Explanation The metal sheet is moving steadily through one inlet and one exit system. Hence, the inlet and exit mass flow rates are equal. m ˙ 1 = m ˙ 2 = m ˙ Write the energy rate balance equation for one inlet and one outlet system. [ Q ˙ 1 + W ˙ 1 + m ˙ ( h 1 + V 1 2 2 + g z 1 ) ] − [ Q ˙ 2 + W ˙ 2 + m ˙ ( h 2 + V 2 2 2 + g z 2 ) ] = Δ E ˙ system (I) Here, the rate of heat transfer is Q ˙ , the rate of work transfer is W ˙ , the enthalpy is h and the velocity is V , the gravitational acceleration is g , the elevation from the datum is z and the rate of change in net energy of the system is Δ E ˙ system ; the suffixes 1 and 2 indicates the inlet and outlet of the system. The system is at steady state. Hence, the rate of change in net energy of the system becomes zero. Δ E ˙ system = 0 In this system, there is no work input and output, no heat input. Only the heat is removed ( Q ˙ 2 ) from the hot metal sheet. Neglect work transfer, heat input at inlet, kinetic and potential energies. The Equations (I) reduced as follows. [ 0 + 0 + m ˙ ( h 1 + 0 + 0 ) ] − [ Q ˙ 2 + 0 + m ˙ ( h 2 + 0 + 0 ) ] = 0 m ˙ h 1 − Q ˙ 2 − m ˙ h 2 = 0 Q ˙ 2 = m ˙ h 1 − m ˙ h 2 Q ˙ 2 = m ˙ ( h 1 − h 2 ) (II) The change in enthalpy is expresses as follow. h 1 − h 2 = c p ( T 1 − T 2 ) Here, the specific heat is c p , the exit temperature is T 2 and the inlet temperature is T 1 . Substitute c p ( T 1 − T 2 ) for h 1 − h 2 in Equation (II). Q ˙ 2 = m ˙ [ c p ( T 1 − T 2 ) ] = m ˙ c p ( T 1 − T 2 ) (III) Write the formula for mass flow rate of metal plate. m ˙ = ρ A V (IV) Here, the density of the steel plate is ρ , the cross-sectional area of steel plate is A and the velocity of the steel plate that is flow through the oil bath is V . The cross-sectional area of the metal plate is expressed as follows

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Author: Yunus A. Cengel Dr., Michael A. Boles

Publisher: McGraw-Hill Education

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Chapter 5.5, Problem 103P

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Plot the rate of heat transfer against the plate velocity varies from 5 m/min to 50 m/min.

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Chapter 5.5, Problem 102P

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USE MATLAB ONLY Turbomachienery . GIven: vx = 185 m/s, flow angle = 60 degrees, R = 0.5, U = 150 m/s, b2 = -a3, a2 = -b3 Find: velocity triangle , a. magnitude of abs vel leaving rotor (m/s) b. flow absolute angles (a1, a2, a3) 3. flow rel angles (b2, b3) d. specific work done e. use code to draw vel. diagram Use this code for plot % plots Velocity Tri. in Ch4 function plotveltri(al1,al2,al3,b2,b3) S1L = [0 1]; V1x = [0 0]; V1s = [0 1*tand(al3)]; S2L = [2 3]; V2x = [0 0]; V2s = [0 1*tand(al2)]; W2s = [0 1*tand(b2)]; U2x = [3 3]; U2y = [1*tand(b2) 1*tand(al2)]; S3L = [4 5]; V3x = [0 0]; V3r = [0 1*tand(al3)]; W3r = [0 1*tand(b3)]; U3x = [5 5]; U3y = [1*tand(b3) 1*tand(al3)]; plot(S1L,V1x,'k',S1L,V1s,'r',... S2L,V2x,'k',S2L,V2s,'r',S2L,W2s,'b',U2x,U2y,'g',... S3L,V3x,'k',S3L,V3r,'r',S3L,W3r,'b',U3x,U3y,'g',...... 'LineWidth',2,'MarkerSize',10),... axis([-1 6 -4 4]), ... title('Velocity Triangle'), ... xlabel('x'),yl

The wall of a furnace has a thickness of 5 cm and thermal conductivity of 0.7 W/m-°C. The inside surface is heated by convection with a hot gas at 402°C and a heat transfer coefficient of 37 W/m²-°C. The outside surface has an emissivity of 0.8 and is exposed to air at 27°C with a heat transfer coefficient of 20 W/m²-ºC. Assume that the furnace is inside a large room with walls, floor and ceiling at 27°C. Show the thermal circuit and determine the heat flux through the furnace wall. h₁ T₁ k -L T. sur ho E

Turbomachienery . GIven: vx = 185 m/s, flow angle = 60 degrees, R = 0.5, U = 150 m/s, b2 = -a3, a2 = -b3 Find: velocity triangle , a. magnitude of abs vel leaving rotor (m/s) b. flow absolute angles (a1, a2, a3) 3. flow rel angles (b2, b3) d. specific work done e. use code to draw vel. diagram Use this code for plot % plots Velocity Tri. in Ch4 function plotveltri(al1,al2,al3,b2,b3) S1L = [0 1]; V1x = [0 0]; V1s = [0 1*tand(al3)]; S2L = [2 3]; V2x = [0 0]; V2s = [0 1*tand(al2)]; W2s = [0 1*tand(b2)]; U2x = [3 3]; U2y = [1*tand(b2) 1*tand(al2)]; S3L = [4 5]; V3x = [0 0]; V3r = [0 1*tand(al3)]; W3r = [0 1*tand(b3)]; U3x = [5 5]; U3y = [1*tand(b3) 1*tand(al3)]; plot(S1L,V1x,'k',S1L,V1s,'r',... S2L,V2x,'k',S2L,V2s,'r',S2L,W2s,'b',U2x,U2y,'g',... S3L,V3x,'k',S3L,V3r,'r',S3L,W3r,'b',U3x,U3y,'g',...... 'LineWidth',2,'MarkerSize',10),... axis([-1 6 -4 4]), ... title('Velocity Triangle'), ... xlabel('x'),ylabel('y'), grid

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Plot the rate of heat transfer against the plate velocity varies from 5 m/min to 50 m/min .

Solution Summary: The author plots the rate of heat transfer against the plate velocity in Figure 1. The metal sheet is moving steadily through one inlet and one exit system.

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Plot the rate of heat transfer against the plate velocity varies from 5 m/min to 50 m/min.

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