m/s, the cloud and scatter plots are shown as Figure 4 and Figure 5.As shown in the figure above.When the flow rate is high, the fluid does not receive much heat from the heat source.Because in the process of convective heat transfer, due to the small convective heat transfer coefficient between the wall and the fluid, the heat cannot be transferred to the fluid quickly, and the heat is largely stored in the fluid tube wall.Under this condition, the influence of the internal thermal conductivity of the fluid can be basically ignored, so the fluid is basically maintained at a uniform temperature [5].
If the fluid is changed into air, the cloud image can be expressed as Figure 6.It can be seen from here that the specific heat of air is less than that of water due to the change of materials, so the temperature of air rises quickly and the final temperature is higher than that of water.But water conducts heat better than air.As can be seen from the x-z diagram, the temperature distribution of the air is not so uniform.
After the above study, if we want to heat the fluid, then we should control the flow rate and materials, choose materials with better thermal conductivity, and pay attention to whether the temperature distribution in the fluid is uniform and whether it meets the requirements.
When cooling the tube walls with liquid, care should be taken not to allow the flow rate to be too fast.When choosing a liquid, it is necessary to choose a liquid with a larger specific heat capacity.If possible, increase the temperature difference between the wall and the fluid for better cooling [6].

Conclusion
In this paper, the theoretical formula and current research results are introduced first, and then the specific formula and application range of forced convection heat transfer are introduced.The difference in temperature distribution under the influence of different parameters is obtained after deducing the theoretical formula and verifying the Ansys simulation.It has practical significance for us to carry out pipeline heat transfer in reality: when heating the fluid, the speed should not be too fast, otherwise, the heating effect will be very poor; if we choose to cool the pipe, we should choose an appropriate coolant that is larger than the heat and so on.Of course, there are still some defects in this study.More experimental data are needed to support this conclusion, and further quantitative experiments should be conducted to obtain more instructive data.

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Bulk Fluid: largely constant at temperature: Tf • Solid part: linear T variation (Tw -Temperature at wall) • A thin layer (film) near wall (rapid & nonlinear variation) Thin Fluid Film ('Thermal Boundary Layer') Convective Heat Transfer Coefficient Heat transfer through a boundary layer by convection is expressed by Newton's Law of Cooling as Q = hA(T w − T f )=hAΔT (6)Ais surface area over which heat is being transferred ΔT = (T w − T f )is differences temperature between wall and Fluid.The following describes the actual situation of several heat transfer processes: For single-layer thin plates, convection heat and heat conduction are combined as Figure1
film heat transfer coefficient bulk mean flow velocity= fluid density μ=fluid dynamic viscosity at bulk fluid temperature k= fluid thermal conductivity cp=fluid specific heat capacity L= = characteristic length (e.g.pipe diameter d).Nu: indicates the intensity of convective heat transfer Re: represents the ratio of inertial force and viscous force level to determine the fluid flow state.
And the total Nu: integral can be obtained Nu L = 0.0664 Re L When the fluid is turbulent: (Re>5*10 5 ) Nu ⅆ = 0.023Re ⅆ 0.8 Pr n (19) n = 0.4 for heating, n = 0.3 for cooling In the boundary layer of the temperature reading plate, speed and temperature are not distributed in the same way.