Two slabs of thicknesses d,2d;and thermal conductivities k and 2k,are joined face to face in the longitudinal way Under steady - Physics - Kinetic Theory and Thermodynamics

Question

Two slabs of thicknesses d,2d;and thermal conductivities k and
2k,are joined face to face in the longitudinal way Under steady
state condition find rate of heat transfer per unit face area and
the temperature at the interface

Sanjay Singh · Accepted Answer

Dear student

a) Thermal Resistance of the first slab is R1=dkA  (A:face area) Thermal Resistance of the second slab is R2=d2kA  (A:face area)As these slaba are connected in series so equivalent thermal resistance isReqv=R1+R2Reqv=dkA+d2kAReqv=3d2kALet the temperature of one face of the slab =T1 and the temperature of the other side of the slab is T2heat current i=T1 - T2Reqv=2kA(T1 - T2)3drate transfer per unit area is =iA=2k(T1 - T2)3db)Let temperature of the interface is T0heat current through first slab=T1 - ToR1T1 - ToR1=T1 - T2ReqvT1 - TodkA=T1 - T23d2kAT1 - T0=23(T1 - T2)3T1-3T0=2T1-2T23T0=T1+2T2T0=T1+2T23Regards

Two slabs of thicknesses d,2d;and thermal conductivities k and 2k,are joined face to face in the longitudinal way.Under steady state condition find rate of heat transfer per unit face area and the temperature at the interface