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mehadi06me
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Hello brothers
Anyone please help me derivation of this integro-partial differential equation (attached below).This is a governing equation for simultaneous conduction-radiation heat transfer within a cylinder.The figure is attached below.where ρ is the density, Cp is the heat capacity, κ is the thermal conductivity, σ is Stefan’s constant (the Stefan-Boltzmann constant), ε is the emissivity, and k(x, x') is the kernel corresponding to the radiation view factor. This equation arises in the physical description of 1D heat conduction and radiation along a pipe. Figure 5-7 shows the model geometry.
Before setting up the model, make the following assumptions:
• Inside the tube, neglect convection and consider only radiation and conduction.
• Assume blackbody radiation with ε = 1.
• Model heat transfer only in the x direction (assume θ symmetry).
• The pipe’s outer wall is perfectly insulated so that no heat escapes to the outside world by either radiation or conduction.
The definition of the kernel k(x, x') is given as a function of ξ (attached below)
where ξ = | x − x' |/ Di ;Help me please...
Anyone please help me derivation of this integro-partial differential equation (attached below).This is a governing equation for simultaneous conduction-radiation heat transfer within a cylinder.The figure is attached below.where ρ is the density, Cp is the heat capacity, κ is the thermal conductivity, σ is Stefan’s constant (the Stefan-Boltzmann constant), ε is the emissivity, and k(x, x') is the kernel corresponding to the radiation view factor. This equation arises in the physical description of 1D heat conduction and radiation along a pipe. Figure 5-7 shows the model geometry.
Before setting up the model, make the following assumptions:
• Inside the tube, neglect convection and consider only radiation and conduction.
• Assume blackbody radiation with ε = 1.
• Model heat transfer only in the x direction (assume θ symmetry).
• The pipe’s outer wall is perfectly insulated so that no heat escapes to the outside world by either radiation or conduction.
The definition of the kernel k(x, x') is given as a function of ξ (attached below)
where ξ = | x − x' |/ Di ;Help me please...