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Heat transfer Chapter 2 - Heat transfer ME 431 by Dr Afif...

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Heat transfer ME 431, by Dr. Afif Hasan ----------------------------------------------------------------------------------------------------------- - Chapter 2 Introduction to conduction Conduction heat transfer in a medium due to temperature gradient is governed by Fourier law of cooling. Heat flux : A q dx dT k q x x = - = q :is normal to the cross section area “A” or direction of heat flow will be always normal to surface of constant temperature.(isothermal surface). In general: n T k q n - = n: is normal to an isotherm. Heat flux is a vector quantity and can be written as T k q - = ) ( z T k y T j x T i k + + - = gradient. Or z y x q k q j q i q + + = Where: ; x T k q x - = ; y T k q y - = ; z T k q z - = k: is independent of direction (same in all directions) or isotropic. Note: Fourier law apply to all matter: liquid, solid, gas 1 dx dT x kA q - = n q x q y q n y x Two- dimensional system Conduction Isotherm
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Heat transfer ME 431, by Dr. Afif Hasan ----------------------------------------------------------------------------------------------------------- - magnitude& mechanism could be different?. Thermal conductivity : From Fourier law, thermal conductivity is defined as: ; x T q k x - = thermal conductivity of solid is larger than that of liquid which is larger than that of gases. As shown in figure 2.4 page 46 “k” of solids may be four orders of magnitude of that of gas . K solid >>K liquid >>K gas. 1-Solids: Conduction in solids due to two mechanisms: (i) lattice vibration waves (ii)Migration of free electrons. Solid comprised of free electrons and atoms bounded in periodic arrangement called the lattice thus thermal energy is transported by both lattice vibration and movement of free electrons. k= k e +k L where; k e : free electron k L: lattice vibration. For pure metals: k e = L 0 T/ ρ e L 0 : Lorenz number ρ e : electrical resistivity, where ρ e = ρ 0+ ρ / T.
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