One Dimensional Polar Geometries For Conduction with Heat

Radial Systems For one-dimensional, steady-state conduction in an isotropic homogeneous medium with constant properties:

Cartridge Heaters A Reliable heater should continue to provide superior heat transfer, uniform temperatures

Central Condition for a solid cylinder: One dimensional conduction is possible only if there

Surface boundary condition: Dirichlet Boundary Condition: At r = r. O T(r. O) =

Surface Convection Boundary Condition: All the heat generated in the cylinder of length L,

Current Carrying Conductor • An important practical application. • Cooling of current carrying conductors

Maximum Temperature at the axis of the cylinder:

Hollow Cylinder with Heat Generation • Hollow cylinder geometry has significant applications as a

Solid Propellant Rocket Solid propellant rockets burn a solid block made of fuel, oxidizer,

Positron Rocket Heat Generation is inside the matrix. The outer surface and core of

In-Situ Thermal Processing of Shale Oil Heat Generation/absorption is inside the shale oil. The

Boundary Conditions - I Solution : Inner surface insulated: r. O Convection cooling of

Boundary Conditions - II Solution : Heating of Inner surface : r. O Insulated

Sphere with Uniform Heat Generation GF- 3 US Baseball Grenade Bombs

Encapsulation of pharmaceutical products.

Solid Sphere with heat generation: Surface convection cooling: Surface radiative cooling:

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One Dimensional Polar Geometries For Conduction with Heat Generation P M V Subbarao Associate Professor Mechanical Engineering Department IIT Delhi A Basis for Generation of Tremendous Power….

Radial Systems For one-dimensional, steady-state conduction in an isotropic homogeneous medium with constant properties: q’’’

Cartridge Heaters A Reliable heater should continue to provide superior heat transfer, uniform temperatures and resistance to oxidation and corrosion even at high temperatures.

Central Condition for a solid cylinder: One dimensional conduction is possible only if there is axial Symmetry of temperature profile. q’’’

Surface boundary condition: Dirichlet Boundary Condition: At r = r. O T(r. O) = TO Maximum temperature occurs at center.

Surface Convection Boundary Condition: All the heat generated in the cylinder of length L, is transferred to ambient fluid by Convection heat transfer. q’’’

Current Carrying Conductor • An important practical application. • Cooling of current carrying conductors enhances their current carrying capacity. • Knowledge of temperature distribution is required to make sure that the conductor is not reaching its burn out condition. • Uniform internal heat generation occurs due to Joule heating. • Rate of heat generation per unit volume: Current Density : i/AC

Maximum Temperature at the axis of the cylinder:

Hollow Cylinder with Heat Generation • Hollow cylinder geometry has significant applications as a nuclear fuel rods. • Hollow electrical conductors of cylindrical shape are used for high current carrying applications, where the cooling is done by a fluid (Hydrogen) flowing on the inside. • Annual reactors insulated from inside or outside are used in Chemical Processes.

Solid Propellant Rocket Solid propellant rockets burn a solid block made of fuel, oxidizer, and binder (plastic or rubber). The block is called grain.

Hybrid Rocket Section A-A

Positron Rocket Heat Generation is inside the matrix. The outer surface and core of the cooled by liquid hydrogen. The inner surface is treated as insulated. This is a problem of heat generation in a hallow cylinder with inner surface insulated.

In-Situ Thermal Processing of Shale Oil Heat Generation/absorption is inside the shale oil. The outer surface of the shale oils is surrounded by rock. The inner surface is electrical heated. This is a problem of heat generation in a hallow cylinder with outer surface insulated.

Boundary Conditions - I Solution : Inner surface insulated: r. O Convection cooling of outer surface: ri

Boundary Conditions - II Solution : Heating of Inner surface : r. O Insulated outer surface: ri

Sphere with Uniform Heat Generation GF- 3 US Baseball Grenade Bombs

Encapsulation of pharmaceutical products.

Solid Sphere with heat generation: Surface convection cooling: Surface radiative cooling: