Heat conduction Analysis 1 d and 3 d

Heat conduction Analysis (1 d and 3 d)

Conduction • Fourier’s Law q : Heat transfer rate : Temperature gradient in direction of the heat flow

Heat Conduction Analysis- 1 D 1 -D (plane wall) Situation: Consider general case where T changing with t & heat source present within the body. So, the energy balance;

Heat Conduction Analysis- 1 D 1 -Dimension Heat Conduction general equation:

Heat Conduction Analysis-3 D Spherical coordinates Cartesian coordinates Cylindrical coordinates

Cartesian coordinates

Cartesian coordinates General 3 -Dimension Heat Conduction equation: If, k = constant Thermal Diffusivity of the material

Thermal Diffusivity • The larger value of α, the faster heat will diffuse through the material. • So, α can be higher value if i) Thermal conductivity, K higher ii) Thermal heat capasity, ρc lower

Heat Conduction Analysis- 3 3 -Dimension Heat Conduction equation: Cylindrical coordinates Spherical coordinates

Heat Conduction Analysis- 3 D Cylinder Coordinates Sphere Coordinates

Analysis: conclusion Steady-state 1 D heat flow (no heat generation): Steady-state 1 D heat flow in cylinder coordinates (no heat generation): Steady-state 1 D heat flow with heat sources: 2 D Steady-state conduction without heat sources:

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