A 25 cm-diameter oil line is buried with its centerline 60 cm below the ground. Assuming a soi

A 25 cm-diameter oil line is buried with its centerline 60...

A $25 \mathrm{~cm}$-diameter oil line is buried with its centerline $60 \mathrm{~cm}$ below the ground. Assuming a soil temperature of $10^{\circ} \mathrm{C}$ and a soil thermal conductivity of $0.8 \mathrm{~W} / \mathrm{m}$ $\mathrm{K}$, estimate the steady-state heat loss from the pipe (in W/m) when the oil is at $90^{\circ} \mathrm{C} .$ (i) Ignore the inside thermal resistance. (ii) Recalculate your result if the inside heat transfer coefficient is $300 \mathrm{~W} / \mathrm{m}^{2} \mathrm{~K}$.

A $25 \mathrm{~cm}$-diameter oil line is buried with its centerline $60 \mathrm{~cm}$ below the ground. Assuming a soil temperature of $10^{\circ} \mathrm{C}$ and a soil thermal conductivity of $0.8 \mathrm{~W} / \mathrm{m}$ $\mathrm{K}$, estimate the steady-state heat loss from the pipe (in W/m) when the oil is at $90^{\circ} \mathrm{C} .$
(i) Ignore the inside thermal resistance.
(ii) Recalculate your result if the inside heat transfer coefficient is $300 \mathrm{~W} / \mathrm{m}^{2} \mathrm{~K}$.

Key Concepts

Steady-State Heat Conduction

This concept involves analyzing heat flow when temperatures and energy transfers remain constant over time. In steady-state conditions, all energy entering a system equals the energy leaving it, which simplifies the analysis by removing any time-dependent aspects and letting one focus on the balance of conduction (and convection when applicable) through various materials.

Thermal Resistance Network

Heat transfer problems can often be broken down into a series of resistances that impede the flow of heat, analogous to electrical resistances in a circuit. In the context of a buried pipe, various layers (such as the pipe wall, any insulation, and the surrounding soil) each contribute a resistance; the total resistance determines the overall rate of heat loss for a given temperature difference.

Cylindrical Heat Transfer

For systems like pipes, heat conduction needs to be analyzed using cylindrical coordinates, which leads to logarithmic expressions when calculating thermal resistance. This approach accounts for the radial conduction through the pipe wall and surrounding soil, which is crucial when accurately determining heat losses from cylindrical geometries.

Convective Heat Transfer

This concept pertains to the transfer of heat between a solid surface and a fluid (or gas) in motion, characterized by a heat transfer coefficient. In the case of a pipe carrying hot oil, the internal convective resistance becomes significant when it is not negligible, affecting the overall heat transfer by adding another layer of resistance in series with conductive resistances.

Transcript

00:01 Here we have another heat exchanger, but now we have hot oil and cold water.

00:05 So this is the oil now, and this is the water.

00:11 We're also given some dimensions for these things, and i don't know exactly they're not, there's no, there's no, unless we wanted to figure, if they wanted us to ask the velocity or something, or the heat transfer per unit length or something, we wouldn't have used these, but they didn't ask us for anything.

00:31 Of that so i'm not sure why they gave us these dimensions for these the pipes.

00:37 Um, i guess the diameter of the tube, i guess the tube would mean the tube here, the water tube.

00:46 So the oil comes in at 150 degrees c, again our units are here, with a mass flow rate of two kilograms per second, an exit at the temperature of 40 degree c, we're given the heat capacity to be about 2 .20 kilojoules per kilogram kelvin.

01:08 And then we have the oil or the water.

01:13 The water enters here at 22 degrees c.

01:17 It is a mass flow rate of 1 .5 kilograms per second, and the heat capacity is 4 .18 as usual for water.

01:29 So it's steady state.

01:30 So we have the energy flowing in, has to be the energy flowing out.

01:34 And so if we look at just the oil, we just kind of do a control volume around the oil, we have the mass flow rate of the oil, times the heat capacity of the oil, is the temperature difference between the inlet and the exit.

01:50 And that is the heat transferred out of the oil.

01:54 And so plugging all those numbers in, we get 484 kilowatts...

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