Derive a formula for the thermal resistance, R., for a spherical shell assuming one- dimensional heat...

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Derive a formula for the thermal resistance, R., for a spherical shell assuming one- dimensional heat flux in the radial direction. The inside and outside radii of the spherical shell are r; and r., respectively, and the shell is made of a material having thermal conductivity k. Assume the temperatures at the inside and outside surfaces of the shell are T; and T.. respectively. The thermal resistance formula assumes the rate of heat transfer through the spherical shell, Q. is constant. The heat flux is in the radial direction for this one-dimensional case, and the heat flux is given by Fourier's law: q, = -k The rate of heat transfer through a dT dr spherical surface is Q = q, A where A = 4r. Derive the formula for the thermal 1 1 1 resistance for a spherical shell answer: R = 4k r Derive a formula for the thermal resistance, R., for a spherical shell assuming one- dimensional heat flux in the radial direction. The inside and outside radii of the spherical shell are r; and r., respectively, and the shell is made of a material having thermal conductivity k. Assume the temperatures at the inside and outside surfaces of the shell are T; and T.. respectively. The thermal resistance formula assumes the rate of heat transfer through the spherical shell, Q. is constant. The heat flux is in the radial direction for this one-dimensional case, and the heat flux is given by Fourier's law: q, = -k The rate of heat transfer through a dT dr spherical surface is Q = q, A where A = 4r. Derive the formula for the thermal 1 1 1 resistance for a spherical shell answer: R = 4k r