A porous disk of porosity P, inner radius R,, outer radius R and thickness & is...

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A porous disk of porosity P, inner radius R,, outer radius R and thickness & is heated at its outer rim with a flux q. Coolant at a mass flow rate m and temperature T flows radially through the disk. The specific heat of the coolant is c and the conductivity of the solid-fluid matrix is k. The disk exchanges heat by convection along its upper and lower surfaces. The heat transfer coefficient is h and the ambient temperature is 7, Assume that the Biot number is small compared to unity and the inner surface temperature is at T. in h,T R h,T R.- [a] Show that the steady state fin equation is given by d'T dT + (1 - B)r dr 4 Bi 2(T-T)=0, dr2 82 where Bi = hổ /2k and B= mc pf /2n8 k. %3D %3D [b] Determine the temperature of the heated surface. A porous disk of porosity P, inner radius R,, outer radius R and thickness & is heated at its outer rim with a flux q. Coolant at a mass flow rate m and temperature T flows radially through the disk. The specific heat of the coolant is c and the conductivity of the solid-fluid matrix is k. The disk exchanges heat by convection along its upper and lower surfaces. The heat transfer coefficient is h and the ambient temperature is 7, Assume that the Biot number is small compared to unity and the inner surface temperature is at T. in h,T R h,T R.- [a] Show that the steady state fin equation is given by d'T dT + (1 - B)r dr 4 Bi 2(T-T)=0, dr2 82 where Bi = hổ /2k and B= mc pf /2n8 k. %3D %3D [b] Determine the temperature of the heated surface.

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To create a tractable equation for the heat transfer of a fin many assumptions need to be made 1 Ste... View the full answer