Heat conduction through hollow cylinder | Heat transfer for GATE 2022 | Chemical Engineering

Heat conduction through hollow cylinder | Heat transfer for gate 2022 | Chemical Engineering.
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About this Video :
In this video we are going to talk about the
Heat Conduction through a hollow cylinder then we will drive the equation of heat transfer from Fourier's law of conduction for this hollow cylinder geometry.
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[@jeeneshpatel4176]

Thank you ❤❤

[@akashlalremruot131]

The log mean radius is used in the derivation of heat flow in a hollow cylinder because it provides a better approximation of the average radius for heat transfer purposes.
When heat flows through a hollow cylinder, it is distributed over the cross-sectional area of the cylinder. The amount of heat flowing through a given cross-sectional area is proportional to the distance from the center of the cylinder, as given by Fourier's law of heat conduction.
To calculate the average radius for heat transfer purposes, we could simply take the arithmetic mean of the inner and outer radii of the cylinder. However, this would not take into account the fact that heat flows more easily through regions of the cylinder that are closer to the center.
The log mean radius provides a better approximation of the average radius for heat transfer purposes because it takes into account the logarithmic relationship between the distance from the center and the amount of heat transferred.
The formula for the log mean radius is:
r_lm = (ln(r_o/r_i)) / (2*ln(r_o/r_i))
where r_i and r_o are the inner and outer radii of the cylinder, respectively. The log mean radius is used in the heat flow equation for a hollow cylinder, which is:
Q = (2*pi*k*L / ln(r_o/r_i)) * (T_1 - T_2)
where Q is the rate of heat transfer, k is the thermal conductivity of the material, L is the length of the cylinder, T_1 and T_2 are the temperatures at the inner and outer surfaces of the cylinder, respectively. The log mean radius appears in the denominator of the natural logarithm, reflecting the fact that the heat flow rate depends on the logarithmic difference in radii.

[@akashlalremruot131]

In the study of heat flow in a hollow cylinder, we use some assumptions to simplify the problem and make it easier to solve. Here are a few reasons why we use assumptions:
1. Simplification of the problem: Heat flow problems can become quite complicated if we consider all the variables involved. By making certain assumptions, we can simplify the problem and make it more manageable.
2. Practicality: In many cases, it is not practical to consider all the factors that affect heat flow. For example, we may not have access to data on the exact thermal properties of the materials involved, or we may not be able to measure the temperatures at various points inside the cylinder. By making assumptions, we can still make useful calculations without having to know everything about the system.
3. Accuracy: Although assumptions are simplifications, they can still provide accurate results within certain limits. By understanding the limitations of the assumptions we make, we can ensure that the results we obtain are reasonably accurate.
Some common assumptions made in the study of heat flow in a hollow cylinder include:
- Steady-state conditions (i.e., the temperature distribution in the cylinder does not change with time)
- One-dimensional heat flow (i.e., heat flows only in the radial direction, with no variation in the axial or circumferential directions)
- Constant thermal conductivity and specific heat of the material
- Negligible heat transfer by radiation or convection
- Uniform heat generation inside the cylinder (if applicable)

[@officialrahulverma7000]

Sir you are explane very well...good bless your ❤️❤️❤️

[@vishalheera3939]

We use assumptions in derivation because heat does not flow radially in real life practical,heat flow in all directions , so we do use assumptions for calculation purpose.

[@umeshjoshi501]

Sir please make a video about fins