This is question 3.5 in Fundamentals of Heat and Mass Transfer (7th). Incropera.

Question

This is question 3.5 in Fundamentals of Heat and Mass Transfer (7th). Incropera. A dormitory at a large university, built 50 years ago, has exterior walls constructed of L(sheathing) = 25-mm-thick sheathing with a thermal conductivity of k(sheathing) = 0.1 W/m*K. To reduce heat losses in the winter, the university decides to encapsulate the entire dormatory by applying an L(insulation) = 25-mm-thick layer of extruded insulation characterized by k(insulation) = 0.029 W/m*K to the exterior of the original sheating. The extruded insulation is, in turn, covered with an L(glass) = 5-mm-thick architectural glass with k(glass) = 1.4 W/m*K. Determine the heat flux through the original and retrofitted walls when the interior and exterior air temperatures are T(infinti, inside) = 22 degrees C and T(infiniti, outside) = -20 degrees C, respectively. The inner and outer convection heat transfer coefficients are h(inside) = 5 W/m^2 *K and h(outside) = 25 W/m^2 *K, respectively.

Explanation / Answer

we can model this problem using the electric circuit analogy heat flux = -k(dT/dx) = (-dT)/(dx/k) with (-dT) as thermal driving force, thermal resistance of each insulation is dx/k so we find the thermal resistance of each layers of insulation for sheathing dx = 25 mm = 0.025 m k = 0.1 W/m.K so thermal resistance = dx/k = 0.25 (m^2.K/W) for insulation dx = 25 mm = 0.025 m k = 0.029 W/m.K so thermal resistance = dx/k = 0.8621 (m^2.K/W) for glass dx = 5 mm = 0.005 m k = 1.4 W/m.K so thermal resistance = dx/k = 0.0036 (m^2.K/W) now all these thermal resistances are in series. net resistance when only the first sheathing is there is 0.25 (m^2.K/W) and net resistance when all three are in series is [0.25 + 0.8641 + 0.0036] = 1.1177(m^2.K/W) for both cases temperature difference at the ends of the wall = dT= (-22)-(20) = -42 K put it in formula for heat flux = (-dT)/(dx/k) heat flux through original coating = -(-42)/0.25 = 168 W/m^2 heat flux through the new combined system = -(-42)/1.1177 = 35.58 W/m^2

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.