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Generalized molecular flux equation Generalized molecular flux equation

Generalized molecular flux equation Generalized molecular flux equation

Modified generalized molecular flux equation

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Generalized molecular flux equation

Modified generalized molecular flux equation

Generalized molecular flux equation

Modified generalized molecular flux equation

Generalized molecular flux equation

Modified generalized molecular flux equation

Convective flux equation

Generalized molecular flux equation

Modified generalized molecular flux equation

Convective flux equation

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Generalized molecular flux equation

Modified generalized molecular flux equation

Convective flux equation

Total flux equation

Interphase flux Interphase flux

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Interphase flux Interphase flux

Analytical Vs Experimental

Interphase flux

Analytical Vs Experimental

Friction factorHeat transfer coefficientMass Transfer coefficient

Interphase flux in heat transfer

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Interphase flux in heat transfer

Consider flat plate suspended in a uniform stream ofair with thermal conductivity k, velocity v∞ andtemperature T∞ as shown in figure. Derive generalizedequation for rate of heat transfer from plate surfaceand give physical interpretation of heat transfercoefficient

Interphase flux in heat transfer

Consider flat plate suspended in a uniform stream ofair with thermal conductivity k, velocity v∞ andtemperature T∞ as shown in figure. Derive generalizedequation for rate of heat transfer from plate surfaceand give physical interpretation of heat transfercoefficient

Interphase flux in heat transfer

Total heat flux from plate to flowing stream

Consider flat plate suspended in a uniform stream ofair with thermal conductivity k, velocity v∞ andtemperature T∞ as shown in figure. Derive generalizedequation for rate of heat transfer from plate surfaceand give physical interpretation of heat transfercoefficient

Interphase flux in heat transfer

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Interphase flux in heat transfer

(1)

Interphase flux in heat transfer

(1)

No slip boundary conditionNo slip boundary condition

Interphase flux in heat transfer

(1)

No slip boundary conditionNo slip boundary condition

Interphase flux in heat transfer

(1)

No slip boundary conditionNo slip boundary condition

(2)

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Rate of heat transfer Rate of heat transfer

(3)

Rate of heat transfer

(3)

Rate of heat transfer

(3)

Temperature gradient at wall in presence of flowTemperature gradient at wall in presence of flow

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Rate of heat transfer

(3)

Temperature gradient at wall in presence of flowTemperature gradient at wall in presence of flow

Experimental calculation of heat flux in terms of convective heat transfer

Rate of heat transfer

(3)

Temperature gradient at wall in presence of flowTemperature gradient at wall in presence of flow

Experimental calculation of heat flux in terms of convective heat transfer

(4)

Rate of heat transfer

(3)

Temperature gradient at wall in presence of flowTemperature gradient at wall in presence of flow

Experimental calculation of heat flux in terms of convective heat transfer

(4)

Newton's law of cooling

Rate of heat transfer

(3)

(4)

Combining and rearranging equation (3) and (4)

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Rate of heat transfer

(3)

(4)

Combining and rearranging equation (3) and (4)

Rate of heat transfer

(3)

(4)

Combining and rearranging equation (3) and (4)

(5)(5)

Rate of heat transfer

(3)

(4)

Combining and rearranging equation (3) and (4)

(5)(5)

Where <h> is defined as

Rate of heat transfer

(3)

(4)

Combining and rearranging equation (3) and (4)

(5)(5)

Where <h> is defined as

(6)

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Rate of heat transfer

(3)

(4)

(5)

(6)

Combining equation 1-6Generalized equation for rate of heat transfer

AH = Total area , (ΔT)ch characteristic temperature difference

(7)

Interphase flux in heat transfer

Consider flat plate suspended in a uniform stream ofair with thermal conductivity k, velocity v∞ andtemperature T∞ as shown in figure. Derive generalizedequation for rate of heat transfer from plate surfaceand give physical interpretation of heat transfercoefficient

Physical interpretation of heat transfer coefficient

(1)

(2)

Combining and rearranging equation (1) and (2)

(3)(3)

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Total actual resistance ~ resistance of stagnant film of thickness δt Total actual resistance ~ resistance of stagnant film of thickness δt

(3)

Total actual resistance ~ resistance of stagnant film of thickness δt

(4)

Physical interpretation of heat transfer coefficient

(1)

(2)

(3)

(4)

Combining equation (3) & (4)

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Physical interpretation of heat transfer coefficient

(1)

(2)

(3)

(4)

Combining equation (3) & (4)

(5)

Physical interpretation of heat transfer coefficient

(1)

(2)

(3)

(4)

Combining equation (3) & (4)

(5)

Film heat transfer coefficient

In the system shown below, the rate of heat generationis 800 W/m3 in Region A, which is perfectly insulated onthe left-hand side. Given the conditions indicated in thefigure, calculate the heat flux and temperature at theright-hand side, i.e., at x = 100 cm, under steady-stateconditions.

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Interphase flux in mass transfer

Let us consider a flat plate suspended in a uniformstream of fluid (species B) having a velocity v∞ andspecies A concentration cA∞ as shown in Figure Thesurface of the plate is also coated with species A withconcentration cAw . If DAB is diffusivity of A in B, Derivegeneralized equation for rate of mass transfer fromplate surface and give physical interpretation of masstransfer coefficient

Rate of mass transfer from plate surface

Rate of mass transfer from plate surface

(1)

Rate of mass transfer from plate surface

(1)

(2)

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Rate of mass transfer from plate surface

(1)

(2)

Rate of mass transfer from plate surface

(1)

(2)

(3)

Rate of mass transfer from plate surface

(1)

(2)

(3)

Rate of mass transfer from plate surface

(1)

(2)

(3)

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Rate of mass transfer from plate surface

(1)

(2)

(3)

Rate of mass transfer from plate surface

(1)

(2)

(3)

Rate of mass transfer from plate surface

(1)

(2)

(3)

Rate of mass transfer from plate surface

(1)

(2)

(3)

(4)

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Rate of mass transfer from plate surface

(1)

(4)

Rate of mass transfer from plate surface

(1)

(4)

(5)

Rate of mass transfer from plate surface

(1)

(4)

(5)

Slattery equationor

Newton’s law of mass transfer

Rate of mass transfer from plate surface

(1)

(4)

(5)

(1) & (5)(1) & (5)

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Rate of mass transfer from plate surface

(1)

(4)

(5)

(1) & (5)(1) & (5)

Rate of mass transfer from plate surface

(1)

(4)

(5)

(1) & (5)(1) & (5)

Rate of mass transfer from plate surface

(1)

(4)

(5)

(1) & (5)(1) & (5)

(6)

Rate of mass transfer from plate surface

(1)

(6)

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Rate of mass transfer from plate surface

(1)

(6)

(7)

Rate of mass transfer from plate surface

(1)

(6)

(7)

(8)

Rate of mass transfer from plate surface

(1)

(6)

(7)

(8)

Physical interpretation of mass transfer coefficient

(4)

(5)

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Physical interpretation of mass transfer coefficient

(4)

(5)

Combining (4) & (5)

Physical interpretation of mass transfer coefficient

(4)

(5)

Combining (4) & (5)

Physical interpretation of mass transfer coefficient

(4)

(5)

Combining (4) & (5)

(9)

Physical interpretation of mass transfer coefficient

(9)

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Physical interpretation of mass transfer coefficient

(9)

Physical interpretation of mass transfer coefficient

(9)

Physical interpretation of mass transfer coefficient

(9)

Physical interpretation of mass transfer coefficient

(9)

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Physical interpretation of mass transfer coefficient

(9)

(10)

Physical interpretation of mass transfer coefficient

(9)

(10)

Combining (10) & (11)

Physical interpretation of mass transfer coefficient

(9)

(10)

(11)

Combining (10) & (11)

Evaluation of inter-phase concentration CAw

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Evaluation of inter-phase concentration CAw Evaluation of inter-phase concentration CAw

Evaluation of inter-phase concentration CAw Evaluation of inter-phase concentration CAw

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Evaluation of inter-phase concentration CAw Q. 0.5 L of ethanol is poured into a cylindrical tank of 2 Lcapacity and the top is quickly sealed. The total height ofthe cylinder is 1 m. Calculate the mass transfer coefficientif the ethanol concentration in the air reaches 2% of itssaturation value in 5 minutes. The cylinder temperature iskept constant at 20 °C

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Interphase flux in momentum transfer

Let us consider a flat plate of length L and width Wsuspended in a uniform stream having an approachvelocity v∞ as shown in Figure. Derive generalizedequation for drag force in direction of flow and givephysical interpretation of friction factor

Drag force in direction of flow

Drag force in direction of flow

(1)

Drag force in direction of flow

(1)

(2)

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Drag force in direction of flow

(1)

(2)

Drag force in direction of flow

(1)

(2)

(3)

Drag force in direction of flow

(1)

(2)

(3)

No Slip boundary condition

Drag force in direction of flow

(1)

(2)

(3)

(4)

No Slip boundary condition

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Drag force in direction of flow

(1)

(4)

Drag force in direction of flow

(1)

(4)

(5)

Drag force in direction of flow

(1)

(4)

(5)

Finning

Drag force in direction of flow

(1)

(4)

(5)

(1) & (5)(1) & (5)

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Drag force in direction of flow

(1)

(4)

(5)

(1) & (5)(1) & (5)

Drag force in direction of flow

(1)

(4)

(5)

(1) & (5)(1) & (5)

Drag force in direction of flow

(1)

(4)

(5)

(1) & (5)(1) & (5)

(6)

Drag force in direction of flow

(1)

(6)

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Drag force in direction of flow

(1)

(6)

(7)

Drag force in direction of flow

(1)

(6)

(7)

Drag force in direction of flow

(1)

(6)

(7)

(8)Where

Drag force in direction of flow

(1)

(6)

(7)

(8)Where

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Calculation of Power Calculation of Power

Calculation of Power Calculation of Power

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Physical interpretation of friction factor Physical interpretation of friction factor

(4)

(5)

Physical interpretation of friction factor

(4)

(5)

Combining (4) & (5)

Physical interpretation of friction factor

(4)

(5)

Combining (4) & (5)

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Physical interpretation of friction factor

(4)

(5)

Combining (4) & (5)

(9)

Physical interpretation of friction factor

(9)

Physical interpretation of friction factor

(9)

Physical interpretation of friction factor

(9)

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Physical interpretation of friction factor

(9)

Physical interpretation of friction factor

(9)

Physical interpretation of friction factor

(9)

(10)

Physical interpretation of friction factor

(9)

(10)

Combining (9) & (10)

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Physical interpretation of friction factor

(9)

(10)

(11)

Combining (9) & (10)

(11)

Physical interpretation of friction factor

(9)

(10)

(11)

Combining (9) & (10)

(11)

Rearranging the equation

Physical interpretation of friction factor

(9)

(10)

(11)

Combining (9) & (10)

(11)

Rearranging the equation

Physical interpretation of friction factor

(9)

(10)

(11)

Combining (9) & (10)

(11)

Rearranging the equationMultiplying by

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Physical interpretation of friction factor

(9)

(10)

(11)

Combining (9) & (10)

(11)

Rearranging the equationMultiplying by

Physical interpretation of friction factor

(9)

(10)

(11)

Combining (9) & (10)

(11)

Rearranging the equationMultiplying by

(12)

Physical interpretation of friction factor

(9)

(10)

(11)

Combining (9) & (10)

(11)

Rearranging the equationMultiplying by

Where (12)

Q : Sports cars, usually have a friction factor of around 0.24.If the car has a width of 2 m and a height of 1.5 m,a) Determine the power consumed by the car when it isgoing at 100 km/h with no wind blowing.b) Repeat part (a) if the wind blows at a velocity of 30 km/hopposite to the direction of the car.c) Repeat part (a) if the wind blows at a velocity of 30 km/hin the direction of the carin the direction of the car.

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Q : Sports cars, usually have a friction factor of around 0.24.If the car has a width of 2 m and a height of 1.5 m,a) Determine the power consumed by the car when it isgoing at 100 km/h with no wind blowing.b) Repeat part (a) if the wind blows at a velocity of 30 km/hopposite to the direction of the car.c) Repeat part (a) if the wind blows at a velocity of 30 km/hin the direction of the carin the direction of the car.

Q : Sports cars, usually have a friction factor of around 0.24.If the car has a width of 2 m and a height of 1.5 m,a) Determine the power consumed by the car when it isgoing at 100 km/h with no wind blowing.b) Repeat part (a) if the wind blows at a velocity of 30 km/hopposite to the direction of the car.c) Repeat part (a) if the wind blows at a velocity of 30 km/hin the direction of the carin the direction of the car.

Dimensionless Number

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Dimensionless NumberInterphase flux in momentum transferDrag force in direction of flow

Dimensionless Number

Dimensionless Number

(1)

Dimensionless Number

(1)

Interphase flux in heat transferRate of heat transfer

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Dimensionless Number

(1)

Dimensionless Number

(1)(2)

Dimensionless Number

(1)(2)

Interphase flux in mass transferRate of mass transfer

Dimensionless Number

(2)(1)

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Dimensionless Number

(2)

(3)

(1)

Dimensionless Number

(2)

(3)

(1)

Newton (2)

(3)

(1)

Dimensionless Number

(2)

(3)

(1)

Newton

Slattery

(2)

(3)

(1)

Dimensionless Number

(2)

(3)

(1)

Newton

Slattery

(2)

(3)

(1)John Thomas Fanning

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Dimensionless Number

(2)

(3)

(1)

Dimensionless Number

(2)

(3)

(1)

Dimensionless Number

(2)

(3)

(1)

Dimensionless Number

(2)

(3)

(1)

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Dimensionless Number

(2)

(3)

(1)

Dimensionless Number

(5)

(6)

(4)

Dimensionless Number

(5)

(6)

(4)

Dimensionless NumberGeneralized Transfercoefficient

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Dimensionless NumberGeneralized Transfercoefficient

Dimensionless NumberGeneralized Transfercoefficient

Dimensionless NumberGeneralized Transfercoefficient

Dimensionless NumberGeneralized Transfercoefficient

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Dimensionless NumberGeneralized Transfercoefficient

Dimensionless Number

(A)

(B)

Dimensionless Number

(A)

(B)

Dimensionless Number

(A)

(B)

(C)(C)

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Dimensionless Number

(A)

(B)

(C)(C)

Dimensionless Number

(A)

(B)

(C)(C)

Combining equation (A), (B) and (C)

Dimensionless Number

(A)

(B)

(C)(C)

Combining equation (A), (B) and (C)

Dimensionless Number

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Dimensionless Number Dimensionless Number

Dimensionless Number Dimensionless Number

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Dimensionless Number Dimensionless Number

Dimensionless Number Dimensionless Number

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Dimensionless Number Dimensionless Number