Answer Happy

You have been asked to design a hot air gun that heats air from an inlet temperature of Tin to Tout. This consists of a fan located within a tube of diameter Due, blowing air over a wire of diameter Dwire and length L that is coiled into a heater element (see Figure Q1). For this analysis, you can consider the heat transfer coefficient of the heater element to be that of a wire mounted orthogonally to the direction of air flow. Physical properties of the air and wire are shown in Table Q1-1 and operating parameters and dimensions of the hot air gun are shown in Table Q1- 2. Figure Q1 - an example of a wire coiled heater element. Air 1.85x10 Pa.s Dynamic viscosity Air Density 1.16 kg/m³ Air 0.0263 W/mK Air Thermal conductivity Specific heat capacity Thermal conductivity Specific heat capacity Density 1006 J/kgK 11.3 W/mK Wire Wire 450 J/kgk 8400 kg/m² Wire Table Q1-1: Physical properties of air and wire Tube Diameter 0.05 m Air Air velocity Air Inlet temperature Wire diameter 20 C 1 x 10³ m Heater Heater Wire length Heater Maximum wire 10 m 1150 C temperature Electrical Voltage V Current I 240 V 5 A Electrical Table Q1-2: properties of the air heater system a) Sketch a suitable arrangement for the air heater carefully showing the layout of the parts and label with appropriate nomenclature for the properties of the system. [4 marks] b) Derive an expression that gives the temperature difference between the air inlet and air outlet as a function of the voltage V and current I within the wire, the velocity (m/s) of the air, the diameter Drube of the tube and other relevant physical properties. [4 marks] c) Where h is the convective heat transfer coefficient (Wm³K¹), show that the temperature within the wire is given by VI Twire = Dwire Lh+Tin d) Calculate the temperature of the air. [4 marks] [2 marks] e) Calculate the temperature of the wire, given an approximate heat transfer coefficient correlation for the wire of: h = 10.25 v 1/2 where is the heat transfer coefficient (Wm³K¹) and the air velocity (ms) [4 marks] The air exiting the heater is used to heat treat a polymer rod, initially at the inlet air temperature, and held in the heated air for a short time. You wish to increase the rate of treatment by reducing the time the rod is held in the air. In relation to this, describe the consequences of increasing or decreasing the air velocity of the heater unit, making reference to the equations and solutions of parts b-d of this question. [7 marks] 11 m/s