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Show answer & explanation
Fouling refers to the accumulation of unwanted material on heat transfer surfaces, which acts as an additional insulating layer. This increases the total thermal resistance of the system, thereby reducing the overall heat transfer coefficient.
Step-by-step Derivation:
Step 1: Define the Overall Heat Transfer Coefficient (U). For a heat exchanger, the reciprocal of U represents the total thermal resistance: 1/U = 1/h_i + R_{f,i} + (L/k) + R_{f,o} + 1/h_o, where h represents convection coefficients, L/k is the wall resistance, and R_f represents the fouling factors.
Step 2: Analyze the effect of the fouling factor (R_f). As fouling increases, the value of R_f increases.
Step 3: Observe the mathematical relationship. Since 1/U is the sum of resistances, an increase in any individual resistance term (like R_f) increases the total value of 1/U.
Step 4: Conclude that if 1/U increases, U (the overall heat transfer coefficient) must decrease. Therefore, a high fouling factor decreases the overall heat transfer coefficient due to added thermal resistance.