PROBLEM 2.27KNOWN:Temperature distribution and distribution of heat generation in central layer of a solarpond.FIND:(a) Heat fluxes at lower and upper surfaces of the central layer, (b) Whether conditions aresteady or transient, (c) Rate of thermal energy generation for the entire central layer.SCHEMATIC:ASSUMPTIONS:(1) Central layer is stagnant, (2) One-dimensional conduction, (3) ConstantpropertiesANALYSIS:(a) The desired fluxes correspond to conduction fluxes in the central layer at the lowerand upper surfaces. A general form for the conduction flux isʹʹ=−=−+±!"$#qkTxkAkaeBcond-ax∂.Hence,==−+±!"$#==−+±!"$#qqkAkaeB qqkAkaBlcond x=L-aLucond x=016.<(b) Conditions are steady if ∂T/∂t = 0. Applying the heat equation,α∂α211TxqkTt-AkeAkeTt2-ax-ax
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