General differential equation of heat conduction in cylindrical coordinates
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⬆️⬆️⬆️⬆️⬆️⛔⛔⛔♦️♦️♦️The heat equation may also be expressed in cylindrical and spherical coordinates. The general heat conduction equation in cylindrical coordinates can be obtained from an energy balance on a volume element in cylindrical coordinates and using the Laplace operator, Δ, in the cylindrical and spherical form.
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⬆️⬆️⬆️⬆️⬆️⛔⛔⛔♦️♦️♦️The heat equation may also be expressed in cylindrical and spherical coordinates. The general heat conduction equation in cylindrical coordinates can be obtained from an energy balance on a volume element in cylindrical coordinates and using the Laplace operator, Δ, in the cylindrical and spherical form.
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ɪɴ ᴇɴɢɪɴᴇᴇʀɪɴɢ, ᴛʜᴇʀᴇ ᴀʀᴇ ᴘʟᴇɴᴛʏ ᴏғ ᴘʀᴏʙʟᴇᴍs, ᴛʜᴀᴛ ᴄᴀɴɴᴏᴛ ʙᴇ sᴏʟᴠᴇᴅ ɪɴ ᴄᴀʀᴛᴇsɪᴀɴ ᴄᴏᴏʀᴅɪɴᴀᴛᴇs.
ᴛʜᴇ ɢᴇɴᴇʀᴀʟ ʜᴇᴀᴛ ᴄᴏɴᴅᴜᴄᴛɪᴏɴ ᴇǫᴜᴀᴛɪᴏɴ ɪɴ ᴄʏʟɪɴᴅʀɪᴄᴀʟ ᴄᴏᴏʀᴅɪɴᴀᴛᴇs ᴄᴀɴ ʙᴇ ᴏʙᴛᴀɪɴᴇᴅ ғʀᴏᴍ ᴀɴ ᴇɴᴇʀɢʏ ʙᴀʟᴀɴᴄᴇ ᴏɴ ᴀ ᴠᴏʟᴜᴍᴇ ᴇʟᴇᴍᴇɴᴛ ɪɴ ᴄʏʟɪɴᴅʀɪᴄᴀʟ ᴄᴏᴏʀᴅɪɴᴀᴛᴇs ᴀɴᴅ ᴜsɪɴɢ ᴛʜᴇ ʟᴀᴘʟᴀᴄᴇ ᴏᴘᴇʀᴀᴛᴏʀ, Δ, ɪɴ ᴛʜᴇ ᴄʏʟɪɴᴅʀɪᴄᴀʟ ᴀɴᴅ sᴘʜᴇʀɪᴄᴀʟ ғᴏʀᴍ.
ɪɴ ᴇɴɢɪɴᴇᴇʀɪɴɢ, ᴛʜᴇʀᴇ ᴀʀᴇ ᴘʟᴇɴᴛʏ ᴏғ ᴘʀᴏʙʟᴇᴍs, ᴛʜᴀᴛ ᴄᴀɴɴᴏᴛ ʙᴇ sᴏʟᴠᴇᴅ ɪɴ ᴄᴀʀᴛᴇsɪᴀɴ ᴄᴏᴏʀᴅɪɴᴀᴛᴇs.
ᴛʜᴇ ɢᴇɴᴇʀᴀʟ ʜᴇᴀᴛ ᴄᴏɴᴅᴜᴄᴛɪᴏɴ ᴇǫᴜᴀᴛɪᴏɴ ɪɴ ᴄʏʟɪɴᴅʀɪᴄᴀʟ ᴄᴏᴏʀᴅɪɴᴀᴛᴇs ᴄᴀɴ ʙᴇ ᴏʙᴛᴀɪɴᴇᴅ ғʀᴏᴍ ᴀɴ ᴇɴᴇʀɢʏ ʙᴀʟᴀɴᴄᴇ ᴏɴ ᴀ ᴠᴏʟᴜᴍᴇ ᴇʟᴇᴍᴇɴᴛ ɪɴ ᴄʏʟɪɴᴅʀɪᴄᴀʟ ᴄᴏᴏʀᴅɪɴᴀᴛᴇs ᴀɴᴅ ᴜsɪɴɢ ᴛʜᴇ ʟᴀᴘʟᴀᴄᴇ ᴏᴘᴇʀᴀᴛᴏʀ, Δ, ɪɴ ᴛʜᴇ ᴄʏʟɪɴᴅʀɪᴄᴀʟ ᴀɴᴅ sᴘʜᴇʀɪᴄᴀʟ ғᴏʀᴍ.
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