Ratio of temperature difference for given time elapsed Solution

STEP 0: Pre-Calculation Summary
Formula Used
Temperature Ratio = exp(-(Convection Heat Transfer Coefficient*Surface Area*Time Elapsed)/(Density*Total volume*Specific Heat Capacity))
Tratio = exp(-(h*A*t)/(ρ*VT*Co))
This formula uses 1 Functions, 7 Variables
Functions Used
exp - n an exponential function, the value of the function changes by a constant factor for every unit change in the independent variable., exp(Number)
Variables Used
Temperature Ratio - Temperature ratio is the ratio of temperatures at different instances of any process or environment.
Convection Heat Transfer Coefficient - (Measured in Watt per Square Meter per Kelvin) - Convection Heat Transfer Coefficient is the rate of heat transfer between a solid surface and a fluid per unit surface area per unit temperature.
Surface Area - (Measured in Square Meter) - The Surface Area of a three-dimensional shape is the sum of all of the surface areas of each of the sides.
Time Elapsed - (Measured in Second) - Time elapsed after a particular task is started.
Density - (Measured in Kilogram per Cubic Meter) - The Density of a material shows the denseness of that material in a specific given area. This is taken as mass per unit volume of a given object.
Total volume - (Measured in Cubic Meter) - Total volume is the overall amount of space that a substance or object occupies or that is enclosed within a container.
Specific Heat Capacity - (Measured in Joule per Kilogram per K) - Specific Heat Capacity is the heat required to raise the temperature of the unit mass of a given substance by a given amount.
STEP 1: Convert Input(s) to Base Unit
Convection Heat Transfer Coefficient: 0.04 Watt per Square Meter per Kelvin --> 0.04 Watt per Square Meter per Kelvin No Conversion Required
Surface Area: 18 Square Meter --> 18 Square Meter No Conversion Required
Time Elapsed: 12 Second --> 12 Second No Conversion Required
Density: 5.51 Kilogram per Cubic Meter --> 5.51 Kilogram per Cubic Meter No Conversion Required
Total volume: 63 Cubic Meter --> 63 Cubic Meter No Conversion Required
Specific Heat Capacity: 4 Joule per Kilogram per K --> 4 Joule per Kilogram per K No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
Tratio = exp(-(h*A*t)/(ρ*VT*Co)) --> exp(-(0.04*18*12)/(5.51*63*4))
Evaluating ... ...
Tratio = 0.993796866683215
STEP 3: Convert Result to Output's Unit
0.993796866683215 --> No Conversion Required
FINAL ANSWER
0.993796866683215 0.993797 <-- Temperature Ratio
(Calculation completed in 00.004 seconds)

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13 Transient Heat Conduction Calculators

Instantaneous heat transfer rate
Go Heat Rate = Convection Heat Transfer Coefficient*Surface Area*(Initial Temperature-Fluid Temperature)*(exp(-(Convection Heat Transfer Coefficient*Surface Area*Time Elapsed)/(Density*Total volume*Specific Heat Capacity)))
Temperature after given time elapsed
Go Temperature = ((Initial Temperature-Fluid Temperature)*(exp(-(Convection Heat Transfer Coefficient*Surface Area*Time Elapsed)/(Density*Total volume*Specific Heat Capacity))))+Fluid Temperature
Time taken to reach given temperature
Go Time Elapsed = ln((Final Temperature-Fluid Temperature)/(Initial Temperature-Fluid Temperature))*((Density*Total volume*Specific Heat)/(Convection Heat Transfer Coefficient*Surface Area))
Change in Internal energy of Lumped body
Go Change in Internal Energy = Density*Specific Heat*Total volume*(Initial Temperature-Fluid Temperature)*(1-(exp(-(Biot Number*Fourier Number))))
Total Heat Transfer during Time Interval
Go Heat Transfer = Density*Specific Heat*Total volume*(Initial Temperature-Fluid Temperature)*(1-(exp(-(Biot Number*Fourier Number))))
Ratio of temperature difference for given time elapsed
Go Temperature Ratio = exp(-(Convection Heat Transfer Coefficient*Surface Area*Time Elapsed)/(Density*Total volume*Specific Heat Capacity))
Product of Biot and Fourier Number given System Properties
Go Product of Biot And Fourier Numbers = (Convection Heat Transfer Coefficient*Surface Area*Time Elapsed)/(Density*Total volume*Specific Heat Capacity)
Power on exponential of temperature-time relation
Go Constant B = -(Convection Heat Transfer Coefficient*Surface Area*Time Elapsed)/(Density*Total volume*Specific Heat Capacity)
Time Constant in unsteady state heat transfer
Go Time Constant = (Density*Specific Heat Capacity*Total volume)/(Convection Heat Transfer Coefficient*Surface Area)
Thermal Diffusivity
Go Thermal Diffusivity = Thermal Conductivity/(Density*Specific Heat Capacity)
Thermal Capacitance
Go Thermal Capacitance = Density*Specific Heat Capacity*Volume
Ratio of Temperature difference for Time Elapsed given Biot and Fourier Number
Go Temperature Ratio = exp(-(Biot Number*Fourier Number))
Power on Exponential of Temperature-time Relation given Biot and Fourier Number
Go Constant B = -(Biot Number*Fourier Number)

Ratio of temperature difference for given time elapsed Formula

Temperature Ratio = exp(-(Convection Heat Transfer Coefficient*Surface Area*Time Elapsed)/(Density*Total volume*Specific Heat Capacity))
Tratio = exp(-(h*A*t)/(ρ*VT*Co))

What is Temperature-Time relation?

The temperature-time relationship of unsteady-state heat transfer helps to determine the rate of heat transfer that has been conducted in the lumped system in a given time period.

How to Calculate Ratio of temperature difference for given time elapsed?

Ratio of temperature difference for given time elapsed calculator uses Temperature Ratio = exp(-(Convection Heat Transfer Coefficient*Surface Area*Time Elapsed)/(Density*Total volume*Specific Heat Capacity)) to calculate the Temperature Ratio, Ratio of temperature difference for given time elapsed formula calculates the exponential term given in the temperature-time relationship for a lumped body. Temperature Ratio is denoted by Tratio symbol.

How to calculate Ratio of temperature difference for given time elapsed using this online calculator? To use this online calculator for Ratio of temperature difference for given time elapsed, enter Convection Heat Transfer Coefficient (h), Surface Area (A), Time Elapsed (t), Density (ρ), Total volume (VT) & Specific Heat Capacity (Co) and hit the calculate button. Here is how the Ratio of temperature difference for given time elapsed calculation can be explained with given input values -> 0.993797 = exp(-(0.04*18*12)/(5.51*63*4)).

FAQ

What is Ratio of temperature difference for given time elapsed?
Ratio of temperature difference for given time elapsed formula calculates the exponential term given in the temperature-time relationship for a lumped body and is represented as Tratio = exp(-(h*A*t)/(ρ*VT*Co)) or Temperature Ratio = exp(-(Convection Heat Transfer Coefficient*Surface Area*Time Elapsed)/(Density*Total volume*Specific Heat Capacity)). Convection Heat Transfer Coefficient is the rate of heat transfer between a solid surface and a fluid per unit surface area per unit temperature, The Surface Area of a three-dimensional shape is the sum of all of the surface areas of each of the sides, Time elapsed after a particular task is started, The Density of a material shows the denseness of that material in a specific given area. This is taken as mass per unit volume of a given object, Total volume is the overall amount of space that a substance or object occupies or that is enclosed within a container & Specific Heat Capacity is the heat required to raise the temperature of the unit mass of a given substance by a given amount.
How to calculate Ratio of temperature difference for given time elapsed?
Ratio of temperature difference for given time elapsed formula calculates the exponential term given in the temperature-time relationship for a lumped body is calculated using Temperature Ratio = exp(-(Convection Heat Transfer Coefficient*Surface Area*Time Elapsed)/(Density*Total volume*Specific Heat Capacity)). To calculate Ratio of temperature difference for given time elapsed, you need Convection Heat Transfer Coefficient (h), Surface Area (A), Time Elapsed (t), Density (ρ), Total volume (VT) & Specific Heat Capacity (Co). With our tool, you need to enter the respective value for Convection Heat Transfer Coefficient, Surface Area, Time Elapsed, Density, Total volume & Specific Heat Capacity and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.
How many ways are there to calculate Temperature Ratio?
In this formula, Temperature Ratio uses Convection Heat Transfer Coefficient, Surface Area, Time Elapsed, Density, Total volume & Specific Heat Capacity. We can use 1 other way(s) to calculate the same, which is/are as follows -
  • Temperature Ratio = exp(-(Biot Number*Fourier Number))
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