A heat exchanger will be used to cool 150 kg/h fruit juice containing 12% dry matter from 80 °C to 30 °C. The inlet temperature of the cooling water is 15 °C. Calculate the amount of cooling water required for the outlet temperature of the cooling water to be 25 °C. If the water flow rate is increased by 20% during the process, what will the cooling water outlet temperature be?

(a) What is the heat loss per unit length of the pipe?(b) The pipe material is switched to PTFE (k = 0.38 W/(m⋅K)). To maintain the same heat loss as theprevious question, if all other parameters are to remain the same as before, what is the required thicknessof the pipe wall in centimeters?

In a chemical production facility, a mixture containing 80% acetone and 20% water by mol will be transported through the pipeline. This mixture can be transported in liquid form or in vapor form. Transport of the steam mixture through the pipeline is carried out by a centrifugal pump. In order for the pump vanes to be unaffected by wear and to continue their operation without interruption, the mixture must have only a vapor structure. Determine the highest pump fluid pressure value at which the mixture will not form liquid, based on the temperature of the mixture in the pump being 100 °C. The mixture can be well represented by the following activity coefficient model (van Laar model): 4₁2 = 2.05 In y₁ = A₁₂ 1+ = diz[14 A₂ = 1.50 A₁2 x₁ A21 X₂ In 7₂ = A21 An ( 1 + Aj X₂ A₁2 X₁ 12

2 A wire of diameter D = 2 mm and uniform temperature T has an electrical resistance of 0.01 N/m and a current flow of 20 A. (a) What is the rate at which heat is dissipated per unit length of wire? What is the heat dissipation per unit volume within the wire? (b) If the wire is not insulated and is in ambient air and large surroundings for which T = Tsur = 20°C, what is the temperature T of the wire? The wire has an emissivity of 0.3, and the coefficient associated with heat transfer by natural convection may be approximated by an expression of the form, h = C[(T-T)/D]¹/4, where C = 1.25 W/m7/4.K5/4 (c) If the wire is coated with plastic insulation of 2-mm thickness and a thermal conductivity of 0.25 W/m.K, what are the inner and outer surface temperatures of the insulation? The insulation has an emissivity of 0.9, and the convection coefficient is given by the expression of part (b). Explore the effect of the insu- lation thickness on the surface temperatures. Note: 1. The metal wire…