2. The pipe with an outer diameter of d=35mm is cooled in an oil cross flow (oil is trans.oil). The oil flow velocity and the average oil temperature are respectively: w =0.5m/s and t_(1)=25^circ C Determine what temperature of the pips surface must be maintained so that the heat flux will be equal to q=30W/m^2 and what will be the value of the heat transfer coefficient?

Question

Answer 1

To determine the temperature of the pipe's surface that must be maintained so that the heat flux will be equal to

, we can use the formula for heat transfer by conduction:

where:-

is the heat flux (in

)-

is the heat transfer coefficient (in

)-

is the average oil temperature (in

)-

is the temperature of the pipe's surface (in

)We need to find

, so we rearrange the formula:

To find the value of the heat transfer coefficient, we can use the convection heat transfer equation:

where:-

is the Nusselt number (dimensionless)-

is the convective heat transfer coefficient (in

)For turbulent flow, the Nusselt number can be estimated using the Dittus-Boelter equation:

where:-

is the Reynolds number-

is the Prandtl numberThe Reynolds number can be calculated as:

where:-

is the oil flow velocity (in

)-

is the outer diameter of the pipe (in

)-

is the kinematic viscosity of the oil (in

)The Prandtl number can be estimated as:

where:-

is the thermal diffusivity of the oil (in

)Assuming typical values for oil, let's take

and

.First, calculate the Reynolds number:

Next, calculate the Prandtl number:

Now, calculate the Nusselt number:

Finally, calculate the heat transfer coefficient:

Now, we can find the temperature of the pipe's surface:

So, the temperature of the pipe's surface must be maintained at approximately

to achieve a heat flux of

, and the value of the heat transfer coefficient is approximately

.

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