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There are two ways to increase the rate of heat transfer • too increase c e se thee convection co vec o heat e transfer s e coefficient coe c e h

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7 8 FinsHEAT CONDUCTION THROUGHFINSPrabal TalukdarAssociate ProfessorDepartment of Mechanical EngineeringIIT DelhiE-mail: prabal@mech.iitd.ac.inpMech/IITDIntroduction&Qconv = hA s (Ts T )There are two ways to increase the rate of heat transfer too increasec e se thee convectionco vec o heate transfers e coefficientcoe c e h to increase the surface area As Increasing h may require the installation of a pump or fan, Or replacingpg the existingg one with a largerg one The alternative is to increase the surface area by attaching to the surface extended surfaces called fins made of highly conductive materials such as aluminumHeat sinksPin finsThe thin plate fins of a car radiator greatlyincrease the rate of heat transfer to the airFins from natureLongitudinal finsRectangularTriangularConvex parabolicTrapezoidalConcave parabolicRadial fins:RectangulargpprofileTriangular profileHyperbolic profilePins:Radial fin coffee cup(a)Cylindrical (b)conical (c) concave parabolic (d) convex parabolicFin EquationdTQ& x = kA cdxd Q& x&&Q x + dx = Q x +dxdx&dQconv = hdA s (T T )Energy Balance:&dQx dx + hdA ( T T )&= Qx +sdxdT h dA s(T T ) = 0dx k dxQ& x = Q& x + dx + d Q& convd Adx d 2Tdx2c1 dA c dT 1 h dA s (T T ) = 0+

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