Cooling Rate for Relatively Thick Plates Calculator

✖Thermal Conductivity is the rate at which heat passes through a material, defined as heat flow per unit time per unit area with a temperature gradient of one degree per unit distance.ⓘ Thermal Conductivity [k]			+10% -10%
✖Temperature for Cooling Rate is the temperature at which the cooling rate is calculated.ⓘ Temperature for Cooling Rate [T_c]			+10% -10%
✖Ambient Temperature Ambient temperature refers to the air temperature of any object or environment where equipment is stored. In a more general sense, it is the temperature of the surrounding.ⓘ Ambient Temperature [t_a]			+10% -10%
✖Net Heat Supplied Per Unit Length refers to the amount of heat energy transferred per unit length along a material or medium.ⓘ Net Heat Supplied Per Unit Length [H_net]			+10% -10%

✖Cooling Rate of Thick Plate is the rate of decrease of temperature of a particular thick sheet of material.ⓘ Cooling Rate for Relatively Thick Plates [R]

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Formula

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Cooling Rate for Relatively Thick Plates

Formula

`"R" = (2*pi*"k"*(("T"_{"c"}-"t"_{"a"})^2))/"H"_{"net"}`

Example

`"13.71165°C/s"=(2*pi*"10.18W/(m*K)"*(("500°C"-"37°C")^2))/"1000J/mm"`

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Cooling Rate for Relatively Thick Plates Solution

STEP 0: Pre-Calculation Summary

Formula Used

Cooling Rate of Thick Plate = (2*pi*Thermal Conductivity*((Temperature for Cooling Rate-Ambient Temperature)^2))/Net Heat Supplied Per Unit Length
R = (2*pi*k*((T_c-t_a)^2))/H_net
This formula uses 1 Constants, 5 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Variables Used

Cooling Rate of Thick Plate - (Measured in Kelvin per Second) - Cooling Rate of Thick Plate is the rate of decrease of temperature of a particular thick sheet of material.
Thermal Conductivity - (Measured in Watt per Meter per K) - Thermal Conductivity is the rate at which heat passes through a material, defined as heat flow per unit time per unit area with a temperature gradient of one degree per unit distance.
Temperature for Cooling Rate - (Measured in Kelvin) - Temperature for Cooling Rate is the temperature at which the cooling rate is calculated.
Ambient Temperature - (Measured in Kelvin) - Ambient Temperature Ambient temperature refers to the air temperature of any object or environment where equipment is stored. In a more general sense, it is the temperature of the surrounding.
Net Heat Supplied Per Unit Length - (Measured in Joule per Meter) - Net Heat Supplied Per Unit Length refers to the amount of heat energy transferred per unit length along a material or medium.

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 for 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*((T_c-t_a)^2))/H_net --> (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 of Thick Plate

(Calculation completed in 00.004 seconds)

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Created by Rajat Vishwakarma

University Institute of Technology RGPV (UIT - RGPV), Bhopal

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Shri Madhwa Vadiraja Institute of Technology and Management (SMVITM), Udupi

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< 13 Heat Flow in Welded Joints Calculators

Peak Temperature Reached at any Point in Material

Go Peak Temperature Reached at Some Distance = 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 Filler 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 Some Distance)*Net Heat Supplied Per Unit Length)/((Temperature Reached at Some Distance-Ambient Temperature)*(Melting Temperature of Base Metal-Ambient Temperature)*sqrt(2*pi*e)*Density of Electrode*Specific Heat Capacity*Thickness of Filler 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 Some Distance-Ambient Temperature)*(Melting Temperature of Base Metal-Ambient Temperature)*sqrt(2*pi*e)*Density of Electrode*Specific Heat Capacity*Thickness of Filler Metal*Distance from the Fusion Boundary)/(Melting Temperature of Base Metal-Temperature Reached at Some Distance)

Net Heat Supplied to achieve given Cooling Rates for Thin Plates

Go Net Heat Supplied Per Unit Length = Thickness of Filler Metal/sqrt(Cooling Rate of Thin Plate/(2*pi*Thermal Conductivity*Density of Electrode*Specific Heat Capacity*((Temperature for Cooling Rate-Ambient Temperature)^3)))

Thickness of Base Metal for Desired Cooling Rate

Go Thickness = Net Heat Supplied Per Unit Length*sqrt(Cooling Rate of Thick Plate/(2*pi*Thermal Conductivity*Density of Electrode*Specific Heat Capacity*((Temperature for Cooling Rate-Ambient Temperature)^3)))

Thermal Conductivity of Base Metal using given Cooling Rate (thin plates)

Go Thermal Conductivity = Cooling Rate of Thin Plate/(2*pi*Density of Electrode*Specific Heat Capacity*((Thickness of Filler Metal/Net Heat Supplied Per Unit Length)^2)*((Temperature for Cooling Rate-Ambient Temperature)^3))

Cooling rate for relatively thin plates

Go Cooling Rate of Thin Plate = 2*pi*Thermal Conductivity*Density of Electrode*Specific Heat Capacity*((Thickness of Filler Metal/Net Heat Supplied Per Unit Length)^2)*((Temperature for Cooling Rate-Ambient Temperature)^3)

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 for Cooling Rate-Ambient Temperature)*Density of Electrode*Specific Heat Capacity))

Relative Plate Thickness Factor

Go Relative Plate Thickness Factor = Thickness of Filler Metal*sqrt(((Temperature for Cooling Rate-Ambient Temperature)*Density of Metal*Specific Heat Capacity)/Net Heat Supplied Per Unit Length)

Net Heat Supplied using Relative Thickness Factor

Go Net Heat Supplied = ((Thickness of Filler Metal/Relative Plate Thickness Factor)^2)*Density of Electrode*Specific Heat Capacity*(Temperature for Cooling Rate-Ambient Temperature)

Thermal Conductivity of Base Metal using given Cooling Rate (thick plates)

Go Thermal Conductivity = (Cooling Rate of Thick Plate*Net Heat Supplied Per Unit Length)/(2*pi*((Temperature for 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 for Cooling Rate-Ambient Temperature)^2))/Cooling Rate of Thick Plate

Cooling Rate for Relatively Thick Plates

Go Cooling Rate of Thick Plate = (2*pi*Thermal Conductivity*((Temperature for Cooling Rate-Ambient Temperature)^2))/Net Heat Supplied Per Unit Length

Cooling Rate for Relatively Thick Plates Formula

Cooling Rate of Thick Plate = (2*pi*Thermal Conductivity*((Temperature for Cooling Rate-Ambient Temperature)^2))/Net Heat Supplied Per Unit Length
R = (2*pi*k*((T_c-t_a)^2))/H_net

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 of Thick Plate = (2*pi*Thermal Conductivity*((Temperature for Cooling Rate-Ambient Temperature)^2))/Net Heat Supplied Per Unit Length to calculate the Cooling Rate of Thick Plate, The Cooling Rate for Relatively Thick Plates formula is defined as the change in weld temperature per unit of time. Cooling Rate of Thick Plate 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 for Cooling Rate (T_c), Ambient Temperature (t_a) & Net Heat Supplied Per Unit Length (H_net) 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*((T_c-t_a)^2))/H_net or Cooling Rate of Thick Plate = (2*pi*Thermal Conductivity*((Temperature for Cooling Rate-Ambient Temperature)^2))/Net Heat Supplied Per Unit Length. Thermal Conductivity is the rate at which heat passes through a material, defined as heat flow per unit time per unit area with a temperature gradient of one degree per unit distance, Temperature for Cooling Rate is the temperature at which the cooling rate is calculated, Ambient Temperature Ambient temperature refers to the air temperature of any object or environment where equipment is stored. In a more general sense, it is the temperature of the surrounding & Net Heat Supplied Per Unit Length refers to the amount of heat energy transferred per unit length along a material or medium.

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 of Thick Plate = (2*pi*Thermal Conductivity*((Temperature for 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 for Cooling Rate (T_c), Ambient Temperature (t_a) & Net Heat Supplied Per Unit Length (H_net). With our tool, you need to enter the respective value for Thermal Conductivity, Temperature for 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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