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**Unformatted text preview: **Extended Surfaces/Fins Convection: Heat transfer between a solid surface and a moving fluid is governed by the Newtons cooling law: q = hA(T s-T ). Therefore, to increase the convective heat transfer, one can Increase the temperature difference (T s-T ) between the surface and the fluid. Increase the convection coefficient h. This can be accomplished by increasing the fluid flow over the surface since h is a function of the flow velocity and the higher the velocity, the higher the h. Example: a cooling fan. Increase the contact surface area A. Example: a heat sink with fins. Extended Surface Analysis x T b q kA dT dx x C = - q q dq dx dx x dx x x + = + dq h dA T T conv S =- ( )( ), where dA is the surface area of the element S A C is the cross-sectional area Energy Balance: if k, A are all constants. x C q q dq q dq dx dx hdA T T kA d T dx dx hP T T dx x dx conv x x S C = + = + +-- +- = + ( ) ( ) , 2 2 P: the fin perimeter A c : the fin cross-sectional area Extended Surface Analysis (cont.) d T dx hP kA T T x T x T d dx m hP kA D m x C e C e C C mx mx 2 2 2 2 2 2 2 1 2-- =-- = =- = = + - ( ) ,...

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