the model you test has a good correlation (RSquare = 0.94) obtained between the in situ inlet velocity and the outlet temperature also the adj RSquare was 0.92. However, statistically you have to calibrate and validate the model using more field observation data, at least more than 30 field observation point for calibration and same for the validation.

@Mohamed Mortada El- Sharkawy how did you fit the curve and please tell me if there is any mathematical relation depicting the velocity and temperature

Using the least squares fit model in SAS statistics software, also I think the attached article will help you "The impact of water-velocity variations on deepwater seismic data"

http://www.slb.com/~/media/Files/industry_challenges/deep_water/industry_articles/200304_le_water-velocity_variations_deepwater_seismic.pdf

Hi Saikumar

you can use this model:

Linear model:

f(x) = a*(sin(x-pi)) + b*((x-10)^2) + c

Coefficients (with 95% confidence bounds):

a = -9996 (-3.625e+04, 1.626e+04)

b = 502.4 (-814.5, 1819)

c = -5.021e+04 (-1.819e+05, 8.148e+04)

Goodness of fit:

SSE: 0.001949

R-square: 0.998

Adjusted R-square: 0.9939

RMSE: 0.04415

using Matlab 2014 and cftool ... please, send me more data. We can use statistical analysis :)

@ Edgar Meza Thanks for the linear model. The values of a,b,c are what values and where you took from the input. because, i never used curve fitting tool in matlab. I have the only data about inlet velocity vs outlet temperature of my comsol model.. I have both minimum and maximum temperature values measured at the outlet.

Also , help me out to know about the tool as well the explain me about the results which you got.

S.No    U0  (m/s)    Outlet Temperature

                                 min(degC)     max(degC)

1          0.00125     28.516             30.182

2          0.0025       27.155              29.037

3          0.00375     26.614              28.606

4          0.005         26.374              28.428

5          0.00625     26.178             28.285

6          0.0075       26.008             28.17

7          0.00875     25.85               28.066

8          0.01            25.726             27.98

@Saikumar please, explain me how this experiments works. Can we use the mean of Outlet temperature?

You can use any model to fit this data! linear, non linear, exponential, lograthmic. Model fitting is a tool to minimize differences to estimate coefficients. Which model do you have? conceptual or numerical or landscape?

fitting statistical models is one thing, and there seems to be correlation. but is their also causation? what effect causes the temperature to vary?

You could also give more details about your experiment. Does discharge also vary with velocity or is it kept constant? the inlet and outlet are parts of what "system"? just a pipe? open channel?

 @Gerald Dörflinger , this is an open channel and it was modeled in comsol multiphysics. i had attached the image of the model. the upper domain is like a cube and one end it is made as inlet and opposite end as outlet. the temperature varies with the flow of water inside the cube at a particular velocity. at the inlet the temperature of water is measured and at the outlet the temperature of water recorded at the domain varies due to the central heater.

The water passes the heater and gets heated up and the temperature of the water is recorded at the outlet.

By the variation in inlet and outlet temperature i need to find back the velocity value of the water. (consider the case where initial velocity value is not given)]

In my experiment temperature at the outlet decays when increase in water velocity at the inlet.

ok I had not seen the sketch. well, my physics have decayed very much since I left University, but from what I understand when you increase velocity, your outlet temperature decreases i.e. your temperature gain is less when velocity is higher. Sounds logical as higher velocity means your water has a shorter residence time around the heater. But I may well fail to see the issue here and its complexity, I am just  trying to explain it for myself in simple terms.

 can anyone try to solve the above model and state me whether it is possible to calculate the velocity from the temperature difference and please specify which relation and formulas can be used to find the velocity.

Yes. In fact there is a thermodynamic function that relates evolution of a tracer plume (and then fluid particles). This formula links mean velocity with parameters as Kelvin temperature, viewing tracer plume as an ideal gas.

What is the media in which the heat transport take place? 

What kind of heat source do you use?

@ valentin wagner

this is to be an underwater application.This sensor design is to be placed over the structure which is like a submarine . Constant temperature method is used . Material is nickel because of its high TCR