The temperature distribution for a plane wall, for steady state heat flow and constant value of thermal conductivity is
The temperature distribution for a hollow cylinder for steady state heat flow and constant value of thermal conductivity is
Since heat transfer in hollow cylinder is given by
Hence heat transfer profile is logarithmic.
The temperature distribution for a sphere for steady state heat flow and constant value of thermal conductivity is
Hence profile will be hyperbolic.
The heat transfer in the hollow cylinder is taking place by conduction and in this case logarithmic mean temperature difference A_{lm} is given by
Heat transfer by conduction through hollow cylinder is given by
Also,
What will be geometric radius of heat transfer for a hollow sphere of inner and outer radii r_{1} and r_{2}?
Heat transfer by conduction through sphere is given by
Geometric mean Area
Geometric mean radius
Thermal diffusivity is given by
Thermal diffusivity is the ratio of thermal conductivity and thermal diffusivity
A composite slab has two layers of different materials with thermal conductivity k_{1} and k_{2}. In each layer had the same thickness, the, equivalent thermal conductivity of the slab would be
A steam pipe is covered with two layers of insulating materials, with the better insulating material forming the outer part. If the two layers are interchanged, the heat conducted
k_{1} < k_{2} [k_{1} better insulator]
Q ∝ k. This means that the material having better insulating materia! should be inside to minimize the heat flux hence if better insulating materia! is placed inside, it will reduce the heat transfer.
In a long cylindrical rod of radius R and a surface heat flux of q_{0} the uniform generation rate is
The critical thickness of insulation for cylinder is given by
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