Definition of the Modeling Problem
Electrical Heating of a Pipe
Glass-coated steel pipes are commonly manufactured by first heating the pipe to the melting range of glass before coming in contact with the hot pipe surface with glass granules. A tightly adhering nonporous coat will be formed as the granules melt and wet the pipe surface. Electric current is passed along the pipe for preheating (Bird, Stewart, & Lightfoot, 2002).
The situation under study is about the electrical heating of a pipe with the assumptions that over a temperature range, electrical conductivity, ke (ohm-1cm-1), is constant, and that the local rate of electrical heat production, Se (E/cm3), is uniform throughout the pipe wall. Heat losses through the pipe are assumed …show more content…
Since the system operates at steady state and is one-dimensional, the right-hand term then is equal to zero and then the y and z derivatives are not taken into account. The equation then reduces to k (∂^2 T)/(∂x^2 )+q_gen "=0
Applying a boundary condition at a surface where heat flux is known, the equation then becomes q_x "=q_x/A=-k dT/dx
This is the Fourier’s law of heat conduction equation which states that the heat transfer rate in the x-direction is proportional to the negative gradient in the temperature and to the area (Bergman, Bergman, Lavine, Incropera, & DeWitt, 2007). The minus sign in the equation refers to the transfer of heat in the direction of decreasing temperature. The constant of proportionality k is the thermal conductivity and the dT/dx term is the temperature gradient.
For the assigned study, cylindrical coordinates are used since the material used is a pipe. Assuming that the temperature is only a function of radius and that the system operates at steady state, Fourier’s law of heat conduction is re-expressed …show more content…
Heat conduction is often used in the industry when analyzing heat losses through pipe walls, heat transfers in heat exchangers, and other similar situations. It is governed by Fourier’s law of heat conduction. As current passes through the wire, there is resistance occurring to hinder the flow of electricity. As a result, heat is generated and this is characterized by the rate of heat production per unit volume Se. When a system operates at steady state conditions, heat flows radially out of the medium into the surroundings (Subramanian,
Electrical Heating of a Pipe
Glass-coated steel pipes are commonly manufactured by first heating the pipe to the melting range of glass before coming in contact with the hot pipe surface with glass granules. A tightly adhering nonporous coat will be formed as the granules melt and wet the pipe surface. Electric current is passed along the pipe for preheating (Bird, Stewart, & Lightfoot, 2002).
The situation under study is about the electrical heating of a pipe with the assumptions that over a temperature range, electrical conductivity, ke (ohm-1cm-1), is constant, and that the local rate of electrical heat production, Se (E/cm3), is uniform throughout the pipe wall. Heat losses through the pipe are assumed …show more content…
Since the system operates at steady state and is one-dimensional, the right-hand term then is equal to zero and then the y and z derivatives are not taken into account. The equation then reduces to k (∂^2 T)/(∂x^2 )+q_gen "=0
Applying a boundary condition at a surface where heat flux is known, the equation then becomes q_x "=q_x/A=-k dT/dx
This is the Fourier’s law of heat conduction equation which states that the heat transfer rate in the x-direction is proportional to the negative gradient in the temperature and to the area (Bergman, Bergman, Lavine, Incropera, & DeWitt, 2007). The minus sign in the equation refers to the transfer of heat in the direction of decreasing temperature. The constant of proportionality k is the thermal conductivity and the dT/dx term is the temperature gradient.
For the assigned study, cylindrical coordinates are used since the material used is a pipe. Assuming that the temperature is only a function of radius and that the system operates at steady state, Fourier’s law of heat conduction is re-expressed …show more content…
Heat conduction is often used in the industry when analyzing heat losses through pipe walls, heat transfers in heat exchangers, and other similar situations. It is governed by Fourier’s law of heat conduction. As current passes through the wire, there is resistance occurring to hinder the flow of electricity. As a result, heat is generated and this is characterized by the rate of heat production per unit volume Se. When a system operates at steady state conditions, heat flows radially out of the medium into the surroundings (Subramanian,