Cooling Rate for Relatively Thick Plates Solution

STEP 0: Pre-Calculation Summary
Formula Used
Cooling Rate = (2*pi*Thermal Conductivity*((Temperature to Calculate Cooling Rate-Ambient Temperature)^2))/Net Heat Supplied per Unit Length
R = (2*pi*k*((Tc-ta)^2))/HNet
This formula uses 1 Constants, 5 Variables
Constants Used
pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288
Variables Used
Cooling Rate - (Measured in Kelvin per Second) - Cooling Rate is the time rate of decrease of temperature of a particular material.
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.
Temperature to Calculate Cooling Rate - (Measured in Kelvin) - Temperature to calculate cooling rate is calculated is the temperature at which the cooling rate is calculated.
Ambient Temperature - (Measured in Kelvin) - Ambient Temperature is the temperature of the surrounding.
Net Heat Supplied per Unit Length - (Measured in Joule per Meter) - Net heat supplied per unit length can also be converted to newton since energy is newton multiplied meter.
STEP 1: Convert Input(s) to Base Unit
Thermal Conductivity: 10.18 Watt per Meter per K --> 10.18 Watt per Meter per K No Conversion Required
Temperature to Calculate Cooling Rate: 500 Celsius --> 773.15 Kelvin (Check conversion here)
Ambient Temperature: 37 Celsius --> 310.15 Kelvin (Check conversion here)
Net Heat Supplied per Unit Length: 1000 Joule per Millimeter --> 1000000 Joule per Meter (Check conversion here)
STEP 2: Evaluate Formula
Substituting Input Values in Formula
R = (2*pi*k*((Tc-ta)^2))/HNet --> (2*pi*10.18*((773.15-310.15)^2))/1000000
Evaluating ... ...
R = 13.7116471383485
STEP 3: Convert Result to Output's Unit
13.7116471383485 Kelvin per Second -->13.7116471383485 Celsius per Second (Check conversion here)
FINAL ANSWER
13.7116471383485 13.71165 Celsius per Second <-- Cooling Rate
(Calculation completed in 00.004 seconds)

Credits

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University Institute of Technology RGPV (UIT - RGPV), Bhopal
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13 Heat Flow in Welded Joints Calculators

Peak Temperature Reached at any Point in Material
Go Peak Temperature Reached at a Distance of y = Ambient Temperature+(Net Heat Supplied per Unit Length*(Melting Temperature of Base Metal-Ambient Temperature))/((Melting Temperature of Base Metal-Ambient Temperature)*sqrt(2*pi*e)*Density of Metal*Thickness of the Metal*Specific Heat Capacity*Distance from the Fusion Boundary+Net Heat Supplied per Unit Length)
Position of peak temperature from fusion boundary
Go Distance from the Fusion Boundary = ((Melting Temperature of Base Metal-Temperature Reached at a Distance of y)*Net Heat Supplied per Unit Length)/((Temperature Reached at a Distance of y-Ambient Temperature)*(Melting Temperature of Base Metal-Ambient Temperature)*sqrt(2*pi*e)*Density*Specific Heat Capacity*Thickness of the Metal)
Net heat supplied to weld area to raise it to given temperature from fusion boundary
Go Net Heat Supplied per Unit Length = ((Temperature Reached at a Distance of y-Ambient Temperature)*(Melting Temperature of Base Metal-Ambient Temperature)*sqrt(2*pi*e)*Density*Specific Heat Capacity*Thickness of the Metal*Distance from the Fusion Boundary)/(Melting Temperature of Base Metal-Temperature Reached at a Distance of y)
Net heat supplied to achieve given cooling rates for thin plates
Go Net Heat Supplied per Unit Length = Thickness of the Metal/sqrt(Cooling Rate of Thinplate/(2*pi*Thermal Conductivity*Density*Specific Heat Capacity*((Temperature to Calculate Cooling Rate-Ambient Temperature)^3)))
Thickness of base metal for desired cooling rate
Go Thickness = Net Heat Supplied per Unit Length*sqrt(Cooling Rate/(2*pi*Thermal Conductivity*Density*Specific Heat Capacity*((Temperature to Calculate Cooling Rate-Ambient Temperature)^3)))
Thermal conductivity of base metal using given cooling rate (thin plates)
Go Thermal Conductivity = Cooling Rate of Thinplate/(2*pi*Density*Specific Heat Capacity*((Thickness of the Metal/Net Heat Supplied per Unit Length)^2)*((Temperature to Calculate Cooling Rate-Ambient Temperature)^3))
Cooling rate for relatively thin plates
Go Cooling Rate of Thinplate = 2*pi*Thermal Conductivity*Density*Specific Heat Capacity*((Thickness of the Metal/Net Heat Supplied per Unit Length)^2)*((Temperature to Calculate Cooling Rate-Ambient Temperature)^3)
Relative plate thickness factor
Go Relative Plate Thickness Factor = Thickness of the Metal*sqrt(((Temperature to Calculate Cooling Rate-Ambient Temperature)*Density of Metal*Specific Heat Capacity)/Net Heat Supplied per Unit Length)
Thickness of Base Metal using Relative Thickness Factor
Go Thickness of the Base Metal = Relative Plate Thickness Factor*sqrt(Net Heat Supplied per Unit Length/((Temperature to Calculate Cooling Rate-Ambient Temperature)*Density*Specific Heat Capacity))
Net Heat supplied using Relative Thickness Factor
Go Net Heat Supplied = ((Thickness of the Metal/Relative Plate Thickness Factor)^2)*Density*Specific Heat Capacity*(Temperature to Calculate Cooling Rate-Ambient Temperature)
Thermal conductivity of base metal using given cooling rate (thick plates)
Go Thermal Conductivity = (Cooling Rate*Net Heat Supplied per Unit Length)/(2*pi*((Temperature to Calculate Cooling Rate-Ambient Temperature)^2))
Net heat supplied to achieve given cooling rates for thick plates
Go Net Heat Supplied per Unit Length = (2*pi*Thermal Conductivity*((Temperature to Calculate Cooling Rate-Ambient Temperature)^2))/Cooling Rate
Cooling Rate for Relatively Thick Plates
Go Cooling Rate = (2*pi*Thermal Conductivity*((Temperature to Calculate Cooling Rate-Ambient Temperature)^2))/Net Heat Supplied per Unit Length

Cooling Rate for Relatively Thick Plates Formula

Cooling Rate = (2*pi*Thermal Conductivity*((Temperature to Calculate Cooling Rate-Ambient Temperature)^2))/Net Heat Supplied per Unit Length
R = (2*pi*k*((Tc-ta)^2))/HNet

How heat transfer takes place near heat affected zone ?

Heat transfer in a welded joint is a complex phenomenon involving three dimensional movement of a heat source. Heat from the weld zone is transferred more to the other parts of the base metal by means of conduction. Similarly heat is also lost to surroundings by convection from the surface, with radiation component being relatively small except near the weld pool. Thus the analytical treatment of the weld zone is extremely difficult.

How to Calculate Cooling Rate for Relatively Thick Plates?

Cooling Rate for Relatively Thick Plates calculator uses Cooling Rate = (2*pi*Thermal Conductivity*((Temperature to Calculate Cooling Rate-Ambient Temperature)^2))/Net Heat Supplied per Unit Length to calculate the Cooling Rate, The cooling rate for relatively thick plates formula is defined as the change in weld temperature per unit of time. Cooling Rate is denoted by R symbol.

How to calculate Cooling Rate for Relatively Thick Plates using this online calculator? To use this online calculator for Cooling Rate for Relatively Thick Plates, enter Thermal Conductivity (k), Temperature to Calculate Cooling Rate (Tc), Ambient Temperature (ta) & Net Heat Supplied per Unit Length (HNet) and hit the calculate button. Here is how the Cooling Rate for Relatively Thick Plates calculation can be explained with given input values -> 13.71165 = (2*pi*10.18*((773.15-310.15)^2))/1000000.

FAQ

What is Cooling Rate for Relatively Thick Plates?
The cooling rate for relatively thick plates formula is defined as the change in weld temperature per unit of time and is represented as R = (2*pi*k*((Tc-ta)^2))/HNet or Cooling Rate = (2*pi*Thermal Conductivity*((Temperature to Calculate Cooling Rate-Ambient Temperature)^2))/Net Heat Supplied per Unit Length. 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, Temperature to calculate cooling rate is calculated is the temperature at which the cooling rate is calculated, Ambient Temperature is the temperature of the surrounding & Net heat supplied per unit length can also be converted to newton since energy is newton multiplied meter.
How to calculate Cooling Rate for Relatively Thick Plates?
The cooling rate for relatively thick plates formula is defined as the change in weld temperature per unit of time is calculated using Cooling Rate = (2*pi*Thermal Conductivity*((Temperature to Calculate Cooling Rate-Ambient Temperature)^2))/Net Heat Supplied per Unit Length. To calculate Cooling Rate for Relatively Thick Plates, you need Thermal Conductivity (k), Temperature to Calculate Cooling Rate (Tc), Ambient Temperature (ta) & Net Heat Supplied per Unit Length (HNet). With our tool, you need to enter the respective value for Thermal Conductivity, Temperature to Calculate Cooling Rate, Ambient Temperature & Net Heat Supplied per Unit Length 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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