Average temperature difference between plate and fluid Solution

STEP 0: Pre-Calculation Summary
Formula Used
Average Temperature Difference = ((Heat Flux*Distance L/Thermal Conductivity))/(0.679*(Reynolds Number at Location L^0.5)*(Prandtl Number^0.333))
δTavg = ((q'*L/k))/(0.679*(ReL^0.5)*(Pr^0.333))
This formula uses 6 Variables
Variables Used
Average Temperature Difference - (Measured in Kelvin) - Average temperature difference is the the average value of temperature difference between two values.
Heat Flux - (Measured in Watt per Square Meter) - Heat Flux is the heat transfer rate per unit area normal to the direction of heat flow. It is denoted by the letter "q".
Distance L - (Measured in Meter) - Distance L is the distance from the leading edge.
Thermal Conductivity - (Measured in Watt per Meter per K) - Thermal Conductivity is rate of heat passes through specified material, expressed as amount of heat flows per unit time through a unit area with a temperature gradient of one degree per unit distance.
Reynolds Number at Location L - Reynolds number at location L is denoted by the symbol ReL. It is used to determine the type of flow pattern as laminar or turbulent while flowing through a pipe.
Prandtl Number - The Prandtl number (Pr) or Prandtl group is a dimensionless number, named after the German physicist Ludwig Prandtl, defined as the ratio of momentum diffusivity to thermal diffusivity.
STEP 1: Convert Input(s) to Base Unit
Heat Flux: 40 Watt per Square Meter --> 40 Watt per Square Meter No Conversion Required
Distance L: 0.05 Meter --> 0.05 Meter No Conversion Required
Thermal Conductivity: 10.18 Watt per Meter per K --> 10.18 Watt per Meter per K No Conversion Required
Reynolds Number at Location L: 8 --> No Conversion Required
Prandtl Number: 0.7 --> No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
δTavg = ((q'*L/k))/(0.679*(ReL^0.5)*(Pr^0.333)) --> ((40*0.05/10.18))/(0.679*(8^0.5)*(0.7^0.333))
Evaluating ... ...
δTavg = 0.115199290033001
STEP 3: Convert Result to Output's Unit
0.115199290033001 Kelvin -->-273.034800709967 Celsius (Check conversion here)
FINAL ANSWER
-273.034800709967 -273.034801 Celsius <-- Average Temperature Difference
(Calculation completed in 00.004 seconds)

Credits

Created by Nishan Poojary
Shri Madhwa Vadiraja Institute of Technology and Management (SMVITM), Udupi
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15 Laminar Flow Calculators

Average temperature difference between plate and fluid
Go Average Temperature Difference = ((Heat Flux*Distance L/Thermal Conductivity))/(0.679*(Reynolds Number at Location L^0.5)*(Prandtl Number^0.333))
Free stream velocity given local friction coefficient
Go Free Stream Velocity = sqrt((2*Wall Shear Stress)/(Density*Local Friction Coefficient))
Density given local friction coefficient
Go Density = 2*Wall Shear Stress/(Local Friction Coefficient*(Free Stream Velocity^2))
Wall shear stress
Go Wall Shear Stress = (Local Friction Coefficient*Density*(Free Stream Velocity^2))/2
Local friction coefficient for external flow
Go Local Friction Coefficient = 2*Wall Shear Stress/(Density*Free Stream Velocity^2)
Hydrodynamic boundary layer thickness at distance X from leading edge
Go Hydrodynamic Boundary Layer Thickness = 5*Distance from Point to YY Axis*Reynolds Number(x)^(-0.5)
Thermal boundary layer thickness at distance X from leading edge
Go Thermal Boundary Layer Thickness = Hydrodynamic Boundary Layer Thickness*Prandtl Number^(-0.333)
Film temperature
Go Film temperature = (Plate Surface Temperature+Free Stream Fluid Temperature)/2
Free stream fluid temperature
Go Free Stream Fluid Temperature = 2*Film temperature-Plate Surface Temperature
Plate surface temperature
Go Plate Surface Temperature = 2*Film temperature-Free Stream Fluid Temperature
Coefficient of friction given Stanton number
Go Coefficient of Friction = 2*Stanton Number*(Prandtl Number^(2/3))
Displacement thickness
Go Displacement Thickness = Hydrodynamic Boundary Layer Thickness/3
Average friction coefficient
Go Average Friction Coefficient = 1.328*Reynolds Number(x)^(-0.5)
Local Friction Coefficient given Reynolds Number
Go Local Friction Coefficient = 0.664*Reynolds Number(x)^(-0.5)
Momentum thickness
Go Momentum Thickness = Hydrodynamic Boundary Layer Thickness/7

Average temperature difference between plate and fluid Formula

Average Temperature Difference = ((Heat Flux*Distance L/Thermal Conductivity))/(0.679*(Reynolds Number at Location L^0.5)*(Prandtl Number^0.333))
δTavg = ((q'*L/k))/(0.679*(ReL^0.5)*(Pr^0.333))

What is external flow?

In fluid mechanics, external flow is such a flow that boundary layers develop freely, without constraints imposed by adjacent surfaces. Accordingly, there will always exist a region of the flow outside the boundary layer in which velocity, temperature, and/or concentration gradients are negligible. It can be defined as the flow of a fluid around a body that is completely submerged in it.

An example includes fluid motion over a flat plate (inclined or parallel to the free stream velocity) and flow over curved surfaces such as a sphere, cylinder, airfoil, or turbine blade, air flowing around an airplane and water flowing around the submarines.

How to Calculate Average temperature difference between plate and fluid?

Average temperature difference between plate and fluid calculator uses Average Temperature Difference = ((Heat Flux*Distance L/Thermal Conductivity))/(0.679*(Reynolds Number at Location L^0.5)*(Prandtl Number^0.333)) to calculate the Average Temperature Difference, The Average temperature difference between plate and fluid formula is defined as the ratio between heat transfer by convection (α) and heat transfer by conduction alone. Average Temperature Difference is denoted by δTavg symbol.

How to calculate Average temperature difference between plate and fluid using this online calculator? To use this online calculator for Average temperature difference between plate and fluid, enter Heat Flux (q'), Distance L (L), Thermal Conductivity (k), Reynolds Number at Location L (ReL) & Prandtl Number (Pr) and hit the calculate button. Here is how the Average temperature difference between plate and fluid calculation can be explained with given input values -> -546.184801 = ((40*0.05/10.18))/(0.679*(8^0.5)*(0.7^0.333)).

FAQ

What is Average temperature difference between plate and fluid?
The Average temperature difference between plate and fluid formula is defined as the ratio between heat transfer by convection (α) and heat transfer by conduction alone and is represented as δTavg = ((q'*L/k))/(0.679*(ReL^0.5)*(Pr^0.333)) or Average Temperature Difference = ((Heat Flux*Distance L/Thermal Conductivity))/(0.679*(Reynolds Number at Location L^0.5)*(Prandtl Number^0.333)). Heat Flux is the heat transfer rate per unit area normal to the direction of heat flow. It is denoted by the letter "q", Distance L is the distance from the leading edge, Thermal Conductivity is rate of heat passes through specified material, expressed as amount of heat flows per unit time through a unit area with a temperature gradient of one degree per unit distance, Reynolds number at location L is denoted by the symbol ReL. It is used to determine the type of flow pattern as laminar or turbulent while flowing through a pipe & The Prandtl number (Pr) or Prandtl group is a dimensionless number, named after the German physicist Ludwig Prandtl, defined as the ratio of momentum diffusivity to thermal diffusivity.
How to calculate Average temperature difference between plate and fluid?
The Average temperature difference between plate and fluid formula is defined as the ratio between heat transfer by convection (α) and heat transfer by conduction alone is calculated using Average Temperature Difference = ((Heat Flux*Distance L/Thermal Conductivity))/(0.679*(Reynolds Number at Location L^0.5)*(Prandtl Number^0.333)). To calculate Average temperature difference between plate and fluid, you need Heat Flux (q'), Distance L (L), Thermal Conductivity (k), Reynolds Number at Location L (ReL) & Prandtl Number (Pr). With our tool, you need to enter the respective value for Heat Flux, Distance L, Thermal Conductivity, Reynolds Number at Location L & Prandtl Number and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.
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